A Simple Guide To The Analysis Of Social Science Quantitative Data
Upcoming SlideShare
Loading in...5
×
 

A Simple Guide To The Analysis Of Social Science Quantitative Data

on

  • 8,331 views

One of the complexities for many undergraduate students and for first time researchers is ‘How to blend their socialization with the systematic rigours of scientific inquiry?’ For some, the ...

One of the complexities for many undergraduate students and for first time researchers is ‘How to blend their socialization with the systematic rigours of scientific inquiry?’ For some, the socialization process would have embedded in them hunches, faith, family authority and even ‘hearsay’ as acceptable modes of establishing the existence of certain phenomena. These are not principles or approaches rooted in academic theorizing or critical thinking. Despite insurmountable scientific evidence that have been gathered by empiricism, the falsification of some perspectives that students hold are difficulty to change as they still want to hold ‘true’ to the previous ways of gaining knowledge. Even though time may be clearly showing those issues are obsolete or even ‘mythological’, students will always adhere to information that they had garnered in their early socialization. The difficulty in objectivism is not the ‘truths’ that it claims to provide and/or how we must relate to these realities, it is ‘how do young researchers abandon their preferred socialization to research findings? Furthermore, the difficulty of humans and even more so upcoming scholars is how to validate their socialization with research findings in the presence of empiricism.

Within the aforementioned background, social researchers must understand that ethic must govern the reporting of their findings, irrespective of the results and their value systems. Ethical principles, in the social or natural research, are not ‘good’ because of their inherent construction, but that they are protectors of the subjects (participants) from the researcher(s) who may think the study’s contribution is paramount to any harm that the interviewees may suffer from conducting the study. Then, there is the issue of confidentiality, which sometimes might be conflicting to the personal situations faced by the researcher. I will be simplistic to suggest that who takes precedence is based on the code of conduct that guides that profession. Hence, undergraduate students should be brought into the general awareness that findings must be reported without any form of alteration. This then give rise to ‘how do we systematically investigate social phenomena?’

Statistics

Views

Total Views
8,331
Views on SlideShare
8,330
Embed Views
1

Actions

Likes
1
Downloads
234
Comments
0

1 Embed 1

https://bb.grcc.edu 1

Accessibility

Categories

Upload Details

Uploaded via as Microsoft Word

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

A Simple Guide To The Analysis Of Social Science Quantitative Data A Simple Guide To The Analysis Of Social Science Quantitative Data Document Transcript

  • A Simple Guide to the Analysis of Quantitative Data An Introduction with hypotheses, illustrations and references By Paul Andrew Bourne
  • A Simple Guide to the Analysis of Quantitative Data: An Introduction with hypotheses, illustrations and references By Paul Andrew Bourne Health Research Scientist, the University of the West Indies, Mona Campus Department of Community Health and Psychiatry Faculty of Medical Sciences The University of the West Indies, Mona Campus, Kingston, Jamaica 2
  • © Paul Andrew Bourne 2009 A Simple Guide to the Analysis of Quantitative Data: An Introduction with hypotheses, illustrations and references The copyright of this text is vested in Paul Andrew Bourne and the Department of Community Health and Psychiatry is the publisher, no chapter may be reproduced wholly or in part without the expressed permission in writing of both author and publisher. All rights reserved. Published April, 2009 Department of Community Health and Psychiatry Faculty of Medical Sciences The University of the West Indies, Mona Campus, Kingston, Jamaica. National Library of Jamaica Cataloguing in Publication Data A catalogue record for this book is available from the National Library of Jamaica ISBN 978-976-41-0231-1 (pbk) Covers were designed and photograph taken by Paul Andrew Bourne 3
  • Table of Contents Page Preface 8 Menu bar – Contents of the Menu bar in SPSS 11 Function - Purposes of the different things on the menu bar 12 Mathematical symbols (numeric operations), in SPSS 13 Listing of Other Symbols 14 The whereabouts of some SPSS functions, or commands 16 Disclaimer 19 Coding Missing Data 20 Computing Date of Birth 21 List of Figures 26 List of Tables 29 How do I obtain access to the SPSS PROGRAM? 35 1. INTRODUCTION ……………………………………………………………........ 43 1.1.0a: steps in the analysis of hypothesis…………………………………… 45 1.1.1a Operational definitions of a variable………………………………… 47 1.1.1b Typologies of variable ………………..………………………………. 49 1.1.1 Levels of measurement………..………………………………………... 50 1.1.3 Conceptualizing descriptive and inferential statistics ……………….. 59 2. DESCRIPTIVE STATISTICS ANALYZED ….……………………………........ 62 2.1.1 Interpreting data based on their levels of measurement………..……. 64 2.1.2 Treating missing (i.e. non-response) cases…………………….………. 84 3. HYPOTHESES: INTRODUCTION …………………………….………………. 87 3.1.1 Definitions of Hypotheses………………..……..………………………. 88 3.1.2: Typologies of Hypothesis……………………………………………… 89 3.1.3: Directional and non-Directional Hypotheses………………………….. 90 3.1.4 Outliers (i.e. skewness)…………………………….……………………. 91 3.1.5 Statistical approaches for treating skewness…………….……………… 93 4. Hypothesis 1…[using Cross tabulations and Spearman ranked ordered correlation] ……………………………………………………….. 96 A1. Physical and social factors and instructional resources will directly influence the academic performance of students who will write the Advanced Level Accounting Examination; A2. Physical and social factors and instructional resources positively influence the academic performance of students who write the Advanced level Accounting examination and that the relationship varies according to gender; 4
  • B1. Pass successes in Mathematics, Principles of Accounts and English Language at the Ordinary/CXC General level will positively influence success on the Advanced level Accounting examination; B2. Pass successes in Mathematics, Principles of Accounts and English Language at the Ordinary. 5. Hypothesis 2…………[using Crosstabulations]..…………………………….. 152 There is a relationship between religiosity, academic performance, age and marijuana smoking of Post-primary schools students and does this relationship varies based on gender. 6. Hypothesis 3……….…..…[Paired Sample t-test]…….……………………… 164 There is a statistical difference between the pre-Test and the post-Test scores. 7. Hypothesis 4….………[using Pearson Product Moment Correlation]…..…........ 184 Ho: There is no statistical relationship between expenditure on social programmes (public expenditure on education and health) and levels of development in a country; and H1: There is a statistical association between expenditure on social programmes (i.e. public expenditure on education and health) and levels of development in a country 8. Hypothesis 5….. ………[using Logistic Regression]…………………………........ 199 The health care seeking behaviour of Jamaicans is a function of educational level, poverty, union status, illnesses, duration of illnesses, gender, per capita consumption, ownership of health insurance policy, and injuries. [ Health Care Seeking Behaviour = f( educational levels, poverty, union status, illnesses, duration of illnesses, gender, per capita consumption, ownership of health insurance policy, injuries)] 9. Hypothesis 6….. ……[using Linear Regression] ….………………………….. 207 There is a negative correlation between access to tertiary level education and poverty controlled for sex, age, area of residence, household size, and educational level of parents 10. Hypothesis 7….. ……[using Pearson Product Moment Correlation Coefficient and Crosstabulations]………………………....................... 223 There is an association between the introduction of the Inventory Readiness Test and the Performance of Students in Grade 1 5
  • 11. Hypothesis 8….…………[using Spearman rho]……………………………….... 232 The people who perceived themselves to be in the upper class and middle class are more so than those in the lower (or working) class do strongly believe that acts of incivility are only caused by persons in garrison communities 12. Hypothesis 9………………………………………………………………........ 235 Various cross tabulations 13. Hypothesis 10………[using Pearson and Crosstabulations]………………........ 249 There is no statistical difference between the typology of workers in the construction industry and how they view 10-most top productivity outcomes 14. Hypothesis 11….…[using Crosstabulations and Linear Regression]……........ 265 Determinants of the academic performance of students 15. Hypothesis 12….……[using Spearman ranked ordered correlation]…........ 278 People who perceived themselves to be within the lower social status (i.e. class) are more likely to be in-civil than those of the upper classes. 16. Data Transformation…………………………………………………........ 281 Recoding 291 Dummying variables 309 Summing similar variables 331 Data reduction 340 Glossary……………..….. ………………………………………………………........ 350 Reference…..………….…………………………………………………………........ 352 Appendices…………..….. ………………………………………………………........ 356 Appendix 1- Labeling non-responses 356 6
  • Appendix 2- Statistical errors in data 357 Appendix 3- Research Design 359 Appendix 4- Example of Analysis Plan 366 Appendix 5- Assumptions in regression 367 Appendix 6- Steps in running a bivariate cross tabulation 368 Appendix 7- Steps in running a trivariate cross tabulation 380 Appendix 8- What is placed in a cross tabulations table, using the above SPSS output 394 Appendix 9- How to run a Regression in SPSS 395 Appendix 10- Running Regression in SPSS 396 Appendix 11a- Interpreting strength of associations 407 Appendix 11b - Interpreting strength of association 408 Appendix 12- Selecting cases 409 Appendix 13- ‘UNDO’ selecting cases 417 Appendix 14- Weighting cases 420 Appendix 15- ‘Undo’ weighting cases 429 Appendix 15- Statistical symbolisms 440 Appendix 16 – Converting from ‘string’ to ‘numeric’ data – Apparatus One – Converting from string data to numeric data 443 Apparatus Two – Converting from alphabetic and numeric data to all ‘numeric data 447 Appendix 17- Steps in running Spearman rho 454 Appendix 18- Steps in running Pearson’s Product Moment Correlation 459 Appendix 19-Sample sizes and their appropriate sampling error 464 Appendix 20 – Calculating sample size from sampling error(s) 465 Appendix 21 – Sample sizes and their sampling errors 467 Appendix 22 - Sample sizes and their sampling errors 468 Appendix 23 – If conditions 469 Appendix 24 – The meaning of ρ value 477 Appendix 25 – Explaining Kurtosis and Skewness 478 Appendix 26 – Sampled Research Papers 479-560 7
  • PREFACE One of the complexities for many undergraduate students and for first time researchers is ‘How to blend their socialization with the systematic rigours of scientific inquiry?’ For some, the socialization process would have embedded in them hunches, faith, family authority and even ‘hearsay’ as acceptable modes of establishing the existence of certain phenomena. These are not principles or approaches rooted in academic theorizing or critical thinking. Despite insurmountable scientific evidence that have been gathered by empiricism, the falsification of some perspectives that students hold are difficulty to change as they still want to hold ‘true’ to the previous ways of gaining knowledge. Even though time may be clearly showing those issues are obsolete or even ‘mythological’, students will always adhere to information that they had garnered in their early socialization. The difficulty in objectivism is not the ‘truths’ that it claims to provide and/or how we must relate to these realities, it is ‘how do young researchers abandon their preferred socialization to research findings? Furthermore, the difficulty of humans and even more so upcoming scholars is how to validate their socialization with research findings in the presence of empiricism. Within the aforementioned background, social researchers must understand that ethic must govern the reporting of their findings, irrespective of the results and their value systems. Ethical principles, in the social or natural research, are not ‘good’ because of their inherent construction, but that they are protectors of the subjects (participants) from the researcher(s) who may think the study’s contribution is paramount to any harm that the interviewees may suffer from conducting the study. Then, there is the issue of confidentiality, which sometimes might be conflicting to the personal situations faced by the researcher. I will be simplistic to suggest that who takes precedence is based on the code of conduct that guides that profession. Hence, undergraduate students should be brought into the general awareness that findings must be reported without any form of alteration. This then give rise to ‘how do we systematically investigate social phenomena?’ The aged old discourse of the correctness of quantitative versus qualitative research will not be explored in this work as such a debate is obsolete and by rehashing this here is a pointless dialogue. Nevertheless, this textbook will forward illustrations of how to analyze quantitative data without including any qualitative interpretation techniques. I believe that the problems faced by students as how to interpret statistical data (ie quantitative data), must be addressed as the complexities are many and can be overcome in a short time with assistance. My rationale for using ‘hypotheses’ as the premise upon which to build an analysis is embedded in the logicity of how to explore social or natural happenings. I know that hypothesis testing is not the only approach to examining current germane realities, but that it is one way which uses more ‘pure’ science techniques than other approaches. Hypothesis testing is simply not about null hypothesis, Ho (no statistical relationships), or alternative hypothesis, Ha, it is a systematic approach to the investigation of observable phenomenon. In attempting to make undergraduate students recognize the rich annals of hypothesis testing and how they are paramount to the discovery of social fact, I will 8
  • recommend that we begin by reading Thomas S. Kuhn (the Scientific Revolution), Emile Durkheim (study on suicide), W.E.B. DuBois (study on the Philadelphian Negro) and the works of Garth Lipps that clearly depict the knowledge base garnered from their usage. In writing this book, I tried not to assume that readers have grasped the intricacies of quantitative data analysis as such I have provided the apparatus and the solutions that are needed in analyzing data from stated hypotheses. The purpose for this approach is for junior researchers to thoroughly understand the materials while recognizing the importance of hypothesis testing in scientific inquiry. Paul Andrew Bourne, Dip Ed, BSc, MSc, PhD Health Research Scientist Department of Community Health and Psychiatry Faculty of Medical Sciences The University of the West Indies Mona-Jamaica. 9
  • ACKNOWLEDGEMENT This textbook would not have materialized without the assistance of a number of people (scholars, associates, and students) who took the time from their busy schedule to guide, proofread and make invaluable suggestions to the initial manuscript. Some of the individuals who have offered themselves include Drs. Ikhalfani Solan, Samuel McDaniel and Lawrence Nicholson who proofread the manuscript and made suggestions as to its appropriateness, simplicities and reach to those it intend to serve. Furthermore, Mr. Maxwell S. Williams is very responsible for fermenting the idea in my mind for a book of this nature. Special thanks must be extended to Mr. Douglas Clarke, an associate, who directed my thoughts in time of frustration and bewilderment, and on occasions gave me insight on the material and how it could be made better for the students. In addition, I would like to extend my heartiest appreciation to Professor Anthony Harriott and Dr. Lawrence Powell both of the department of Government, UWI, Mona- Jamaica, who are my mentors and have provided me with the guidance, scope for the material and who also offered their expert advice on the initial manuscript. Also, I would like to take this opportunity to acknowledge all the students of Introduction to Political Science (GT24M) of the class 2006/07 who used the introductory manuscript and made their suggestions for its improvement, in particular Ms. Nina Mighty. 10
  • Menú Bar Content: A social researcher should not only be cognizant of statistical techniques and modalities of performing his/her discipline, but he/she needs to have a comprehensive grasp of the various functions within the ‘menu’ of the SPSS program. Where and what are constituted within the ‘menu bar’; and what are the contents’ functions? ‘Menu bar’ contains the following: - File - Edit - View - Data - Transform - Analyze - Graph - Utilities - Add-ons - Window - Help The functions of the various contents of the ‘menu bar’ are explored overleaf Box 1: Menu Function 11
  • Menu Bar Functions: Purposes of the different things on the menu bar File – This icon deals with the different functions associated with files such as (i) opening .., (ii) reading …, (iii) saving …, (iv) existing. Edit – This icon stores functions such as – (i) copying, (ii) pasting, (iii) finding, and (iv) replacing. View – Within this lie functions that are screen related. Data – This icon operates several functions such as – (i) defining, (ii) configuring, (iii) entering data, (iv) sorting, (v) merging files, (vi) selecting and weighting cases, and (vii) aggregating files. Transform – Transformation is concerned with previously entered data including (i) recoding, (ii) computing, (iii) reordering, and (vi) addressing missing cases. Analyze – This houses all forms of data analysis apparatus, with a simply click of the Analyze command. Graph – Creation of graphs or charts can begin with a click on Graphs command Utilities – This deals with sophisticated ways of making complex data operations easier, as well as just simply viewing the description of the entered data 12
  • MATHEMATICAL SYMBOLS (NUMERIC OPERATIONS), in SPSS NUMERIC OPERATIONS FUNCTIONS + Add - Subtract * Multiply / Divide ** Raise to a power () Order of operations < Less than > Greater than <= Less than or equal to >= Greater than or equal to = Equal ~= Not equal to & and: both relations must be true I Or: either relation may be true ~ Negation: true between false, false become true Box 2: Mathematical symbols and their Meanings 13
  • LISTING OF OTHER SYMBOLS SYMBOLS MEANINGS YRMODA (i.e. yr. month, day) Date of birth (e.g. 1968, 12, 05) a Y intercept b Coefficient of slope (or regression) f frequency n Sample size N Population R Coefficient of correlation, Spearman’s r Coefficient of correlation , Pearson Sy Standard error of estimate W ot Wt Weight µ Mu or population mean β Beta coefficient 3 or χ Measure of skewness ∑ summation σ Standard deviation χ2 Chi-Square or chi square, this is the value use to test for goodness of fit CC Coefficient of Contingency fa Frequency of class interval above modal group fb Frequency of class interval below modal group X A single value or variable _ Adjusted r, which is the coefficient of R correlation corrected for the number of cases _ _ Arithmetic mean of X or Y X or Y RND Round off to the nearest integer SYSMIS This denotes system-missing values MISSING All missing values Type I Error Claiming that events are related (or means are different when they are not Type II Error This assumes that events (or means are not different) when they are Φ Phi coefficient r2 The proportion of variation in the dependent variable explained by the independent variable(s) 14
  • LISTING OF OTHER SYMBOLS SYMBOLS MEANINGS P(A) Probability of event A P(A/B) Probability of event A given that event B has happened CV Coefficient of variation SE Standard error O Observed frequency X Independent (explanatory, predictor) variable in regression Y Dependent (outcome, response, criterion) variable in regression df Degree of freedom t Symbol for the t ratio (the critical ratio that follows a t distribution R2 Squared multiple correlation in multiple regression 15
  • FURTHER INFORMATION ON TYPE I and TYPE II Error The Real world The null hypothesis is really…….. True False Finding from your Survey You found that True No Problem Type 2 Error the null hypothesis is: False Type 1 Error No Problem THE WHEREABOUTS OF SOME SPSS FUNCTIONS Functions or Commands Whereabouts, in SPSS (the process in arriving at various commands) Mean, Analyze Mode, Descriptive statistics Median, Frequency Standard deviation, Skewness, or kurtosis, Statistics Range Minimum or maximum Analyze Chi-square Descriptive statistics crosstabs 16
  • Analyze Pearson’s Moment Correlation Correlate bivariate Analyze Spearman’s rho Correlate Bivariate (ensure that you deselect Pearson’s, and select Spearman’s rho) Analyze Linear Regression Regression Linear Analyze Logistic Regression Regression Binary Analyze Discriminant Analysis Classify Discriminant Analyze Mann-Whitney U Test Nonparametric Test 2 Independent Samples Independent –Sample t-test Analyze Compare means Independent Samples T-Test Analyze Wilcoxon matched-pars test or Nonparametric Test 2 Independent Samples Wilcoxon signed-rank test Analyze t-test Compare means Analyze Paired-samples t-test Compare means Paired-samples T-test Analyze One-sample t-test Compare means One-samples T-test Analyze One-way analysis of variance Compare means One-way ANOVA 17
  • Analyze Factor Analysis Data reduction Factor Analyze Descriptive (for a single metric Descriptive statistics Descriptive variable) Graphs Graphs (select the appropriate type) Pie chart Bar charts Histogram Graphs Scatter plots Scatter… Data Weighting cases Weight cases…. Select weight cases by Graphs Selecting cases Select cases… If all conditions are satisfied Select If Transform Replacing missing values Missing cases values… Box 3: The whereabouts of some SPSS Functions 18
  • Disclaimer I am a trained Demographer, and as such, I have undertaken extensive review of various aspects to the SPSS program. However, I would like to make this unequivocally clear that this does not represent SPSS (Statistical Product and Service Solutions, formerly Statistical Package for the Social Sciences) brand. Thus, this text is not sponsored or approved by SPSS, and so any errors that are forthcoming are not the responsibility of the brand name. Continuing, the SPSS is a registered trademark, of SPSS Inc. In the event that you need more pertinent information on the SPSS program or other related products, this may be forwarded to: SPSS UK Ltd., First Floor, St. Andrews House, West Street, Working GU211EB, United Kingdom. 19
  • Coding Missing Data The coding of data for survey research is not limited to response, as we need to code missing data. For example, several codes indicate missing values and the researcher should know them and the context in which they are applicable in the coding process. No answer in a survey indicates something apart from the respondent’s refusal to answer or did not remember to answer. The fundamental issue here is that there is no information for the respondent, as the information is missing. Table : Missing Data codes for Survey Research Question Refused answer Didn’t know answer No answer recorded Less than 6 categories 7 8 9 More than 7 and less 97 98 99 than 3 digits More than 3 digits 997 998 999 Note Less than 6 categories – when a question is asked of a respondent, the option (or response) may be many. In this case, if the option to the question is 6 items or less, refusal can be 7, didn’t know 8 or no answer 9. Some researchers do not make a distinction between the missing categories, and 999 are used in all cases of missing values (or 99). 20
  • Computing Date of Birth – If you are only given year of birth Step 1 Step 1: First, select transform, and then compute 21
  • Step 2 On selecting ‘compute variable’ it will provide this dialogue box 22
  • Step 3 In the ‘target variable’, write the word which the researcher wants to use to represents the idea 23
  • Step 4 If the SPSS program is more than 12.0 (ie 13 – 17), the next process is to select all in ‘function group’ dialogue box In order to convert year of birth to actual ‘age’, select ‘Xdate.Year’ 24
  • Step 5 Replace the ‘?’ mark with variable in the dataset Having selected XYear, use this arrow to take it into the ‘Numeric Expression’ dialogue box 25
  • LISTING OF FIGURES AND TABLES Listing of Figures Figure 1.1.1: Flow Chart: How to Analyze Quantitative Data? Figure 1.1.2: Properties of a Variable. Figure 1.1.3: Illustration of Dichotomous Variables Figure 1.1.4: Ranking of the Levels of Measurement Figure 1.1.5: Levels of Measurement Figure 2.1.0: Steps in Analyzing Non-Metric Data Figure 2.1.1: Respondents’ Gender Figure 2.1.2: Respondents’ Gender Figure 2.1.3: Social Class of Respondents Figure 2.1.4: Social Class of Respondents Figure 2.1.5: Steps in Analyzing Metric Data Figure 2.1.6: ‘Running’ SPSS for a Metric Variable Figure 2.1.7: ‘Running’ SPSS for a Metric Variable Figure 2.1.8: ‘Running’ SPSS for a Metric Variable Figure 2.1.9: ‘Running’ SPSS for a Metric Variable Figure 2.1.10: ‘Running’ SPSS for a Metric Variable Figure 2.1.11: ‘Running’ SPSS for a Metric Variable Figure 2.1.12: ‘Running’ SPSS for a Metric Variable Figure 2.1.13: ‘Running’ SPSS for a Metric Variable Figure 2.1.14: ‘Running’ SPSS for a Metric Variable Figure 2.1.15: ‘Running’ SPSS for a Metric Variable 26
  • Figure 2.1.16: ‘Running’ SPSS for a Metric Variable Figure 4.1.1: Age - Descriptive Statistics Figure 4.1.2: Gender of Respondents Figure 4.1.3: Respondent’s parent educational level Figure 4.1.4: Parental/Guardian Composition for Respondents Figure 4.1.5: Home Ownership of Respondent’s Parent/Guardian Figure 4.1.6: Respondents’ Affected by Mental and/or Physical Illnesses Figure 4.1.7: Suffering from mental illnesses Figure 4.1.8: Affected by at least one Physical Illnesses Figure 4.1.9: Dietary Consumption for Respondents Figure 6.1.2: Typology of Previous School Figure 6.1.3: Skewness of Examination i (i.e. Test i) Figure 6.1.4: Skewness of Examination ii (i.e. Test ii) Figure 6.1.5: Perception of Ability Figure 6.1.6: Self-perception Figure 6.1.7: Perception of task Figure 6.1.8: Perception of utility Figure 6.1.9: Class environment influence on performance Figure 6.1.10: Perception of Ability Figure 6.1.11: Self-perception Figure 6.1.12: Self-perception Figure 6.1.13: Perception of task Figure 6.1.14: Perception of Utility 27
  • Figure 6.1.15: Class Environment influence on Performance Figure 7.1.1: Frequency distribution of total expenditure on health as % of GDP Figure 7.1.2: Frequency distribution of total expenditure on education as % of GNP Figure 7.1.3: Frequency distribution of the Human Development Index Figure 7.1.4: Running SPSS for social expenditure on social programme Figure 7.1.5: Running bivariate correlation for social expenditure on social programme Figure 7.1.6: Running bivariate correlation for social expenditure on social programme Figure13.1.1: Categories that describe Respondents’ Position Figure13.1.2: Company’s Annual Work Volume Figure13.1.3: Company’s Labour Force – ‘on an averAge per year’ Figure13.1.4: Respondents’ main Area of Construction Work Figure13.1.5: Percentage of work ‘self-performed’ in contrast to ‘sub-contracted’ Figure13.1.6: Percentage of work ‘self-performed’ in contrast to ‘sub-contracted’ Figure 13.1.7: Years of Experience in Construction Industry Figure13.1.8: Geographical Area of Employment Figure13.1.9: Duration of service with current employer Figure13.1.10: Productivity changes over the past five years Figure 14.1.1: Characteristic of Sampled Population Figure 14.1.2: Employment Status of Respondents 28
  • Listing of Tables Table 1.1.1: Synonyms for the different Levels of measurement Table 1.1.2: Appropriateness of Graphs, from different Levels of measurement Table 1.1.3: Levels of measurement1 with examples and other characteristics Table1.1.4: Levels of measurement, and measure of central tendencies and measure of variability Table1.1.5: combinations of Levels of measurement, and types of statistical Test which are application Table 1.1.6a: Statistical Tests and their Levels of Measurement Table 1.1.6b: Table 2.1.1a: Gender of Respondents Table 2.1.1b: General happiness Table 2.1.2: Social Status Table 2.1.3: Descriptive Statistics on the Age of the Respondents Table 2.1.4:“From the following list, please choose what the most important characteristic of democracy …are for you” Table 4.1.1: Respondents’ Age Table 4.1.2 (a) Univariate Analysis of the explanatory Variables Table 4.1.2(b): Univariate Analysis of explanatory Table 4.1.2 (c): Univariate Analysis of explanatory Table 4.1.3: Bivariate Relationships between academic performance and subjective Social Class (n=99) 1 29
  • Table 4.1.4: Bivariate Relationships between comparative academic performance and subjective Social Class (n=108) Table 4.1.5: Bivariate Relationships between academic performance and physical exercise (n= 111) Table 4.1.6 (i): Bivariate Relationships between academic performance and instructional materials (n=113) Table 4.1.6 (ii) Relationship between academic performance and materials among students who will be writing the A’ Level Accounting Examination, 2004 Table 4.1.7: Bivariate Relationships between academic performance and Class attendance (n= 106) Table 4.1.8: Bivariate Relationship between academic performance and attendance Table 4.1.9: Bivariate Relationships between academic performance and breakfast consumption, (n=114) Table 4.1.10: Relationship between academic performances and breakfasts consumption among A’ Level Accounting students, controlling for Gender Table 4.1.11: Bivariate Relationships between academic performance and migraine (n=116) Table 4.1.12: Bivariate Relationships between academic performance and mental illnesses, (n=116) Table 4.1.13: Bivariate Relationships between academic performance and physical illnesses, (n=116) Table 4.1.14: Bivariate Relationships between academic performance and illnesses (n=116) Table 4.1.15. Bivariate Relationships between current academic performance and past performance in CXC/GCE English language Examination, (n= 112) Table 4.1.16: Bivariate Relationships between academic performance and past performance in CXC/GCE English language Examination, controlling for Gender Table 4.1.17: Bivariate Relationships between academic performance and past performance in CXC/GCE Mathematics Examination n= Table 4.1.18 (i): Bivariate Relationships between academic performance and past performance in CXC/GCE principles of accounts Examination (n= 114) 30
  • Table 4.1.19 (ii): Bivariate Relationships between academic performance and past performance in CXC/GCEPOA Examination, controlling for Gender Table 4.1.20: Bivariate Relationships between academic performance and Self-Concept (n= 112) Table 4.1.21: Bivariate Relationships between academic performance and Dietary Requirements (n=116) Table 4.1.22: Summary of Tables Table 5.1.1: Frequency and percent Distributions of explanatory model Variables Table 5.1.2: Relationship between Religiosity and Marijuana Smoking (n=7,869) Table 5.1.3: Relationship between Religiosity and Marijuana Smoking controlled for Gender Table 5.1.4: Relationship between Age and marijuana smoking (n=7,948) Table 5.1.5: Relationship between marijuana smoking and Age of Respondents, controlled for sex Table 5.1.6: Relationship between academic performances and marijuana smoking, (n=7,808) Table 5.1.7: Relationship between academic performances and marijuana smoking, controlled for Gender Table 5.1.8: Summary of Tables Table 6.1.1: Age Profile of respondent Table 6.1.2: Examination Scores Table 6.1.3(a): Class Distribution by Gender Table 6.1.3(b): Class Distribution by Age Cohorts Table 6.1.3(c): Pre-Test Score by Typology of Group Table 6.1.3(c): Pre-Test Score by Typology of Group Table 6.1.4: Comparison of Examination I and Examination II Table 6.1.5: Comparison a Cross the Group by Tests 31
  • Table 6.1.6: Analysis of Factors influence on Test ii Scores Table 6.1.7: Cross-Tabulation of Test ii Scores and Factors Table 6.1.8: Bivariate Relationship between student’s Factors and Test ii Scores Table 7.1.1: Descriptive Statistics - total expenditure on public health (as Percentage of GNP HRD, 1994) Table 7.1.2: Descriptive Statistics of expenditure on public education (as Percentage of GNP, Hrd, 1994) Table 7.1.3: Descriptive Statistics of Human Development (proxy for development) Table 7.1.4: Bivariate Relationships between dependent and independent Variables Table 7.1.5: Summary of Hypotheses Analysis Table8.1.1: Age Profile of Respondents (n = 16,619) Table 8.1.2: Logged Age Profile of Respondents (n = 16,619) Table 8.1.3: Household Size (all individuals) of Respondents Table 8.1.4: Union Status of the sampled Population (n=16,619) Table 8.1.5: Other Univariate Variables of the Explanatory Model Table 8.1.6: Variables in the Logistic Equation Table 8.1.7: Classification Table Table 8.1.1: Univariate Analyses Table 8.1.2: Frequency Distribution of Educational Level by Quintile Table 8.1.3: Frequency Distribution of Jamaica’s Population by Quintile and Gender Table 8.1.4: Frequency Distribution of Educational Level by Quintile Table 8.1.5: Frequency Distribution of Pop. Quintile by Household Size Table 8.1.6: Bivariate Analysis of access to Tertiary Edu. and Poverty Status Table 8.1.7: Bivariate Analysis of access to Tertiary Edu. and Geographic Locality of Residents 32
  • Table 8.1.8: Bivariate Analysis of geographic locality of residents and poverty Status Table 8.1.9: Bivariate Relationship between access to tertiary level education by Gender Table 8.1.10: Bivariate Relationship between Access to Tertiary Level Education by Gender controlled for Poverty Status Table 8.1.11: Regression Model Summary Table 10.1.1: Univariate Analysis of Parental Information Table 10.1.2: Descriptive on Parental Involvement Table 10.1.3: Univariate Analysis of Teacher’s Information Table 10.1.4: Univariate Analysis of ECERS-R Profile Table 10.1.5: Bivariate Analysis of Self-reported Learning Environment and Mastery on Inventory Test Table 10.1.6: Relationship between Educational Involvement, Psychosocial and Environment involvement and Inventory Test Table 10.1.6: Relationship between Educational Involvement, Psychosocial and Environment Involvement and Inventory Test Table 10.1.8: School Type by Inventory Readiness Score Table 11.1.1: Incivility and Subjective Social Status Table 12.1.2: Have you or someone in your family known of an act of Corruption in the last 12 months? Table 12.1.3: Gender of Respondent Table 12.1.4: In what Parish do you live? Table 12.1.5: Suppose that you, or someone close to you, have been a victim of a crime. What would you do...? Table 12.1.6: What is your highest level of Education? Table 12.1.7: In terms of Work, which of these best describes your Present situation? Table 12.1.8: Which best represents your Present position in Jamaica Society? Table 12.1.9: Age on your last Birthday? Table 12.1.10: Age categorization of Respondents 33
  • Table 12.1.11: Suppose that you, or someone close to you, have been a victim of a crime. what would you do... by Gender of respondent Cross Tabulation Table 12.1.12: If involved in a dispute with neighbour and repeated discussions have not made a difference, would you...? by Gender of respondent Cross Tabulation Table 12.1.13: Do you believe that corruption is a serious problem in Jamaica? by Gender of respondent Cross Tabulation Table 12.1.14: have you or someone in your family known of an act of corruption in the last 12 months? by Gender of respondent Cross Tabulation Table 14.1.1: Marital Status of Respondents Table 14.1.2: Marital Status of Respondents by Gender Table 14.1.3: Marital Status by Gender by Age cohort Table 14.1.4: Marital Status by Gender by Age Cohort Table 14.1.5 Educational Level by Gender by Age Cohorts Table 14.1.6: Income Distribution of Respondents Table 14.1.7: Parental Attitude Toward School Table 14.1.8: Parent Involving Self Table 14.1.9: School Involving Parent Table 14.1.8: Regression Model Summary Table 15.1.1: Correlations Table 15.1.2: Cross Tabulation between incivility and social status 34
  • How do I obtain access to the SPSS PROGRAM? Step One: In order to access the SPSS program, the student should select ‘START’ to the bottom left hand corner of the computer monitor. This is followed by selecting ‘All programs’ (see below). Select ‘START’ and then ‘All Program 35
  • Step Two: The next step to the select ‘SPSS for widows’. Having chosen ‘SPSS for widows’ to the right of that appears a dialogue box with the following options – SPSS for widows; SPSS 12.0 (or 13.0…or, 15.0); SPSS Map Geo-dictionary Manager Ink; and last with SPSS Manager. Select ‘SPSS for widows’ 36
  • Step Three: Having done step two, the student will select SPSS 12.0 (or 13.0, or 14.0 or 15.0) for Widows as this is the program with which he/she will be working. Select SPSS 12.0 (or 13.0, or 14.0 or 15.0) for Widows 37
  • Step Four: On selecting ‘SPSS for widows’ in step 3, the below dialogue box appears. The next step is the select ‘OK’, which result in what appears in step five. Select ‘OK’ 38
  • Step Five: 39
  • What should I now do? The student should then select the ‘inner red box’ with the ‘X’. Select the ‘inner red box’ with the X’. 40
  • Step Six: This is what the SPSS spreadsheet looks like (see Figure below). 41
  • 42
  • Step Seven: What is the difference here? Look to the bottom left-hand cover the spreadsheet and you will see two terms – (1) ‘Data View’ and (2) ‘Variable View’. Data View accommodates the entering of the data having established the template in the ‘Variable View’. Thus, the variable view allows for the entering of data (i.e. responses from the questionnaires) in the ‘Data View’. Ergo, the student must ensure that he/she has established the template, before any typing can be done in the ‘Data View. widow looks like ‘Data View’ Observe what the Data View 43
  • 44 Variable View Observe what the ‘Variable View’ widow looks like
  • CHAPTER 1 1.1.0a: INTRODUCTION This book is in response to an associate’s request for the provision of some material that would adequately provide simple illustrations of ‘How to analyze quantitative data in the Social Sciences from actual hypotheses’. He contended that all the current available textbooks, despite providing some degree of analysis on quantitative data, failed to provide actual illustrations of cases, in which hypotheses are given and a comprehensive assessment made to answer issues surrounding appropriate univariate, bivariate and/or multivariate processes of analysis. Hence, I began a quest to pursued textbooks that presently exist in ‘Research Methods in Social Sciences’, ‘Research Methods in Political Sciences’, “Introductory Statistics’, ‘Statistical Methods’, ‘Multivariate Statistics’, and ‘Course materials on Research Methods’ which revealed that a vortex existed in this regard. Hence, I have consulted a plethora of academic sources in order to formulate this text. In wanting to comprehensively fulfill my friend’s request, I have used a number of dataset that I have analyzed over the past 6 years, along with the provision of key terminologies which are applicable to understanding the various hypotheses. I am cognizant that a need exist to provide some information in ‘Simple Quantitative Data Analysis’ but this text is in keeping with the demand to make available materials for aiding the interpretation of ‘quantitative data’, and is not intended to unveil any new materials in the discipline. The rationale behind this textbook is embedded in simple reality that many undergraduate students are faced with the complex task of ‘how to choose the most appropriate statistical test’ and this becomes problematic for them as the issue of wanting to complete an 45
  • assignment, and knowing that it is properly done, will plague the pupil. The answer to this question lies in the fundamental issues of - (1) the nature of the variables (continuous or discrete), and (2) what is the purpose of the analysis – is to mere description, or to provide statistical inference and/or (3) if any of the independent variables are covariates2. Nevertheless, the materials provided here are a range of research projects, which will give new information on particular topics from the hypothesis to the univariate analysis and the bivariate or multivariate analyses. 2 “If the effects of some independent variables are assessed after the effects of other independent variables are statistically removed…” (Tabachnick and Fidell 2001, 17) 46
  • 1.1.0b: STEPS IN ANALYZING A HYPOTHESIS One of the challenges faced by a social researcher is how to succinctly conceptualize (i.e. define) his/her variables, which will also be operationalized (measured) for the purpose of the study. Having written a hypothesis, the researcher should identify the number of variables which are present, from which we are to identify the dependent from the independent variables. Following this he/she should recognize the level of measurement to which each variable belongs, then the which statistical test is appropriate based on the level of measurement combination of the variables. The figure below is a flow chart depicting the steps in analyzing data when given a hypothesis. The production of this text is in response to the provision of a simple book which would address the concerns of undergraduate students who must analyze a hypothesis. Among the issues raise in this book are (1) the systematic steps involved in the completion of analyzing a hypothesis, (2) definitions of a hypothesis, (3) typologies of hypothesis, (4) conceptualization of a variable, (4) types of variables, (5) levels of measurement, (6) illustration of how to perform SPSS operations on the description of different levels of measurement and inferential statistics, (7) Type I and II errors, (8) arguments on the treatment of missing variables as well as outliers, (9) how to transform selected quantitative data, (10) and other pertinent matters. The primary reason behind the use of many of the illustrations, conceptualizations and peripheral issues rest squarely on the fact the reader should grasp a thorough understanding of how the entire process is done, and the rationale for the used method. 47
  • STEP ONE STEP TEN Write your Having used the Hypothesis STEP TWO test, Identify the analyze the data variables from the carefully, based on hypothesis the statistical test STEP TEN STEP THREE Choose the Define and appropriate operationalize statistical test based each variable on the combination selected from the of DV and IVS, and hypothesis STEP NINE STEP FOUR ANALYZING If statistical Inference is needed, look at the QUANTITATIVE Decide on the level combination DV and DATA of measurement IV(s) for each variable STEP EIGHT STEP FIVE If statistical association, causality Decide which or predictability is need, continue, if not variable is DV, and stop! IV STEP SIX STEP SEVEN Check for Do descriptive skewness, and/or statistics for chosen outliers in metric variables selected variables FIGURE 1.1.1: FLOW CHART: HOW TO ANALYZE QUANTITATIVE DATA? This entire text is ‘how to analyze quantitative data from hypothesis’, but based on Figure 1.1.1, it may appear that a research process begins from a hypothesis, but this is not the case. Despite that, I am emphasizing interpreting hypothesis, which is the base for this monograph starting from an actual hypothesis. Thus, before I provide you with operational definitions of 48
  • variables, I will provide some contextualization of ‘what is a variable?’ then the steps will be worked out. 49
  • 1.1.1a: DEFINITIONS OF A VARIABLE Undergraduates and first time researchers should be aware that quantitative data analysis are primarily based on (1) empirical literature, (2) typologies of variables within the hypothesis, (3) conceptualization and operationalization of the variables, (4) the level of measurement for each variables. It should be noted that defining a variable is simply not just the collation a group of words together, because we feel a mind to as each variable requires two critical characteristics in order that it is done properly (see Figure 1.1.2). PROPERITIES OF A VARIABLE MUTUAL EXCLUSIVITIY EXHAUSTIVNESS FIGURE 1.1.2: PROPERTIES OF A VARIABLE. In order to provide a comprehensive outlook of a variable, I will use the definitions of a various scholars so as to give a clear understanding of what it is. “Variables are empirical indicators of the concepts we are researching. Variables, as their name implies, have the ability to take on two or more values...The categories of each variable must have two requirements. They should be both exhaustive and mutually exclusive. By exhaustive, we mean that the categories of each variable must be comprehensive enough that it is possible to categorize every observation” (Babbie, Halley, and Zaino 2003, 11). “.. Exclusive refers to the fact that every observation should fit into only one category “(Babbie, Halley and Zaino 2003, 12) “A variable is therefore something which can change and can be measured.” (Boxill, Chambers and Wint 1997, 22) 50
  • “The definition of a variable, then, is any attribute or characteristic of people, places, or events that takes on different values.” (Furlong, Lovelace, Lovelace 2000, 42) “A variable is a characteristic or property of an individual population unit” (McClave, Benson and Sincich 2001, 5) “Variable. A concept or its empirical measure that can take on multiple values” (Neuman 2003, 547). “Variables are, therefore, the quantification of events, people, and places in order to measure observations which are categorical (i.e. nominal and ordinal data) and non-categorical (i.e. metric) in an attempt to be informed about the observation in reality. Each variable must fill two basic conditions – (i) Exhaustiveness – the variable must be so defined that all tenets are captured as its is comprehensive enough include all the observations, and (ii) mutually exclusivity – the variable should be so defined that it applies to one event and one event only – (i.e. Every observation should fit into only one category) (Bourne 2007). One of the difficulties of social research is not the identification of a variable or variables in the study but it’s the conceptualization and oftentimes the operationalization of chosen construct. Thus, whereas the conceptualization (i.e. the definition) of the variable may (or may not) be complex, it is the ‘how do you measure such a concept (i.e. variable) which oftentimes possesses the problem for researchers. Why this must be done properly bearing in mind the attributes of a variable, it is this operational definition, which you will be testing in the study (see Typologies of Variables, below). Thus, the testing of hypothesis is embedded within variables and empiricism from which is used to guide present studies. Hypothesis testing is a technique that is frequently employed by demographers, statisticians, economists, psychologists, to name new practitioners, who are concerned about the testing of theories, and the verification of reality truths, and the modifications of social realities within particular time, space and settings. With this being said, researchers must ensure that a variable is properly defined in an effort to ensure that the stated phenomenon is so defined and measured. 51
  • 1.1.1b TYPOLOGIES of VARIABLE (examples, using Figure 1.1.2, above) Health care seeking behaviour: is defined as people visiting a health practitioner or health consultant such as doctor, nurse, pharmacist or healer for care and/ or advice. Levels of education: This is denominated into the number of years of formal schooling that one has completed. Union status – It is a social arrangement between or among individuals. This arrangement may include ‘conjugal’ or a social state for an individual. Gender: A sociological state of being male or female. Per capita income: This is used a proxy for income of the individual by analyzing the consumption pattern. Ownership of Health insurance: Individuals who possess of an insurance polic/y (ies). Injuries: A state of being physically hurt. The examples here are incidences of disability, impairments, chronic or acute cuts and bruises. Illness: A state of unwellness. Age: The number of years lived up to the last birthday. Household size - The numbers of individuals, who share at least one common meal, use common sanitary convenience and live within the same dwelling. Now that the premise has been formed, in regard to the definition of a variable, the next step in the process is the category in which all the variables belong. Thus, the researcher needs to know the level of measurement for each variable - nominal; ordinal; interval, or ration (see 1.1.2a). 52
  • 1.1.2a: LEVELS OF MEASUREMENT3: Examples and definitions Nominal - The naming of events, peoples, institutions, and places, which are coded numerical by the researcher because the variable has no normal numerical attributes. This variable may be either (i) dichotomous, or (ii) non-dichotomous. Dichotomous variable – The categorization of a variable, which has only two sub- groupings - for example, gender – male and female; capital punishment – permissive and restrictive; religious involvement – involved and not involved. Non-dichotomous variable – The naming of events which span more than two sub-categories (example Counties in Jamaica – Cornwall, Middlesex and Surrey; Party Identification – Democrat, Independent, Republican; Ethnicity – Caucasian, Blacks, Chinese, Indians; Departments in the Faculty of Social Sciences – Management Studies, Economics, Sociology, Psychology and Social Work, Government; Political Parties in Jamaica – Peoples’ National Party (PNP), Jamaica Labour Party (JLP), and the National Democratic Movement (NDM); Universities in Jamaica – University of the West Indies; University of Technology, Jamaica; Northern Caribbean University; University College of the Caribbean; et cetera) Ordinal - Rank-categorical variables: Variables which name categories, which by their very nature indicates a position, or arrange the attributes in some rank ordering (The examples here are as follows i) Level of Educational Institutions – Primary/Preparatory, All-Age, Secondary/High, Tertiary; ii) Attitude toward gun control – strongly oppose, oppose, favour, strongly favour; iii) Social status – upper--upper, upper-middle, middle-middle, lower-middle, lower class; iv) Academic achievement – A, B, C, D, F. Interval or ratio These variables share all the characteristics of a nominal and an ordinal variable along with an equal distance between each category and a ‘true’ zero value – (for example – age; weight; height; temperature; fertility; votes in an election, mortality; population; population growth; migration rates, . Now that the definitions and illustrations have been provided for the levels of measurement, the student should understand the position of these measures (see 1.1.2b). 3 Stanley S. Stevens is created for the development of the typologies of scales – level of measurement – (i) nominal, (ii) ordinal, (iii) interval and (iv) ratio. (see Steven 1946, 1948, 1968; Downie and Heath 1970) 53
  • Dichotomy (or Dichotomous variable Typologies of Gender Science Book Non- Fictional Male Female Pure Applied Fictional Alive Dead Induction Deduction Non- Parametric Burial Non-burial parametric statistics statistics Religious Non-religious Non- use primary use secondary Decomposed data data service service decomposed Figure 1.1.3: Illustration of dichotomous variables 54
  • 1.1.2b: RANKING LEVELS OF MEASUREMENT RATIO highes t INTERVAL ORDINAL lowest NOMINAL Figure 1.1.4: Ranking of the levels of measurement The very nature of levels of measurement allows for (or do not allow for) data manipulation. If the level of measurement is nominal (for example fiction and non-fiction books), then the researcher does not have a choice in the reconstruction of this variable to a level which is below it. If the level of measurement, however, is ordinal (for example no formal education, primary, secondary and tertiary), then one may decide to use a lower level of measure (for example below secondary and above secondary). The same is possible with an interval variable. The social scientist may want to use one level down, ordinal, or two levels down, nominal. This is equally the same of a ratio variable. Thus, the further ones go up the pyramid, the more scope exists in data transformation. 55
  • Table 1.1.1: Synonyms for the different Levels of measurement Levels of Measurement Other terms Nominal Categorical; qualitative, discrete4 Ordinal Qualitative, discrete; rank-ordered; categorical Interval/Ratio Numerical, continuous5, quantitative; scale; metric, cardinal Table 1.1.2: Appropriateness of Graphs for different levels of measurement Levels of Measurement Graphs Bar chart Pie chart Histogram Line Graph Nominal √ √ __ __ √ √ __ __ Ordinal __ __ √ √ Interval/Ratio (or metric) 4 Discrete variable – take on a finite and usually small number of values, and there is no smooth transition from one value or category to the next – gender, social class, types of community, undergraduate courses 5 Continuous variables are measured on a scale that changes values smoothly rather than in steps 56
  • Table 1.1.3: Levels of measurement6 with Examples and Other Characteristics Levels of Measurement Nominal Ordinal Interval Ratio Examples Gender Social class Temperature Age Religion Preference Shoe size Height Political Parties Level of education Life span Weight Race/Ethnicity Gender equity Reaction time Political Ideologies levels of fatigue Income; Score on an Exam. Noise level Fertility; Population of a country Job satisfaction Population growth; crime rates Mathematical properties Identity Identity Identity Identity ____ Magnitude Magnitude Magnitude ____ _____ Equal Interval Equal interval ____ _____ _____ True zero Mathematical Operation(s) None Ranking Addition; Addition; Subtraction Subtraction; Division; Multiplication Compiled: Paul A. Bourne, 2007; a modification of Furlong, Lovelace and Lovelace 2000, 74 6 “Levels of measurement concern the essential nature of a variable, and it is important to know this because it determines what one can do with a variable (Burham, Gilland, Grant and Layton-Henry 2004, 114) 57
  • Table1.1.4: Levels of measurement, Measure of Central Tendency and Measure of Variability Levels of Measurement Measure of central tendencies Measure of variability Mean Mode Median Mean deviation Standard deviation Nominal NA √ NA NA NA Ordinal NA √ √ NA NA Interval/Ratio7 √ √ √ √ √ NA denotes Not Applicable 7 Ratio variable is the highest level of measurement, with nominal being first (i.e. lowest); ordinal, second; and interval, third. 58
  • Table1.1.5: Combinations of Levels of measurement, and types of Statistical test which are applicable8 Levels of Measurement Statistical Test Dependent Independent Variable Nominal Nominal Chi-square Nominal Ordinal Chi-square; Mann-Whitney Nominal Interval/ratio Binomial distribution; ANOVA; Logistic Regression; Kruskal-Wallis Discriminant Analysis Ordinal Nominal Chi-square Ordinal Ordinal Chi-square; Spearman rho; Ordinal Interval/ratio Kruskal-Wallis H; ANOVA Interval/ratio Nominal ANOVA; Interval/ratio Ordinal Interval/ratio Interval/ratio Pearson r, Multiple Regression Independent-sample t test Table 1.1.5 depicts how a dependent variable, which for example is nominal, which when combined with an independent variable, Nominal, uses a particular statistical test. 8 One of the fundamental issues within analyzing quantitative data is not merely to combine then interpret data, but it is to use each variable appropriately. This is further explained below. 59
  • STATISTICAL TESTS AND THEIR LEVELS OF MEASUREMENT Test Independent Dependent Variable variable Chi-Square (χ2) Nominal, Ordinal Nominal, Ordinal Mann-Whitney U Dichotomous Nominal, Ordinal test Kruskal-Wallis H Non-dichotomous, Ordinal, or skewed9 test Ordinal Metric Pearson’s r Normally distributed10 Normally distributed Metric Metric Linear Regress Normally distributed Normally distributed Metric, dummy Metric Independent Dichotomous Normally distributed Samples Metric T-test AVONA Nominal, Ordinal Normally distributed (non-dichotomous11) Metric Logistic regression Metric, dummy Dichotomous (skewed values or otherwise Discriminant Metric, dummy Dichotomous (normally distributed analysis value) Notes to Table 1.1.6b Chi-Square (χ2) Used to test for associations between two variables Mann-Whitney U test Used to determine differences between two groups Kruskal-Wallis H test Used to determine differences between three or more groups Pearson’s r Used to determine strength and direction of a relationship between two values Linear Regression Used to determine strength and direction of a relationship between two or more values Independent Samples T-test Used to determine difference between two groups AVONA Used to determine difference between three or more groups Logistic regression Used to predict relationship between many values Discriminant analysis Used to predict relationship between many values 9 Skewness indicates that there is a ‘pileup’ of cases to the left or right tail of the distribution 10 Normality is observed, whenever, the values of skewness and kurtosis are zero 11 Non-dichotomous (i.e. polytomous) which denotes having many (i.e. several) categories 61
  • LEVELS OF MEASURMENT AND THEIR MEASURING ASSOCIATION LEVELS OF MEASUREMENT NOMINAL ORDINAL INTERVAL/RATIO Lambda Gamma Pearson’s r Cramer’s V Somer’s D Contingency coefficients Kendall ‘s tau-B Phi Kendall’s tau-c Figure 1.1.5: Levels of measurement ‫ג‬ Lambda ( ) – This is a measure of statistical relationship between the uses of two nominal variables Phi (Φ) – This is a measure of association between the use of two dichotomous variables (i.e. dichotomous dependent and dichotomous independent) – [Φ = √[ χ2/N] Cramer’s V (V) – This is a measure of association between the use of two nominal variables (i.e. in the event that there is dichotomous dependent and dichotomous independent) – V = √[ χ2/N(k – 1)] is identical to phi. γ Gamma ( ) – This is used to measure the statistical association between ordinal by ordinal variable Contingency coefficient (cc) – Is used for association in which the matrix is more than 2 X 2 (i.e. 2 for dependent and 2 for the independent – for example 2X3; 3X2; 3X3 …) - √ [χ2/ χ2 + N] Pearson’s r – This is used for non-skewed metric variables - n∑xy - ∑x.∑y √ [n∑x2 – (∑x) 2 - [n∑y2 – (∑y) 2 62
  • 1.1.3: CONCEPTUALIZING DESCRIPTIVE AND INFERENTIAL STATISTICS Research is not done in isolation from the reality of the wider society. Thus, the social researcher needs to understand whether his/her study is descriptive and/or inferential as it guides the selection of certain statistical tools. Furthermore, an understanding of two constructs dictate the extent to which the analyst will employ as there is a clear demarcation between descriptive and inferential statistics. In order to grasp this distinction, I will provide a number of authors’ perspectives on each terminology. “Descriptive statistics describe samples of subjects in terms of variables or combination of variables” (Tabachnick and Fidell 2001, 7) “Numerical descriptive measures are commonly used to convey a mental image of pictures, objects, tables and other phenomenon. The two most common numerical descriptive measures are: measures of central tendencies and measures of variability (McDaniel 1999, 29; see also Watson, Billingsley, Croft and Huntsberger 1993, 71) “Techniques such as graphs, charts, frequency distributions, and averages may be used for description and these have much practical use” (Yamane 2973, 2; see also Blaikie 2003, 29; Crawshaw and Chambers 1994, Chapter 1) “Descriptive statistics – statistics which help in organizing and describing data, including showing relationships between variables” (Boxill, Chamber and Wind 1997, 149) 63
  • “We’ll see that there are two areas of statistics: descriptive statistics, which focuses on developing graphical and numeral summaries that describes some…phenomenon, and inferential statistics, which uses these numeral summaries to assist in making… decisions” (McClave, Benson, Sinchich 2001, 1) “Descriptive statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set, and to present the information in a convenient form” (McClave, Benson and Sincich 2001, 2) “Inferential statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data” (McClave, Benson and Sincich 2001, 2) “The phrase statistical inference will appear often in this book. By this we mean, we want to “infer” or learn something about the real world by analyzing a sample of data. The ways in which statistical inference are carried out include: estimating…parameters; predicting…outcomes, and testing…hypothesis …” (Hill, Griffiths and Judge 2001, 9). Inferential statistics is not only about ‘causal’ relationships; King, Keohane and Verba argue that it is categorized into two broad areas: (1) descriptive, and (2) causal inference. Thus, descriptive inference speaks to the description of a population from what is made possible, the sample size. According to Burham, Gilland, Grant and Layton-Henry (2004) state that: Causal inferences differ from descriptive ones in one very significant way: they take a ‘leap’ not only in terms of description, but in terms of some specific causal 64
  • process [i.e. predictability of the variables]” (Burham, Gilland, Grand and Layton- Henry 2004, 148). In order that this textbook can be helping and simple, I will provide operational definitions of concepts as well as illustration of particular terminologies along with appropriateness of statistical techniques based on the typologies of variable and the level of measurement (see in Tables 1.1.1 – 1.1.6, below). 65
  • CHAPTER 2 2.1.0: DESCRIPTIVE STATISTICS The interpretation of quantitative data commences with an overview (i.e. background information on survey or study – this is normally demographic information) of the general dataset in an attempt to provide a contextual setting of the research (descriptive statistics, see above), upon which any association may be established (inferential statistics, see above). Hence, this chapter provides the reader with the analysis of univariate data (descriptive statistics), with appropriate illustration of how various levels of measurement may be interpreted, and/or diagrams chosen based on their suitability. A variable may be non-metric (i.e. nominal or ordinal) or metric (i.e. scale, interval/ratio). It is based on this premise that particular descriptive statistics are provide. In keeping with this background, I will begin this process with non-metric, then metric data. The first part of this chapter will provide a thorough outline of how nominal and/or ordinal variables are analyzed. Then, the second aspect will analyze metric variables. 66
  • STEP ONE Ensure that the STEP TEN variable is non- Analyze the output metric (e.g. Gender, STEP TWO (use Table 2.1.1a) general happiness) Select Analyze STEP TEN STEP THREE Select descriptive select paste or ok statistics HOW TO DO DESCRIPTIVE STEP NINE STATISTICS FOR A STEP FOUR NO-METRIC Choose bar or pie graphs VARIABLE? select frequency STEP FIVE STEP EIGHT select the non-metric select Chart variable STEP SEVEN STEP SIX select mode or mode and median (based on if the select statistics at the variable is nominal or end ordinal respective Figure 2.1.0: Steps in Analyzing Non-metric data 67
  • 2.1.1a: INTERPRETING NON-METRIC (or Categorical) DATA NOMINAL VARIABLE (when there are not missing cases) Table 2.1.1a: Gender of respondents Frequency Percent Valid Percent Male 150 69.4 69.4 Gender: Female 66 30.6 30.6 Total 216 100.0 100.0 Identifying Non-missing Cases: When there are no differences between the percent column and those of the valid percent column, then there are no missing cases. How is the table analyzed? Of the sampled population (n=21612), 69.4% were males compared to 30.6% females. 12 The total number of persons interviewed for the study. It is advisable that valid percents are used in descriptive statistics as there may be some instances then missing cases are present with the dataset, which makes the percent figure different from those of the valid percent (Table 2.1.1b). 68
  • NOMINAL VARIABLE: Establishment of when missing cases Table 2.1.1b: General Happiness Frequency Percent Valid Percent Very happy 467 30.8 31.1 General Happiness: Pretty happy 872 57.5 58.0 Not too happy 165 10.9 11.0 Missing Cases 13 0.9 - Total 1,517 100.0 100.0 Identifying Missing Cases: In seeking to ascertain missing data (which indicates that some of the respondents did no answer the specified question), there is a disparity between the values for percent and those in valid percent. In this case, 13 of 1,517 respondents did not answer question on ‘general happiness’. In cases where there is a difference between the two aforementioned categories (i.e. percent and valid percent), the student should remember to use the valid percent. The rationale behind the use of the valid percent is simple, the research is about those persons who have answered and they are captured in the valid percent column. Hence, it is recommended that the student use the valid percent column at all time in analyzing quantitative data. Interpretation: Of the sampled population (n=1,517), the response rate is 99.1% (n=1,504)13. Of the valid responses (n=1,504), 31.1% (n=467) indicated that they were ‘very happy’, with 58.0% (n=872) reported being ‘pretty happy’, compared to 11.0% (n=165) who said ‘not too happy’. 13 Because missing cases are within the dataset (13 or 0.9%), there is a difference between percent and valid percent. Thus, care should be taken when analyzing data. This is overcome when the valid percents are used. 69
  • Owing to the typology of the variable (i.e. nominal), this may be presented graphical by either a pie graph or a bar graph. Pie graph Female, 30.6, 31% Male, 69.4, 69% Figure 2.1.1: Respondents’ gender OR Bar graph 70 60 50 40 30 20 10 0 Male Female Figure 2.1.2: Respondents’ gender 70
  • ORDINAL VARIABLE Table 2.1.2: Subjective (or self-reported) Social Class Frequency Percent Valid Percent Social class: Lower 100 46.3 46.3 Middle 104 48.1 48.1 Upper 12 5.6 50.6 Total 216 100.0 100.0 Interpreting the Data in Table 2.1.2: When the respondents were asked to select what best describe their social standing, of the sampled population (n=216), 46.3% reported lower (working) class, 48.1% revealed middle class compared to 5.6% who said upper middle class. Based on the typology of variable (i.e. ordinal), the graphical options are (i) pie graph and/or (2) bar graph. Note: In cases where there is no difference between the percent column and that of valid percent, researchers infrequently use both columns. The column which is normally used is valid percent as this provides the information of those persons who have actually responded to the specified question. Instead of using ‘valid percent’ the choice term is ‘percent’. 71
  • 50 45 48.1 40 46.3 35 30 25 20 15 10 5 5.6 0 Lower class Middle class Upper middle class Figure 2.1.3: Social class of respondents Or Upper middle class, 5.6 Lower class, 46.3 Middle class, 48.1 Figure 2.1.4: Social class of respondents 72
  • 2.1.1b: STEPS IN INTERPRETING METRIC VARIABLE: METRIC (i.e. scale or interval/ratio) STEP ONE STEP TEN Know the metric variable (Age) STEP TWO Analyze the output (use Table 2.1.3) Select Analyze STEP TEN STEP THREE Select descriptive select paste or ok statistics HOW TO DO STEP NINE DESCRIPTIVE STATISTICS FOR STEP FOUR Choose histogram A METRIC with normal curve VARIABLE? select frequency STEP FIVE STEP EIGHT select Chart select the metric variable STEP SIX STEP SEVEN select mean, select statistics at standard deviation, the end skewness Figure 2.1.5: Steps in Analyzing Metric data 73
  • INTERPRETING METRIC DATA: METRIC (i.e. scale or interval/ratio) VARIABLE Table 2.1.3: Descriptive statistics on the Age of the Respondents N Valid 216 Missing 0 Mean 20.33 Median 20.00 Mode 20 Std. Deviation 1.692 Skewness 2.868 Std. Error of Skewness .166 Of the sampled population (n=216), the mean age of the sample was 20 yrs and 4 months (i.e. 4 = 0.33 x 12) ± 1 yr. and 8 months (i.e. 8 = 0.692 x 12), with a skewness of 2.868 yrs. Statistically an acceptable skewness must be less than or equal to 1.0. Hence, this skewness in this sample is unacceptable, as it is an indicator of errors in the reporting of the data by the respondents. With this being the case, the researcher (i.e. statistician) has three options available at his/her disposal. They are (1) to remove the skewness, (2) not use the data – because of the high degree of errors and (3) use the median instead of the mean. It should be noted that all the measure of central tendencies (i.e. the arithmetic mean, arithmetic mode and the arithmetic median) are about the same (i.e. mean – 20.33, mode – 20.0, and median – 20.0). This situation is caused by extreme values in the data set. Hence, in this case, the arithmetic mean is disported by the values (or value) and so it is not advisable this be used to indicate the centre of the distribution. (See below how this is done in SPSS) The figure below is to enable readers to have a systematic plan of ‘how to arrive at the SPSS output’ for analyzing a metric variable (for example age of respondents). Following the figure, I implement the plan in an actual SPSS illustration of how this is done. 74
  • Step One: ANALYZE Figure 2.1.6: ‘Running’ SPSS for a Metric variable 75
  • Step Two: Descriptive statistics Figure 2.1.7: ‘Running’ SPSS for a Metric variable 76
  • Step Three: select Frequency Figure 2.1.8: ‘Running’ SPSS for a Metric variable 77
  • Step Four: Select the metric variable – The metric variable – in this case is age Figure 2.1.9: ‘Running’ SPSS for a Metric variable 78
  • Step Five select the metric variable from over here to to here Figure 2.1.10: ‘Running’ SPSS for a Metric variable 79
  • to the end of Step Five, you’ll see statistics select it Figure 2.1.11: ‘Running’ SPSS for a Metric variable 80
  • Step Six: A metric variable requires that you do the me an Choose the following: SD, minimum, range select skewness, kurtosis Figure 2.1.12: ‘Running’ SPSS for a Metric variable 81
  • Step Seven: To the end of Step Five, you will see Charts; this means you should select Histogram with normal curve Figure 2.1.13: ‘Running’ SPSS for a Metric variable 82
  • Step Nine: select ‘run’, which is this Key Step Eight: Highlight the argument Figure 2.1.14: ‘Running’ SPSS for a Metric variable 83
  • Step Ten: Final Output, which the researcher will now analyze Figure 2.1.15: ‘Running’ SPSS for a Metric variable 84
  • Histogram 120 Step Eleven: 100 This is pictorial of the distribution of the metric variable, age 80 60 n u q F y c e r 40 20 Mean = 34.95 Std. Dev. = 13.566 0 N = 1,280 20 40 60 80 Age on your last birthday? Figure 2.1.16: ‘Running’ SPSS for a Metric variable 85
  • 2.1.2a: MISSING (i.e. NON-RESPONSE) CASES Table 2.1.4: “From the following list, please choose what the most important characteristic of democracy …are for you” Frequency Percent Open and fair election 314 23.5 An economic system that guarantees a dignified salary 177 13.2 Freedom of speech 321 24.0 Equal treatment for everybody 295 22.0 Respect for minority 35 2.6 Majority rules 54 4.0 Parliamentarians who represented their electorates 52 3.9 A competitive party system 47 3.5 Don’t know/No answer 43 3.214 Total 1338 100.0 Source: Powell, Bourne and Waller 2007, 11 Of the sampled population (n=1,338), when asked “From the following list, please choose what is four you the most important characteristic of democracy …?”, 23.5% (n=314) ‘open and fair elections’ 13.2% (n=177) remarked ‘An economic system that guarantees a dignified salary’, 24.0% (n=321) said ’Freedom of speech’ , 22.0% (n=295) indicated ‘Equal treatment for everybody by courts of law’, 2.6% (n=35) mentioned ‘Respect for minorities’, 4.0% (n=54) felt ‘Majority rule’, 3.9% (n=52) believed ‘Members of Parliament who represent their electors’, and 3.5% (n=47) informed that ‘A competitive party system’ compared to 3.2% (n=43) who had no answer – (i.e. ‘Don’t know/No answer), which is referred to as ‘missing values’ or, see note 4. 14 “Don’t know/no answer” is an issue of fundamental importance in survey research. This is called non- response. 86
  • The issue of non-response becomes problematic whenever it is approximately 5%, or more (see for example George and Mallery 2003, chapter 4; Tabachnick and Fidell 2001, chapter 4; Thirkettle 1988, 10). Missing data are simply not just about ‘non-response’, but they may distort the interpretation of data in case of ‘inferential statistics’. In some instances that they are so influential that they create what is called, Type II error. According to Thirkettle 1998, “Unless every person to be interviewed is interviewed the results will not be valid. Non-response must therefore be kept to negligible proportions” (Thirkettle 1988, 10). Thirkettle’s perspective is idealistic, and this is not supported by ant of the other scholars to which I have read (see for example Babbie, Halley and Zaino 2003; George and Mallery 2003; Tabachnick and Fidell 2001; Bobko 2001; Willemsen 1974). The issue of what is an unacceptable ‘non-response rate’ is 20%. When this marker is reached or surpassed, researchers are inclined not to use the variable. Thus, in the case of Table 2.1.4, a non-response rate of 3.2% is considered to be negligible. Furthermore, missing data is simply not about ‘non-response’ from the interviewed but it is the difficulty of generalizability that it may cause, which posses the problem in data analysis. “Its seriousness depends on the pattern of missing data, how much is missing, and why it is missing” (Tabachnick and Fidell 2001, 58). According to Tabachnick and Fidell (2001): The pattern of missing data is more important than the amount missing. Missing values scattered randomly through a data matrix pose less serious problems. Nonrandomly missing values, on the other hand, are serious no matter how few of them there are because they affect the generalizability of results (Tabachnick and Fidell 2001, 58). He continues that If only a few data points, say, 5% or less, are missing in a randomly pattern form a large data set, the problems are less serious and almost any procedure for handling missing vales yields similar results (Tabachnick and Fidell 2001, 59). 87
  • 2.1.2b: TREATING MISSING (i.e. NON-RESPONSES) CASES Unlike a dominant theory which is generally acceptable by many scholars, the construct of missing data is fluid. Thus, I will be forwarding some of the arguments that exist on the matter. Fundamentally, the handling of missing cases primarily rest in the following categorizations. These are – (1) if the cases are less than 5%, (2) number of non-response exceeds 20% and (3) randomly or non-randomly distributed with the dataset. Scholars, such as Thirkettle (1988) ands Tabachnick and Fidell (2003) believe that in the event that the number of such cases are less than or equal to 5%, they are acceptable. On the other hand, in the event when such non-responses are more than or equal to 20%, those variables are totally dropped from the data analysis. Thus, according to Tabachnick and Fidell 2001, chapter 4; George and Mallery 2003, chapter 4, these are the available options in manipulating missing cases: • drop all cases with them; • deletion of cases (i.e. this is a default function of SPSS, SAS, and SYSTAT); • impute values for those missing cases-  insert series mean15,16 mean of nearby points, median of nearby points;  using regression – (i) linear trends at point, and (ii) linear interpolation;  expectation maximization (EM)17, 18  using prior knowledge, and  multiple imputation 15 “It is best to avoid mean substitution unless the proportion of missing is very small and there are no other options available to you” (Tabachnick and Fidell 2001, 66) 16 “Series mean is by far the most frequently used method” (George and Mallery 2003, 50) 17 “EM methods offer the simplest and most reasonable approach to imputation of missing data. as long as you have access to SPSS MVA …(Tabachnick and Fidell 2001, 66) 18 “Regression or EM. These methods are the most sophisticated and are generally recommended” (de Vaus 2002, 69) 88
  • CONCLUSION The issue of how to ‘treat missing variables’ is as unresolved as the inconclusiveness of a ‘Supreme Being, God’ and as the divergence of views on the same. One scholar forwards the view that 10% of the data cases can be missing for them to be replaced by ‘mean values’ (Marsh 1988), whereas another group of statisticians Tabachnick and Fidell (2004) believed that not more than 5% of the cases should be absence, for replacement by any approach. The latter scholars, however, do not think that a 5% benchmark in and of itself is an automatic valuation for replacement but that the researcher should test this by way of cross tabulation. This is done with some other variable(s) in an attempt to ascertain if any difference exists between the responses and the non-responses. If on concluding that no-difference is present between the responses and the non-responses, it is only then that they subscribe to replacement of missing data within the dataset. Hence, missing data are replaced by one of the appropriate mathematical technique – ‘series mean’, ‘mean of nearby points’, ‘median of nearby points’, ‘linear interpolation’, and/or ‘linear trends at points’. The perspective is not the dominant viewpoint as within the various disciplines, some scholars are ‘purist’ and so take a fundamental different stance from other who may relax this somewhat. One of the difficulties is for social researchers and upcoming practitioners of the craft are to grasp – their discipline’s delimitations and some of the rationale which are present therein in an effort to concretize their own position grounded by some empiricism. In keeping with this tradition, I will present a discourse on the matter; and I 89
  • will add that scholars should be mindful of what obtains within their craft. It should be noted that sometimes these premises are ‘best practices’ and in other instances, they are merely guide and not ‘laws’. On the other hand, in a dialogue with Professor of Demography at the University of the West Indies, Mona, C. Uche, PhD., he being a ‘purist’ of the Chicago School, believe than the arbitrary substitution of non-responses can be a misrepresentation of the views of the non-respondents, and so he advice researcher do to take that route, even if the cases are less than 5%. In a monologue with Professor of Applied Sociology, Patricia Anderson, PhD., from the same Chicago School held the view that while it is likely to replace missing data point for a variable, in the case in Jamaica non-response should be taken as is. She argued that no answer, in Jamaica, is somewhat different from those who are indicated choiced responses. Thus, if the researcher substitution ‘missing cases’ with mean value or any other technique for that rather, he/she runs the risk of misrepresenting the social reality. With Marsh, Tabachnick and Fidell, Uche, and Anderson, we may conclude this discourse has many more time left in its wake. Thus, the ‘treatment of missing values’ must be left up to the researcher within the context of society and any validation of a chosen perspective. 90
  • CHAPTER 3 3.1.0: HYPOTHESIS: INTRODUCTION All research is based on the premise of an investigation of some unknown phenomenon. Quantitative studies, on the other hand, are not merely to provide information but it is substantially hinged on the foundation of hypothesis testing, as this allows for some logical way of thinking. Therefore, this chapter focuses on the continuation of Chapter 2, while further the research process, which is the use of hypothesis, and the use of appropriate statistical test in an effort to validate the hypothesis of the research, in question. One author argues that it is widely accepted that studies should be geared towards testing hypothesis (Blaikie 2003, 13). He continues that “when research starts out with one or more hypotheses, they should ideally be derived from a theory of some kind, preferably expressed in for of a set of propositions” (Blaikie 2003, 14). The use of hypothesis, in objectivism, is not limited to examination of some past theories, but without this the realities that social scientists seek to explore become more so a maze, with no ending in sight. According to Blaikie 2003, “Hypotheses that are plucked out of thin air, or are just based on hunches, usually makes limited contributions to the development of knowledge because they are unlikely to connect with the existing state of knowledge (Blaikie 2003, 14). Thus, I will begin the definition of the construct, hypothesis. Then I will proceed with a full interpretation of the results beginning with the germane univariate data (see 91
  • for example chapter 2) followed by the most suitable associational test (see chapter 1), given the levels of measurement. 3.1.1: DEFINITIONS OF HYPOTHESIS “A hypothesis is a preposition of a relationship between two variables: a dependent and an independent” (Babbie, Hally, and Zaino 2003, 12). The dependent variable is influenced by external stimuli (or the independent variable), and the independent variable is actually acting on its own to “cause”, or “lead to” an impact on the dependent. According to Babbie, Hally and Zaino, “A dependent variable is the variable you are trying to explain (Babbie, Hally and Zaino 2003, 13). Boxill, Chambers and Wint (1997), on the other hand, write that a “Hypothesis – a non- obvious statement which makes an assertion establishing a testable base about a doubtful or unknown statement (Boxill, Chambers and Wint 1997, 150). With Neuman (2003) stating that a hypothesis is “The statement from a causal explanation or proposition that has a least one independent and one dependent variable, but it has yet to be empirically tested” (Neuman 2003, 536). Another group of scholars write that a hypothesis is “A statement about the (potential) relationship between the variables a researcher is studying. They are usually testable statements in the form of predictions about relationships between the variables, and are used to guide the design of studies.” (Furlong, Lovelace and Lovelace 2000, G8). Every hypothesis must have two attributes. These are (1) a dependent variable, and (2) an independent variable. Thus, embedded within each hypothesis are at least two variables. So as to make this easily understandable, I will a few examples. • There is an association between breakfast consumption and ones academic performance – DV (dependent variable) – academic performance; and IV (independent variable) – breakfast consumption. • Determinants of wellbeing of the Jamaica elderly (such a hypothesis require the use of multiple regression analysis as they possesses a number 92
  • of different causal factors. Hence, the DV is wellbeing. And IVs are – educational attainment; biomedical conditions; age cohorts of the elderly (young elderly, old-elderly and the oldest-old elderly); union status; area of residence; social support; employment status; number of people in household; financial support; environment conditions; income; cost of health care; exercise; 3.1.2: TYPOLOGIES OF HYPOTHESIS In social research hypotheses are categorized as either (1) theoretical or (2) statistical. According to Blaikie (2003) “Statistical hypotheses deal only with the specific problem of estimating whether a relationship found in a probability sample also exists in the population” (Blaikie 2003, 178). This textbook will only use statistical hypotheses. Furthermore, statistical hypotheses are written as null, Ho19 and alternative, Ha20. The Ho indicates no statistical association in the population; whereas the Ha denotes a statistical association in the population between the dependent and the independent variable (s). Furthermore, a statistical hypothesis may be either directional or non-directional. 19 In regression analysis, the null hypothesis, Ho: β = 0. 20 When using regression analytic technique, the alternative hypothesis, Ha : β ≠ 0 93
  • 3.1.3: DIRECTIONAL AND NON-DIRECTIONAL HYPOTHESES NON-DIRECTIONAL HYPOTHESES Non-directional hypotheses exist whenever the researcher has not specified any direction for the hypothesis: The examples here are as follows:  Politicians are more corrupt than Clergymen;  There is an association between number of hours spent studying and the examination results had;  Men are less likely to be personal secretaries than women;  curative care, preventative care, social class, educational attainment, and types of school attended are determinants of well-being DIRECTIONAL HYPOTHESES Directional hypotheses exist when the researcher specifies a direction for the hypothesis: 1. Positive relationship – meaning an increase in one variable sees an increase in other variable(s): -  An increase in ones age is associated with a direct change in more years of worked experiences;  There is a positive relationship between educational attainment and income received;  There is a direct relationship between fertility and population increases. 2. Negative relationship – meaning an increase in one variable result in a reduction in other variable(s): - 94
  •  An increase in ones age is associated with a reduction in physical functioning;  There is an inverse relationship between educational attainment and the fertility of a woman;  There is an inverse relationship between the number of hours the West Indian crickets spent practice and them failing; 3.1.4a: OUTLIERS Despite the fact that it is mathematically appropriate to compute the mean for interval and ratio data [i.e. metric or scale data], there are times when the median may be more descriptive measure of central tendency for interval and ratio data because highly irregular values (called outliers) [exist] in the data set [and these] may affect the value of the mean (especially in small sets of scores), but they have no effect on the value of the median” (Furlong, Lovelace and Lovelace 2000, 94-95). It is on this premise that median is used instead of the mean as a measure of central tendency. Statistically, the mean is affect by extremely large or small values, which explains the reason for the skewness that exists in the descriptive statistics for interval/ratio variables. Thus, care must be taken in using highly skewed data for a hypothesis. In the event that the researcher intends to use the skewed variable as is, he/she should ensure that the statistical test is appropriate for this situation (see Chapter I). Otherwise, the information that is garnered is of no use. 95
  • In the event that outliers are detected within a variable, the researcher should explore his/her available options before a decision is taken on any particular event. If skewness (i.e. an indicator of outliers) is detected, this does not presuppose that mean is inappropriate as some statisticians argue that an acceptable value is approximately ± 1. The social research should be cognizant that outliers are not only an issue in metric variable but may also be present in categorical variables. According to Tabachnick and Fidell: Rummel (1970) suggests deleting dichotomous variables with 90-10 splits between categories or more both because the correlation coefficients between these variables and others are truncated and because the scores for the cases in the small category are more influential than those in the category with numerous cases (Tabachnick and Fidell 2001, 67) 3.1.4b: REASONS for OUTLIERS  data recording entry;  Instrumentation error - the item entered in the particular category, may be different from those previously entered. 3.1.4c: IDENTIFICATION of OUTLIERS  mathematically – using skewness;  graphical approach. 3.1.4d: TREATMENT of OUTLIERS  If data entry – correct this by using the questionnaire, then redo the analysis;  If instrumentation – drop the case(s). 96
  • 3.1.5: STATISTICAL APPROACHES FOR ADDRESSING SKEWNESS However, if the skewness happens to be more than the absolute value of 1 (i.e. the numerical value without taking into consideration the sign for the value), the following should be sought in an attempt to either (i) remove the skewness, or (ii) reduce the skewness. These options are as follows: i) Log10 the value; ii) Loge or ln, the value; iii) Square root, the variable; iv) Square, the variable. In the event that we are unable to reduce or remove skewness, the researcher should not use the mean as a measure of the ‘average’ as it is affect by outliers21 which are present within the dataset. In addition, he/she should ensure that the variable in question, for the purpose of hypothesis testing, is in keeping with a statistical test that is able to accommodate such a skewness (see Chapter I). In order to provide a better understanding the construct in this text, I will present each hypothesis in a new chapter. 21 “An outlier is a case with such an extreme value on one variable ( a univariate outlier) or such a strange combination of scores on two or more variables (multivariate outlier) that they distort statistics (Tabachnick and Fidell 2001, 66) 97
  • 3.1.6: LEVEL OF SIGNIFICANCE and CONFIDENCE INTERVAL Setting the level of confidence is a critical aspect of hypothesis testing in quantitative studies. A confidence interval (CI) of 95% means that we may reject the null hypothesis, Ho, 5% of the time (level of significance = 100% minus CI or CI = 100% minus level of significance). According to Blaikie, If we do not want to make this mistake [level of significance), we should set the level as high as possible, say 99.9%, thus running only a 0.01% risk. The problem is that the higher we set the level, the greater is the risk of a type II error [see Appendix II]. Conversely, the lower we set the level [of significance], the greater is the possibility of committing a type I error [see Appendix II] and the possibility of committing a type II error. (Blaikie 2003, 180) In the attempt to complete research projects and/or assignments, we sometimes fail to execute all the assumptions that are applicable to a particular variable. Even though we would like to examine the association and/or causal relationships that exit between or among different variables (i.e. hypothesis testing), this anxiety should not overshadow ones adherence to the statistical principles, which are there to guide the soundness of the interpretation of the figures. Thus, care is needed in ensuring that we apply mathematical appropriateness prior to the execution of hypothesis testing. The chapters that will proceed from here onwards will utilize the preceding chapter and this one. In that, I will commence each chapter with a hypothesis followed by presentation of the appropriate descriptive and inferential statistics. The social researcher should not that the hypothesis will be separated into variables; this will allow me to apply the most suitable inferential tools as was discussed in chapter I and II. 98
  • I am cognizant that undergraduate students would want a textbook that do their particular study but this book is not that. This textbook seeks to bridge that vortex, which is ‘how do I interpret various descriptive and inferential statistics?’ Hence, I have sought to provide a holistic interpretation of the ‘data analysis’ section of a study, using hypotheses. Hypothesis testing disaggregates generalizations into simple propositions that can be verified by empirical, which is rationale for using them to depict the logical processes in data interpretation. 99
  • CHAPTER 4 It may appear from you reading thus far that descriptive statistics is presented separately from inferential statistics in your paper, and that they are disjoint. A research is a whole, which requires descriptive and sometimes inferential statistics. It should be noted however that a study may be entirely descriptive (see for example Probing Jamaica’s Political Culture by Powell, Bourne and Waller 2007) or it may some association, causality or predictability (i.e. inferential statistics). If project requires inferential statistics, then a fundamental layer in the data analysis is the descriptive statistics. The use of the inferential statistics rests squarely with the level of measurement, the typologies of variable and the set of assumptions which are met by the variables. Tabachnick and Fidell (2001) aptly summarize this fittingly when they said that: Use of inferential and descriptive statistics is rarely on either-or proposition. We are usually interested in both describing and making inferences about a data set. We describe the data, find reliable difference or relationships, and estimate population values for the reliable findings. However, there are more restrictions on inferences than there are on description (Tabachnick and Fidell 2001, 8) In keeping with providing a simple textbook of how to analyze quantitative data, the previously outlined chapters have sought to give a general framework of what is expected in the interpretation of social science research. This is only the base; as such, I will not embark, from henceforth, to provide the readers with worked examples of different hypotheses, in each chapter, and the inclusion of detailed interpretations of those hypotheses, from a descriptive to an inferential statistical perspective. 100
  • HYPOTHESIS 1: General hypotheses A1. Physical and social factors and instructional resources will directly influence the academic performance of students who will write the Advanced Level Accounting Examination; A2. Physical and social factors and instructional resources positively influence the academic performance of students who write the Advanced level Accounting examination and that the relationship varies according to gender. B1. Pass successes in Mathematics, Principles of Accounts and English Language at the Ordinary/CXC General level will positively influence success on the Advanced level Accounting examination; B2. Pass successes in Mathematics, Principles of Accounts and English Language at the Ordinary/CXC General level will positively influence success on the Advanced level Accounting examination and that these relationships vary based on gender. In answering a hypothesis in any research, the student needs to present background information on the sampled population (or sample). This is referred to as descriptive statistics. The description of the data is primary based on the level of measurement (see Table 1.1.1 and Table 1.1.2) as each level of measurement requires a different approach and statistical description. Thus, in order to examine the aforementioned hypothesis, we will illustrate the particular description within the context of the level of measurement. 101
  • How to use SPSS in finding ‘Descriptive Statistics’? The example here is finding descriptive statistics for ‘Ag Age’ 102
  • Step One: Select ‘Analyze’ 103
  • Step Two: Select ‘Descriptive Statistics’ 104
  • Step Four: Go to ‘Frequency’ 105
  • Step Five: Select the ‘Frequency’ Option By selecting the ‘frequency option’, the dialogue box that appears is as follows This is the ‘dialogue box’ 106
  • Step Six: Finding the ‘variable name’ for which you seek to carry out the statistical operation Look in the left- hand side of the dialogue box for the variable in question 107
  • Step Seven (a): Taking the variable over to the ‘right-hand side’ of the dialogue box The identified variable on the ‘left-hand side’ of the dialogue should be taken to the right hand side by way of this arrow. By selecting (or depressing) on the arrow, the variable crosses to the right hand side 108
  • Step Seven (b): This is what ‘step seven’ looks like - 109
  • Step Eight: Select ‘statistics’ in which the ‘descriptive statistics’ are contained in SPSS By selecting ‘statistics’ Having selected ‘statistiss’ this dialogue box appears 110
  • Step Nine: Select the ‘appropriate’ descriptive statistics, which is based on the level of measurement Given that the ‘variable’ is metric, we select the following options – Mean; mode; median; stand deviation, mininum or maximum, and skewness 111
  • Step Ten: Having chosen the ‘appropriate descriptive statistics’, select Continue Having selected ‘continue’, it looks like nothing has happened or back to the initial dialogue box 112
  • Step Eleven: Select OK. Select OK. 113
  • Step Twelve: What appears after ‘Step Eleven?’ A summary of the descriptive statistics appears as well as the metric variable – in this case it is ‘Age of individual’ 114
  • Step Thirteen: Producing a pictorial depiction of the ‘metric variable’ If the student needs a graphical displace of the metric variable, he/she must select ‘Graph’ at the end of the dialogue box Select Graph 115
  • Step Fifteen: Having selected graph, we need to choose the type of ‘graph’ Based on the fact that the variable is a metric one, we should select ‘Histogram’ as well as ‘with normal curve’. The normal curve is a quick display of ‘skewness. Then select ‘continue’ 116
  • Step Sixteen: Select ‘continue’ Select ‘OK’, which produces the graphical display below 117
  • A graphical display of the ‘choosing graph’ Note: The researcher (or student) should make a table of the appropriate descriptive statistics, see overleaf. 118
  • ANALYSES & INTERPRETATION OF FINDINGS SOCIO-DEMOGRAPHIC PROFILE Table 4.1.1: Respondents’ Age Particulars (in years) Mean 17.48 Median 17.0 Standard deviation 1.275 Skewness 2.083 Minimum 16.000 Range 9.000 The findings reported in Table 4.1.1 shows a skewness of 2.083 years for the sampled respondents. This is a clear indication that the age variable within the data set is highly skewed, based on the fact that it is beyond ± 1 (see figure 4.1). As such, the researcher assumed for the purpose of this exercise that this variable cannot be use for any further analysis, as no method was able to reduce skewness below 1. Hence, with the mean age of the sampled population being 17 years and approximately 6 ± 1.275 years, based on the skewness (see Figure 4.1, below), then it follows that a better value to represent the average is 17.0 years, the median. 119
  • Figure 4.1.1: AGE DESCRIPTIVE STATISTICS 120
  • males 43% females 57% Figure 4.1.2: Gender of Respondents22 The sample consists of 136 private and public grammar schools’ students in Kingston and St. Andrew, Jamaica. Of the 136 respondents, one individual did not respond to most of the questions asked including his/her age at last birth however, he/she did respond to the question on major illnesses and on gender. Of the valid sample size (i.e. 136 interviewees), 59 were males and 77 females. 22 SPSS unlike Microsoft Excel does not specialize in graphic presentations of data, which explains a rationale why graphs in the latter are more professional than those produced by the former. Hence, I recommend that we transport the value from the SPSS’s output to Excel. 121
  • 45.00% 40.00% 35.00% 30.00% 25.00% Primary/All Age 20.00% Junior High 15.00% Secondary/Traditional High 10.00% Technical High Vocational 5.00% Teritary 0.00% Primary/All Age Technical High Figure 4.1.3: Respondent’s parent educational level Of sampled population, 42.4 percent of the respondents indicated that their parents had attained a tertiary level education, with some 40.9 percent a secondary level education and 6.1 percent a vocational level education and 10.6 percent at least a junior (all-age) high school level education (see Figure 4.1.3 above). 122
  • 40.00% 35.00% 30.00% 25.00% 20.00% Mother only 15.00% Father only 10.00% Mother and Father 5.00% Other 0.00% Mother only Father only Mother and Other Father Figure 4.1.4: Parental/guardian composition for respondents The findings in this research revealed that approximately 38 percent of the sampled respondents living in a nuclear family structure (with both father and mother), with 36 percent, living with a mother only and 9.6 percent living with their fathers only (see Figure 4.4). 123
  • 70.00% 60.00% 50.00% 40.00% 30.00% Owned by family Rented by family 20.00% 10.00% 0.00% Owned by family Rented by family Figure 4.1.5: Home ownership of respondent’s parent/guardian Most of the respondents indicated that their parents/guardians owned there homes (68.1 percent) with 31.9 percent stated that the family rented the homes that they occupy. 124
  • 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% None One At least two Figure 4.1.6: Respondents’ Affected by Mental and/or Physical illnesses The results in Figure 4.6 above are not surprising. Since a large majority of the respondents was not eating properly and furthermore their diet during the days were predominately carbohydrates (that is, snacks or ‘drunken foods’). Some 31.4 percent of the sampled population indicated that they had a least one type of mental illness. Of the 31.4 percent of respondents with a particular mental illness, approximately 4 percent had at least two such types of illnesses (see Table 4.2). 125
  • 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Yes No Figure 4.1.7: Suffering from mental illnesses Of the various types of mental illnesses that were investigated and responded to by the sampled population, approximately 23 percent of the students suffered from migraine (see Table 4.2). Moreover, the Sixth Form programme is an academic one and so requires the continuous cognitive domain of the students; therefore, researchers even if it does not influence the students’ academic performance must understand this psychological issue. This issue is singled out as it the only one with a value in excess of two percent. 126
  • Have None 32% 68% Figure 4.1.8: Affected by at least one Physical Illnesses Some 31.6 percent of the sample size was affected by at least one physical illness (see Table 4.2). The overwhelming majority of the respondents (14 percent) suffered from asthma attacks and 2.9 percent from numbness of the hands with 1.5 percent indicated that they had arthritis and sickle cell. 127
  • 51.50% 51.00% 50.50% 50.00% 49.50% 49.00% 48.50% 48.00% 47.50% 47.00% Moderate Poor Figure 4.1.9: Dietary consumption for respondents Although this research was not concerned with the number of calories that a male or a female should consume daily, none of the respondents was having all the daily dietary requirements as stipulated by the Caribbean Food and Nutrition Institute. Approximately 48.5 per cent of the respondents indicated that they were eating poorly and simple majority reported a moderate consumption of the dietary requirements. 128
  • TABLE 4.1.2 (a) UNIVARIATE ANALYSIS OF THE EXPLANATORY VARIABLES Details Frequency (%) ACADEMIC PERFORMANCE Distinction 44 (37.9) Credit 20 (17.2) Past 46 (31.7) Fail 6 (5.2) 23 Average Academic Performance 57.2 ± 15.4 (SD) ACADEMIC PERFORMANCE (Perception of respondent) Better 49 (39.5) Same 36 (29.0) Worse 39 (31.5) GENDER Male 58 (43) Female 77 (57) PHYSICAL EXERCISE Infrequent 38 (29.2) Moderate 10 (7.7) Frequent 82 (63.1) PSYCHOLOGICAL ILLNESSES None 92 (67.6) At least one 39 (28.7) At least two 5 (3.7) SUBJECTIVE SOCIAL CLASS Lower class 18 (15.3) Middle class 95 (80.5) Upper class 5 (4.2) PHYSICAL ILLNESS None 93 (68.4) At least one 36 (26.5) At least two 7 (5.1) CLASS ATTENDANCE Very poor 9 (8.5) Poor 37 (34.9) Good 49 (46.2) Excellent 11 (10.4) SD represents standard deviation 23 This indicates 57.2 ± 15.4, mean and SD 129
  • TABLE 4.1.2(b): UNIVARIATE ANALYSIS OF EXPLANATORY Details Frequency (%) MATERIAL RESOURCES Low availability 10 (7.7) Moderate availability 40 (30.8) High availability 80 (61.5) BREAKFAST Frequently 4 (3.0) Moderately 127 (95.5) Infrequently 2 (1.5) Self-rated SELF CONCEPT Negative 61 (46.6) Positive 70 (53.4) AGE GROUP 16 – 17 YRS 77 (57.0) 18 – 19 YRS 52 (38.5) 20 – 25 YRS 6 (4.4) Average Age 17.7 ± 1.0 (SD) 130
  • Table 4.1.2 (c): UNIVARIATE ANALYSIS OF EXPLANATORY VARIABLE FREQUENCY AND (PERCENT) PAST SUCCESSES IN CXC/GCECOURSE: Principles of Accounts Fail 15 (11.2) Grade 1/A 49 (36.6) Grade 2/B 60 (44.8) Grade 3/C 10 (7.5) English Language Fail 8 (6.1) Grade 1/A 43 (32.8) Grade 2/B 50 (38.2) Grade 3/C 30 (22.9) Mathematics Fail 21 (16.2) Grade 1/A 20 (15.4) Grade 2/B 45 (34.6) Grade 3/C 44 (33.8) From Table 4.2 (a), approximately 94.8 percent of the sample had an academic performance (based on the GCE grade system) above an E while 5.2 percent of the sample had failing scores. Academic performance was further classified into four (4) groups as follows; 1. Distinction (i.e. grades A and B – scores from 70), 2.Credit (i.e. C), 3. Pass (i.e. D and E) and 4. Fail (i.e. scores below 40 per cent). Further, the statistics (data) revealed that 40.0 percent of the respondents indicated that their academic performance (test scores - grades ) in Advanced Level Accounting was better this term in comparison to last term while 28.8 percent said their grades were the same in both terms in comparison to 31.2 percent who said their scores were worse. This 31.2 percent indicates a worrying fact that must be diagnosed with immediacy. In that, a marginal 131
  • number of prospective candidates (i.e.39.5 %) were performing better in comparison to those who were performing worse (31.5%) (See Table 4 above) The information in table 4 showed that 3 percent of students were consuming breakfast on a regular basis while 1.5 percent of the same were having breakfast rarely in comparison to 95.5 percent of them who were having the same sometimes (i.e. moderately). Approximately 57.0 percent of the sample was between the age cohorts of 16 to 17 years, while 38.5 percent were between 17 to 19 years in comparison to 4.4 percent above 20 years. Of the sample of Advanced level Accounting students, some 61.5 percent of them had a high availability of instructional resources; some 7.7 percent had little availability to material resources in comparison to 30.8 percent who had an averaged availability of instructional resources. On to the issue of self-concept, 46.6 percent of the sample of students had a low concept of self, 29.8 percent with a moderate concept and 23.7 percent with a high concept of themselves. This brings me to another issue, 15.3 of the sample of students said they were from the lower class, 80.5 percent of them were from the middle class and 4.2 percent from the upper class (see Table 4.2, above). 132
  • STEPS IN HOW TO ‘RUN’ CROSS TABULATIONS? One of the difficulties faced by undergraduate students is ‘how to “run”, and “interpret” quantitative data. In order that I provide assistance to this issue, I will begin the process by “running” the data in SPSS, followed by the interpretation of cross tabulations. (Steps in running cross tabulations24). STEP TWELVE STEP ELEVEN Analyze the output STEP ONE select paste or ok Assume bivariate STEP TEN STEP TWO in percentage, select – row, Select Analyze column and total STEP NINE STEP THREE HOW TO select cells Select RUN CROSS TABULATIONS, descriptive in SPSS? statistics STEP EIGHT STEP FOUR choose chi-Square, contingency select crosstabs coefficient and Phi STEP FIVE STEP SEVEN STEP SIX in row place select statistics either DV or IV in column vice versa to Step 5 24 I am aware that some students may require assistance not only in analyzing cross tabulations, but how to ‘run’ the SPSS program. Hence, I have answered your request in this monograph. (See Appendix VI) 133
  • HOW TO ‘ANALYSE’ CROSS TABULATIONS – when there is no statistical relationship? Table 4.1.3: Bivariate relationships between academic performance and subjective social class (in %), N=99 Subjective Social Class Lower Middle Upper Academic Performance Distinction 40.0 37.0 33.3 Credit 6.7 21.0 0.0 Pass 46.6 37.0 66.7 Fail 6.7 5.0 0.0 Total 15 81 3 χ 2 (4)= 3.147, ρ value = 0.790 From Table 4.1.3, there is no statistical relationship between subjective social class and academic performance [χ 2 (6)25 = 3.147, p= 0.790 >0.0526] based on the population sampled. The Chi square analysis27 was contrasted with Spearman’s correlation, at the two (2) tailed level; and the latter’s Ρ value = 0.883, again indicating that there was no statistical correlation between subjective social class and academic performance based on the population sampled. Statistically this could be a Type II error (see Appendix II). (Note – The analysis does not go beyond what is written, if there is not relationship). Table 4.1.4: Bivariate relationships between comparative academic performance and subjective social class (in %), N=108 25 The ‘6’ is the degree of freedom, df, which is calculated as (number of rows minus 1) times (number of columns minus 1) 26 In this case the level of significance, 5%, is an arbitrary point that the researcher assumes the outcome will be biased, or The probability of rejecting a true null hypothesis; that is, the possibility of make a Type I Error. In this case there is a Type II error (See Appendix II) 27 The social researcher needs to understand that when analyzing Chi Square, one should use the values for the independent variables. If the independent variable is in the column, use the column percentages. However, if the independent variable is in the row, use the row percentage for your analysis. 134
  • Subjective Social Class Lower Middle Upper Comparative Academic Performance Better 31.3 41.4 20.0 Same 37.4 27.6 40.0 Worse 31.3 31.0 40.0 Total 16 87 5 χ 2 (4) = 1.597, ρ value = 0.809 The results (in Table 4.1.4) indicate that there is no statistical relationship [χ 2(4) = 1.597, ρ value 0.809 >0.05] between subjective social class and past and-or present academic performance of the sampled population over the Christmas term in comparison to the Easter term. Even when Spearman’s correlation, at the two-tailed level, was used the P= 0.999 indicating that there was no statistical correlation between the two variables based on the population sampled. 135
  • HOW TO ‘ANALYSE’ CROSS TABULATIONS – when there is no statistical relationship? TABLE 4.1.5: BIVARIATE RELATIONSHIPS BETWEEN ACADEMIC PERFORMANCE AND PHYSICAL EXERCISE (in %), N= 111 Physical Exercise Infrequently Moderately Frequently Academic Performance Distinction 39.4 12.5 41.4 Credit 27.3 12.5 14.3 Pass 33.3 62.5 38.6 Fail 0.0 12.5 5.7 Total 33 8 70 χ 2 (6) = 8.066, ρ value = 0.233 The results (in Table 4.1.5) indicated that there was no statistical relationship between physical exercise and academic performance [χ2 (6) = 8.66, ρ value = 0.233 > 0.05] based on the population sampled. NOTE: Whenever there is no statistical association (or correlation) between variables, the researcher cannot examine the figure for difference as there is no statistical difference between or among the values. 136
  • HOW TO ‘ANALYSE’ CROSS TABULATIONS – when there is a statistical relationship? Table 4.1.6 (i): Bivariate relationships between academic performance and instructional materials (in %), N=113 Instructional Materials Infrequently Moderately Frequently Academic Performance Distinction 20.0 26.4 45.9 Credit 0.0 11.8 21.6 Pass 40.0 61.8 28.4 Fail 40.0 0.0 4.1 Total 5 34 74 χ 2 (6) = 27.455 28 , ρ value = 0.00129 Based on Table 4.1.6(i), the results indicated that there was a statistical relationship between material resources (i.e. instructional materials) and academic performance [χ 2 (2) = 27.455, ρ value = 0.001 <0.05] based on the population sampled. The strength of the relationship is moderate (cc = .44230 or 44.2 % - See Appendix) and this indicated, there is a positive relationship between resources and better academic performance. Based on the coefficient of determination, instructional resources explain approximately 28 This is the Chi Square value (27.455), which is found in the Chi Square Test 29 This figure, 0.0000 (which should be written as 0.001), is found in the Symmetric Measures Table (it is the Approx sig.) – (see for example Corston and Colman 2000, 37) 30 Correlations coefficients, cc, or phi, ф, indicates (1) magnitude of relationship, (2) direction of the association, sign , and (3) strength. 137
  • 20 percent of the proportion of variation in academic performance of the population sampled. Of the students who had indicated infrequent use of instructional materials, 20.0 percent received distinction compared to 26.4 percent of those with moderate use of material resources and 45.9 percent of those with a high availability of instructional materials. Forty percent of those who indicated low (ie infrequent use) of material resources failed their last test compared to 0.0 percent of those who indicated moderate use of instructional materials and 4.1 percent of those who frequent use material resources. 138
  • Table 4.1.6 (ii) Relationship between academic performance and materials resource among students who will be writing the A’ Level Accounting examination By Gender (in %), 2004, N=103 Instructional Resources Instructional Resources Low Moderate High Low Moderate High Male31 Female32 Distinction 0.0 14.3 59.3 50.0 35.0 38.3 Academic performance: Credit 0.0 0.0 22.2 0.0 20.0 21.3 Pass 66.7 85.7 14.8 0.0 45.0 36.2 Fail 33.3 0.0 3.7 50.0 0.0 4.3 Total 3 14 27 2 20 37 From Table 4.1.6 (ii) above, the results indicated that there was a statistical significant relationship between availability of resource materials and academic performance of males and not for females based on the population sampled. The relationship between instructional resources and academic performance was only explained by the male gender. The strength of the relationship was strong (cc = 0.62), meaning that males performance is positively related to the availability of instructional resources. Based on the coefficient of determination, 38.6 percent the proportion of variation of the academic performance among males was explained by material resources based on the population sampled. 31 χ2 (1) = 27.65, ρ value = 0.001, n= 44 32 χ2 (1) = 12.076, ρ value = 0.060, n= 59 139
  • Approximately 59 percent of males who had a high availability of resource materials obtained distinction compared 14 percent of them had moderate number of resource materials and zero percent had low availability of materials. Twenty two percent of those who had a high availability of instructional materials at their disposal received credit on their last Accounting test; zero percent had low and moderate availability of instructional resources. Approximately 15 percent of those who had a high availability of resource materials passed their last test; 86 percent of them had moderate number of instructional materials in comparison to 67 percent with a low availability of materials. Furthermore, the data revealed that 3.7 percent of those who had a high availability of instructional materials failed their last Accounting test in comparison to 33.3 percent and 0.0 with low and moderate availability of materials respectively. 140
  • Table 4.1.7: Bivariate relationships between academic performance and class attendance (in %), N= 90 Class Attendance Very poor Poor Good Excellent Academic Performance Distinction 33.3 31.0 37.0 60.0 Credit 0.0 24.1 19.5 10.0 Pass 50.0 41.4 37.0 30.0 Fail 16.7 3.5 6.5 0.0 Total 6 29 46 10 χ 2 (6) =6.423, ρ value = 0.697 The results (in Table 4.17) indicate that there was no statistical relationship between class attendance and academic performance (χ 2(9) = 6.423, ρ value = 0.697 >0.05) of the population sampled. The researcher further investigated this phenomenon and found that there is a statistical correlation (using Spearman’s correlation) between comparative academic performance (i.e. students’ performance this term - Easter in comparison to last term – Christmas) and class attendance (P=0.047). With this finding, the researcher used Chi-Square Analysis and it showed that there was no statistical correlation between the two (2) previously mentioned variables based on the population sampled (see Table 4.1.9 (b) overleaf). 141
  • Table 4.1.9: Bivariate relationships between academic performance By Breakfast consumption (in %), N=114 Breakfast consumption Frequently Moderate None Academic Performance Distinction 0.0 39.8 0.0 Credit 75.0 15.7 0.0 Pass 25.0 38.9 100 Fail 0.0 5.6 0.0 Total 4 108 2 χ 2 (6) =12.878, ρ value = 0.045 Based on Table 4.1.9 above, the results indicate that there is a positive relationship between breakfast consumption and academic performance (χ 2(6) = 12.878, ρ value 0.045 <0.05). The results indicated that there is a statistical significant relationship between the two variables previously mentioned based on the population sampled. Being an in increase of breakfast will see an increase in ones academic performance. It should be noted that the strength of the relationship is weak (cc = 0.319). Nevertheless, 10.18 percent of the proportion of variation in academic performance was explained by consuming breakfast (the coefficient of determination). Approximately 40 percent of those who had breakfast received distinction on their last Accounting test in comparison to zero in the category of frequently and none. Seventy five percent of those who frequently had breakfast got credit on the last Accounting test in comparison to 16 percent who had the same on a moderate basis, and ) 142
  • percent who had none. On the other hand, 25.0 percent of those who did not consume breakfast on a regular passed the last Accounting test in comparison to 38.9 percent who had the same on a moderate basis and 100 percent of them saying no breakfast whatsoever. In regards to breakfast consumption, 5.6 percent of those who had breakfast on a moderate basis failed their last Accounting test compared to 0 percent who had none and 0 percent had it on a frequent basis Table 4.1.10: Relationship between academic performances and breakfasts consumption among A’ Level Accounting students, controlling for gender, N=103 Breakfast consumption Breakfast consumption Freq Moderate None Freq Moderate None Male33 Female34 Distinction 0.0 39.5 0.0 0.0 40.0 0.0 Academic performance: Credit 100.0 11.6 0.0 66.7 18.5 0.0 Pass 0.0 44.2 100.0 33.3 35.4 100.0 Fail 0.0 4.7 0.0 0.0 6.1 0.0 Total 1 43 1 3 65 1 The results (in Table 4.1.10) indicate that there is no statistical relationship between academic performance and eating breakfast when controlled for gender (χ 2(6) =7.884 and 6.478 for males and females respectively with Ρ value s >0.05. Therefore, gender does not explain the statistical relationship between eating breakfast and academic performance. 33 χ2 (1) = 27.65, ρ value = 0.24, n= 45 34 χ2 (1) = 6.478, ρ value = 0.37, n= 69 143
  • Table 4.1.11: Bivariate relationships between academic performance By Migraine (in %), N=116 Migraine (i.e. Health condition) No Yes Academic Performance Distinction 38.2 37.0 Credit 15.7 22.2 Pass 40.5 37.0 Fail 5.6 3.8 Total 89 27 χ 2 (6) =0.721, ρ value = 0.868 Based on Table 4.1.11 above, the results indicate that there is no statistical relationship between migraine and academic performance (χ 2(2) = 0.898, p>0.05) of the population sampled. 144
  • Table 4.1.12: Bivariate relationships between academic performance and Self- reported mental illnesses, N=113 Self-reported Mental Illness None One At least two Academic Performance Distinction 40.5 24.2 100.0 Credit 15.2 24.2 0.0 Pass 38.0 48.6 0.0 Fail 6.3 3.0 0.0 Total 79 33 4 χ 2 (6) =10.647, ρ value = 0.100 Based on Table 4.1.12 above, the results indicate that there is no statistical relationship between the experienced mental illnesses and academic performance (χ 2(6) = 10.647, ρ value >0.05). Even when Spearman’s rho35 correlation, at the two-tailed level, was used the P (value) = 0.967 that indicates no statistical correlation between the variables of the population sampled. 35 The rho in Spearman is interpreted similar to that of the r in the Pearson’s Product-Moment Correlation Coefficient (See for example Downie and Heath 1970, 123) 145
  • Table 4.1.13: Bivariate relationships between academic performance and physical illnesses, (n=116) Physical Illness None One At least two Academic Performance Distinction 38.7 34.5 42.8 Credit 17.5 17.2 14.4 Pass 37.5 44.8 42.8 Fail 6.3 3.5 0.0 Total 80 29 7 χ 2 (6) =1.204, ρ value = 0.977 Based on Table 4.1.13 above, the results indicate that there is no statistical relationship between academic performance and physical illnesses (χ 2(6) = 1.204, p>0.05) based on the population sampled. Even when Spearman’s correlation, at the two-tailed level, was used the P (value) = 0.912 that indicates no statistical correlation between the variables based on the population sampled. 146
  • Table 4.1.14: Bivariate relationships between academic performance and general illness (n=116) General Illness None At least One Academic Performance Distinction 38.7 36.1 Credit 17.5 16.7 Pass 37.5 44.4 Fail 6.3 2.8 Total 80 36 χ 2 (6) = 0.936, ρ value = 0.817 Based on Table 4.1.14 above, the results indicate that there is no statistical relationship between physical illnesses and academic performance (χ 2(3) = 0.936, p>0.05) of this population sampled. 147
  • Table 4.1.15. Bivariate relationships between current academic performance and past performance in CXC/GCE English language examination, (n= 112) Past performance in CXC English language GRADE 1/A GRADE 2/B GRADE 3/C FAIL Academic Performance Distinction 37.1 40.9 36.0 50.0 Credit 22.8 11.4 16.0 25.0 Pass 28.6 45.4 44.0 25.0 Fail 11.4 2.3 4.0 0.0 Total 35 44 25 8 χ 2 (6) = 7.955, ρ value = 0.539 Based on Table 4.1.15, the results indicate that there is no relationship between past performance in English Language at the Caribbean Examination Council (CXC) or the Ordinary Level and academic performance at the Advanced level (in Accounting) (χ 2(9) = 7.955, p>0.05). This result continued even when Spearman’s correlation, at the two- tailed level, was used with a P (value) = 0.581 indicating no statistical correlation between past success in English Language at the Ordinary Level or the General Proficiency level (i.e. CXC) and academic performance in Advanced Level Accounting. 148
  • Table 4.1.16: Bivariate relationships between academic performance and past performance in CXC/GCE English language examination, controlling for gender Gender Value df Asymp. Sig. (2-sided) MALE Pearson Chi- Square 10.752(a) 9 .293 Likelihood Ratio 11.092 9 .269 Linear-by-Linear .812 1 .367 Association N of Valid Cases 43 FEMALE Pearson Chi- 3.258(b) 9 .953 Square Likelihood Ratio 3.353 9 .949 Linear-by-Linear .002 1 .969 Association N of Valid Cases 69 P (value) > 0.05 for both gender Table 4.1.16 shows clearly that the academic performance of A’ Level candidates are not statistical related by past performance in CXC/GCEEnglish language. As irrespective of the gender of the population sampled the Ρ value was greater than 0.05 (i.e. 0.293 and 0.953 for males and females respectively). 149
  • Table 4.1.17: Bivariate relationships between academic performance and past performance in CXC/GCE Mathematics examination n= 101 Past Performance in CXC/GCE Mathematics Poor Moderate Good Excellent Academic Performance Distinction 31.58 55.56 44.74 38.46 Credit 26.32 16.67 10.53 26.92 Pass 36.84 27.78 36.84 26.92 Fail 5.26 0.00 7.89 7.69 Total 19 18 38 26 χ 2 (9) = 7.745, ρ value = 0.560 Based on Table 4.1.17, the results indicate that there is no statistical relationship between past performance in CXC/GCE Mathematics examination and today’s academic performance in Advanced level Accounting (χ 2(9) = 7.745, p>0.05). Even when Spearman’s correlation, at the two-tailed level, was used the P (value) = 0.196 which represents no correlation between the two variable of the population sampled. 150
  • Table 4.1.18 (i): Bivariate relationships between academic performance and past performance in CXC/GCE principles of accounts examination (n= 114) Past Performance in CXC/GCE Mathematics Poor Moderate Good Excellent Academic Performance Distinction 30.0 52.1 26.5 28.6 Credit 20.0 22.9 12.2 14.3 Pass 40.0 20.8 59.2 42.9 Fail 10.0 4.2 2.0 14.3 Total 10 48 49 7 χ 2 (9) = 17.968, ρ value = 0.036 Based on Table 4.1.18 (i), the results indicated that there was a statistical relationship between past performance in Principles of Accounts (POA) at the CXC/GCE level and present academic performance at the A’Level (χ 2(9) = 17.968, p<0.05). The results indicated that better a grade in POA at the Ordinary level is directly related to better performance in A’Level Accounting based on the population sampled. The strength of the relationship is moderate (cc = .4). Approximately 14 percent of the proportion of variation in academic performance is explained by passed performance in POA at the Ordinary level coefficient of determination). Based on Table 4.1.18, of the self-reported past performance in CXC/GCE Mathematics, of those who indicated a moderate grade, 52.1% of them claimed that they have been receiving distinction in A’Level Accounting (ie class work) compared to 30% who had received a poor grade in CXC/GCE Mathematics, 26.5% of good CXC/GCE 151
  • grade in Mathematics and 28.6% who mentioned an excellent grade in Mathematics. Only 10.0% of those who claimed a poor grade in CXC/GCE Mathematics were failing A’Level Accounting class work compared to 4.2% of those with moderate, 2.0% with good and 14.3% of an excellent Mathematics score from CXC/GCE Mathematics. Embedded in this finding is the contribution of some mathematical skills in good performance in A’Level Accounting. Excellent mathematical skills are not need to score distinctions in A’Level Accounting, but it aids in current performance on A’Level Accounting. 152
  • Table 4.1.20: Bivariate relationships between academic performance and self- concept (n= 112) Self-reported Self-concept Low Moderate High Academic Performance Distinction 37.5 46.7 34.6 Credit 23.2 16.7 7.7 Pass 33.9 36.7 50.0 Fail 5.4 0.0 7.7 Total 56 30 16 χ 2 (9) = 6.307, ρ value = 0.390 Based on Table 4.1.20 above, the results indicate that there is no statistical relationship between the self-concept of the A’ Level students and their academic performance (χ 2(6) = 6.307, p>0.05) of the population sampled. Spearman’s correlation, at the two-tailed level, concurred [P (value) was 0.541] with the Chi-Squared results above that there was no statistical correlation between ones concept of self and academic performance. Furthermore, even when the researcher looked at self-concept as being positive or negative, there was no statistical significance between it and academic performance [χ 2 (2) = 2.672, P (value)>0.05] of the population sampled. 153
  • Table 4.1.21: Bivariate relationships between academic performance and dietary requirements (n=116) Dietary Requirements Poor Moderate Good Excellent Academic Performance Distinction 35.8 39.7 NA NA Credit 17.0 7.5 NA NA Pass 41.5 38.1 NA NA Fail 5.7 4.8 NA NA Total 53 63 0 0 χ 2 (9) = 0.245, ρ value = 0.970 From Table 4.1.21 above, the results indicate that there was no statistical relationship between dietary requirements and students’ academic performance (χ 2(9) = 0.245, p>0.05) of the population sampled. 154
  • TABLE 4.1.22: SUMMARY OF TABLES VARIABLES – Sampled population (χ 2(2) ) Rejected Null Hypotheses: ACADEMIC PERFORMANCE and MATERIAL RESOURCES 114 (0.001) ACADEMIC PERFORMANCE and BREAKFAST 114 (0.045) ACADEMIC PERFORMANCE and PAST SUCCESS IN CXC/GCEPOA 114 (0.036) COMPARATIVE ACADEMIC PERFORMANCE and INSTRUCTIONAL RESOURCES 103 (0.054) Fail to Reject Null hypotheses: ACADEMIC PERFORMANCE and dietary requirements 116 (0.970) ACADEMIC PERFORMANCE and Self concept 112 (0.390) ACADEMIC PERFORMANCE and Mathematics 112 (0.560) ACADEMIC PERFORMANCE and English Language 112 (0.539) ACADEMIC PERFORMANCE and Physical Illness 116 (0.817) ACADEMIC PERFORMANCE and Mental Illness 116 (0.603) ACADEMIC PERFORMANCE and Migraine 116 (0.868) ACADEMIC PERFORMANCE and Class Attendance 106 (0.697) ACADEMIC PERFORMANCE and Physical Exercise 110 (0.233) ACADEMIC PERFORMANCE and Subjective Social Class 108 (0.790) COMPARATIVE ACADEMIC PERFORMANCE and Subjective Social Class 99 (0.790) 155
  • CHAPTER 5 HYPOTHESIS 2: General hypothesis There is a relationship between religiosity, academic performance, age and marijuana smoking of Post-primary schools students and does this relationship varies based on gender. TABLE 5.1.1: FREQUENCY AND PERCENT DISTRIBUTIONS OF EXPLANATORY MODEL VARIABLES VARIABLE FREQUENCY AND PERCENT MARIJUANA SMOKING Non-Usage 7,356 (92.5%) Usage 593 (7.5%) RELIGIOSITY Low 351 (4.4%) Moderate 1,365 (78.3%) High 6,197 (78.3%) AGE Less Than & Equal 15 Years 4,452 (55.7%) Greater Than & Equal 16 Years 3,543 (44.3%) ACADEMIC PERFORMANCE Below Average 645 (8.2%) Average 690 (8.8%) Above Average 6,510 (83.0%) GENDER Male 3,558 (44.5%) Female 4,437 (55.5%) 156
  • The sample consisted of 7,996 post-primary school Jamaican students. Approximately 7.5 percent (N= 593) of the sample was marijuana smokers compared with 92.5 percent (N= 7,356) who were not. From Table 3 (above), 78.3 percent (N= 6,197) of the sample was highly religious individuals compared with 4.4 percent (N= 351) were of low religiosity and 17.3 percent (N=1,365) of moderate religiosity. Furthermore, the findings revealed that approximately 55.7 percent (N= 4,452) of the sample was below or equal to 15 years of age while 44.3 percent (N= 3,543) were above or equal to 16 years of age. Of the sample of post-primary school students, some 83.0 percent (N= 6,510) of them got grades beyond 70 percent compared with 8.2 percent (N=645) whose grades were below 50 percent while 8.8 percent (N= 690) got average grades. The grades were compiled from data between June and September 1996. In addition, males constituted approximately 45 percent (N= 3,558) of the sample compared with 55 percent (N= 4,437) females (See Table 5.1.1). BIVARIATE RELATIONSHIPS Table 5.1.2: RELATIONSHIP BETWEEN RELIGIOSITY AND MARIJUANA SMOKING (N=7,869) RELIGIOSITY MARIJUANA Number and Percent Number and Percent Number and Percent Low Moderate High SMOKING Non-Usage 294 (84.2%) 1,213(89.2%) 5,780(93.8%) Usage 55 (15.8%) 147(10.8%) 380(6.2%) χ2= 72.313, Ρ value <0.05 Based on the Table 5.1.2, the results indicated that there is a relationship between religiosity and marijuana smoking (χ2(2) = 72.313, p<0.05). From the findings there was a significant relationship between the two variables previously mentioned. 157
  • Approximately 84 percent (N= 294) of respondents who were of low religiosity were non-smokers compared with 89 percent (N= 1,213) of moderate religiosity and 94 percent (N= 5,780) had high religiosity. Also, approximately 6 percent (N=380) of respondents who indicated high religiosity were marijuana smokers compared to 11 percent (N=147) with moderate religiosity while 16 percent (N=55) who had low religiosity. From the findings, students of low religiosity have a higher probability of smoking “weed” in comparison to high believer cohort. The strength of the relationship is very weak (Phi = 0.09542); although, 0.645 percent (i.e. coefficient of determination) of the proportion of variation in marijuana smoking was explained by religiosity. 158
  • Table 5.1.3: RELATIONSHIP BETWEEN RELIGIOSITY AND MARIJUANA SMOKING CONTROLLED FOR GENDER RELIGIOSITY Number and Number and Number and MARIJUANA Percent Percent Percent SMOKING Low Moderate High Non-Usage Male 152(78.4%) Male 673(84.7%) Male 2,231(90.1%) Female 142(91.6%) Female 540(95.6%) Female 3,549 (96.3%) Usage Male 42(21.6%) Male 122(15.3%) Male 244(9.9%) Female 13(8.4%) Female 25(4.4%) Female 136(3.7%) Table 5.1.3 results indicated that there was a statistical significant relationship between religiosity and marijuana smoking irrespective of the sampled gender. From the findings, the data for the males revealed a χ2(2) = 36.708 with a Ρ value of 0.001 compared with χ2(2) = 9.032 with a Ρ value of 0.0109 for the females. Furthermore, 21.6 percent (N=42) of males who smoked ganja either no religiosity or a low religiosity compared with 8.4 percent (N=13) for the females. Of the smokers who had a high belief religion, 9.9 percent were males compared with only 3.7 percent who were females. With regard to the non-smokers, of those who have a high religiosity 90.1 percent (N= 2,231) were males compared with 96.3 percent (N=3,549) who were females. Of the non-smokers with a low religiosity, there were significantly more females (91.6 %) compared with males (78.4%). Even though there was a statistical relationship between 159
  • religiosity and marijuana smoking and that gender did not alter this association, the strength of the relationship for male is very weak (cc = 0.1024) and this was equally so for females (cc = 0.04524). The relationship between the stated variables was even weaker for females (4.4%) compared with that of males (10.24%) with a coefficient of determination (i.e. this explains the proportion of variation of the smoking marijuana due to religiosity) of 0.8876 percent for males and 0.0901 for females. The interpretation here is, 8.876 percent of the variation in “weed” smoking is explained by maleness compared with 9.01 which is explained by femaleness. 160
  • Table 5.1.4: RELATIONSHIP BETWEEN AGE AND MARIJUANA SMOKING (N=7,948) AGE OF RESPONDENTS Number and Percent Number and Percent ≤ 15 years ≥ 16 years MARIJUANA SMOKING Non-Usage 4,143(93.6%) 3,213(91.3%) Usage 285(6.4%) 307(8.7%) Ρ value < 0.05 The results indicated that there is a relationship between the age of the sampled respondents and marijuana smoking (χ2(2) = 14.8567, Ρ value = 0.001). Based on Table 5.1.4, the findings indicated that there is a significant relationship between the two variables previously mentioned but the strength of this relationship is very weak (Phi = 0.04323). Approximately 94 percent (N= 4,143) of respondents who were less than or equal to 15 years old were non-smokers compared with 91 percent (N=3,213) of those 16 years and older. On the other hand, approximately 6 percent (N=285) of respondents 15 years and less were smokers in comparison to 9 percent (N=307) 16 years and older. From Table 6, 0.19 percent of the proportion of variation in marijuana smoking was explained by the age of the sampled population (i.e. coefficient of determination). Table 5.1.5: RELATIONSHIP BETWEEN MARIJUANA SMOKING AND AGE OF RESPONDENTS, CONTROLLED FOR SEX 161
  • AGE OF RESPONDENTS Number and Percent Number and Percent Less Than & Equal to 15 Greater Than & Equal 16 MARIJUANA Years Years Ρ value SMOKING s Non-Usage Male 1788 (89.7%) Male 1320(86.2%) 0.001 Female 2355(96.8%) Female 1893(95.2%) 0.009 Usage Male 206 (10.3%) Male 212(13.8%) 0.001 Female 79 (3.2%) Female 95(4.8%) 0.009 From Table 5.1.5, despite the sampled population gender, the results indicated that there was a statistical significant relationship between age of the respondents and ‘weed’ smoking χ2(1) = 14.8567, Ρ value = 0.001 and χ2(1) = 10.19793, Ρ value = 0.001 for males and females respectively). The strength of the relationship with regard to male sample is very weak (Phi = .05378) and even weaker for the female sampled population (Phi = .03922). The findings revealed that 0.2892 percent of the variation in marijuana smoking was due to the males’ age compared with 0.01538 for females (i.e. Coefficient of determination). The findings showed that, 10.3 percent (N=206) of males who were less than and/ or equal to 15 years of age were smokers compared with 3.2 percent (N=79) of females. On the other hand, 13.8 percent (N=212) of respondents 16 years and older were smoked marijuana compared with only 4.8 percent (N=95) were females. Some 89.7 percent (N=1,788) of male respondents less than or equal to 15 years of age were non-smokers compared to 96.8 percent (N=2,355) female respondents. 162
  • Furthermore, 86.2 percent (N=1,320) of male respondents ages 16 years and older were non-smokers compared to 95.2 percent (N=1,893) of females of the same age. Table 5.1.6: RELATIONSHIP BETWEEN ACADEMIC PERFORMANCES AND MARIJUANA SMOKING, (N=7,808) ACADEMIC PERFORMANCE Number and Number and Number and MARIJUANA Percent Percent Percent SMOKING Above Average Average Below Average Non-Usage 643 (93.6%) 6027 556 (86.6%) (93.0%) Usage 44 (6.4%) 452 (7.0%) 86 (13.4%) ρ<0.05 The findings indicated that there was a statistical relationship between academic performance and marijuana smoking (χ2(2) = 36.094, p<0.001), very weak statistical correlation (cc = 0.06783). Based on Table 8, approximately 94 percent (N=643) of those who had an academic performance that was above average were non-smokers compared with 87 percent (N=556) of those with an academic performance of below average and 93% at the average level. Approximately 6 percent (N=44) of respondents who had an academic performance above average were smokers in comparison to 13 percent (N=86) of them with an academic performance below average and 7 percent at the average grade. 163
  • Table 5.1.7: RELATIONSHIP BETWEEN ACADEMIC PERFORMANCES AND MARIJUANA SMOKING, CONTROLLED FOR GENDER ACADEMIC PERFORMANCES MARIJUANA Number and Number and Number and SMOKING Percent Percent Percent Above Average Average Below Average Male 272 (88.3%) Male 2439 (88.9%) Male 328 (82.2%) Non-Usage Female 371(97.9%) Female 3588(96.1%) Female 228 (93.8%) Usage Male 36 (11.7%) Male 305(11.1%) Male 71(17.8%) Female 8(2.1%) Female 147(3.9%) Female 15(6.2%) ρ value < 0.05 Based on the findings, irrespective of the gender of the sampled population, there was a significant statistical relationship between academic performance and marijuana smoking (χ2(2) = 14.80237, ρ value = 0.001 and χ2(2) =6.59627, ρ value = 0.037 for males and females respectively). The strength of the association between the variable for male is very weak (cc = 0.06549) and even weaker for females (cc = 0.03888). From Table 9, 11.7 percent (N=36) of respondents with academic performance that was above average and less than or equal to 15 years of age smoked ganja compared to 2.1 percent of female respondents of the same age. Some 17.8 percent (N=71) of respondents who indicated that their academic performance was below average were males compared to 6.2 percent of female respondents. 164
  • Continuing, there were approximately 6 times more male than female respondents who had an academic performance in excess of average compared to approximately 3 times more male than respondents who obtained less than below average performance. Furthermore, at an average academic performance level, there were approximately 3 times more male than female respondents. 165
  • TABLE 5.1.8: SUMMARY OF TABLES Dependent Variable MARIJUANA SMOKING Independent Variables Non-Usage Usage Religiosity 294 (84.2%)*** 55 (15.8%)*** Low 1213 (89.2)*** 147 (10.8%)*** Moderate 5780 (93.8)*** 380 (6.2)*** High Religiosity (controlled) male low male moderate 152 (78.4%)*** 42 (21.6%)*** male high 673 (84.7%)*** 122 (15.3%)*** female low 2231 (90.1%)*** 244 (9.9%)*** female moderate 142 (91.6%)*** 13 (8.41%)*** female high 540 (95.6%)*** 25 (4.4%)*** 3549 (96.3%)*** 136 (3.7%)*** Academic Performance Above Average 643 (93.6%)*** 44 (6.4%)*** Average 6027 (93.0%)*** 452 (7.0%)*** Below Average 556 (86.6%)*** 86 (13.4%)*** Academic Performance (controlled) male above average male average 272 (88.3%)*** 36 (11.7%)*** male below average 2439(88.9%)*** 305 (11.1%)*** female above average 328 (82.2%)*** 71 (17.8%)*** female average 371 (97.9%)*** 8 (2.1%)*** female below average 3588 (96.1%)*** 147 (3.9%)*** 228 (93.8%)*** 15 (6.2%)*** 166
  • Age 15 and below 4143(93.6%)*** 285 (6.4%)*** 16 and above 3213 (91.3%)*** 307(8.7%)*** Age (controlled) male 15 and below 1788 (89.7%)*** 206 (10.3%)*** male 16 and above 1320 (86.2%)*** 212 (13.8%)*** female 15 and below 2355 (96.8%)*** 79 (3.2%)*** female 16 and above 1893 (95.2%)*** 25 (4.8%)*** Note: *** represents a Ρ value < 0.05 167
  • CHAPTER 6 Hypothesis 3: There is a statistical difference between the pre-Test and the post-Test scores. Analysis of Findings SOCIO-DEMOGRAPHIC INFORMATION 43% 57% male female Figure 6.1.1: Gender Distribution Of the sampled population of 68 students, 57 percent (n = 39) were females compared to 43 percent (n = 29) males; (See Figure 6.1.1, above) with an averaged age of 14 years 10 months (14.87 yrs.) ± 0.420 years, and a minimum age of 14 years and a range of 2 years (See Table 4.1, below). The sample was further categorized into two groupings. Group One (i.e. the Experimental) had 52.9 percent (n = 36) students compared to Group Two with 47.1 percent (n = 32). In respect the class distribution of the sample, 52.9 percent 168
  • (n = 36) were in grade 9 Class One compared to 47.1 percent (n =32) who were in grade 9 Class Two. primary all age preparatory Figure 6.1.2: Typology of previous School Based on Figure 6.1.2 (above), of the 68 students interviewed, 38.2 percent (n= 26) were from primary schools across Jamaica compared to 30.9 percent (n = 21) of all-all schools and 30.9 percent (n = 21) from preparatory schools. Table 6.1.1: Age Profile of Respondent Details Frequency (n = ) Percentage (in years) 14 11 16.2 15 55 80.9 16 2 2.9 Mean age 14.87 years Standard deviation 0.42 yrs. Based on Table 6.1.1 (above), the majority of the sampled population (80.9 %) was 15 year-old, compared to 2.9 percent and 16.2 percent of ages 16 and 14 years respectively. From the preponderance of 15 year olds, in this sample, the findings of this study are primarily based on this age cohort’s responses. 169
  • Table 6.1.2: Examination scores Details Pre-Test I Post-Test II % % Mean 49.22 70.68 Median 47.50 67.50 Mode 56.00 67.00 Standard deviation 16.165 14.801 Skewness 0.004 -0.119 Minimum 21.00 41.00 Maximum 82.00 98.00 In respect to Examination Scores, on Test I, the average score was 49.22 percent ± 16.165 percent (i.e. standard deviation), with a median of 47.5 percent and a minimum score of 21.0 percent and a maximum score of 82.00 percent (See Table 6.1.2), with the most frequent score being 56.0 percent. The Examination Scores of Test II were higher as the average score of 70.68 percent ± 14.801 (i.e. standard deviation), with a median score of 67.5 percent and minimum and maximum score of 41.0 percent and 98.0 percent respectively. The most frequently occurred score was 67.0 percent; with the Test II skewness being negative 0.119 compared to Test I of 0.004 percentage-point. (See Figures 6.1.3 & 6.1.4, below) 170
  • 16 14 12 10 8 6 Frequency 4 Std. Dev = 16.17 2 Mean = 49.2 0 N = 68.00 20.0 30.0 40.0 50.0 60.0 70.0 80.0 25.0 35.0 45.0 55.0 65.0 75.0 Figure 6.1.3: Skewness of Examination I (i.e. Test I) The sampled population Mathematics test scores on Test I showed a marginally positively skewness of 0.004. The standard deviation of 16.17 squared percentage points indicate that generally the students’ scores are relatively dispersed compared to Test II. 14 12 10 8 6 Frequency 4 2 Std. Dev = 14.80 Mean = 70.7 0 N = 68.00 45.0 55.0 65.0 75.0 85.0 95.0 50.0 60.0 70.0 80.0 90.0 100.0 Figure 6.1.4: Skewness of Examination II (i.e. Test II) Based on Figure 6.1.4, the Test I’s scores are marginally skewed with a standard deviation of 14.80 percentage points. Generally, the individual scores are relatively well dispersed. 171
  • BEFORE INTERVENTION Strongly disagree 15% Undecided 32% Disagree 53% Undecided Disagree Strongly disagree Figure 6.1.5: Perception of Ability Of the sampled population (n = 68), in respect to student’s perception of their ability, 32.0 percent (n = 22) indicated that they were undecided about their ability in Mathematics compared to 53 percent (n=36) who said their ability was poor and 15 percent (n = 10) who reported that their ability was very poor. (See, Figure 6.1.5). Generally, students had a low perception of their ability to apply themselves in successfully problem-solving mathematical questions as needed by their teachers. 50 45 40 35 30 25 20 15 10 5 0 strongly agree agree undecided Figure 6.1.6: Self-perception 172
  • Figure 6.1.6 indicated that prior to the Mathematics intervention mechanism, generally, students self-perception was extremely good (strongly agree, approximately 68 %) and good (agree, 29 %) compared to approximately 3 percent (n = 2) who were undecided none who had a low self-perception within the context of Mathematics. 60 50 40 30 20 10 0 strongly agree agree undecided Figure 6.1.7: Perception of Task From Figure 6.1.7, 77.9 percent (n = 53) of the respondents were ‘undecided’ in regard to the ‘perception of task’. On the other hand, some 22.1 percent of the sampled population were cognizant of their task assignment, of which approximately 3 percent (n= 2) reported that knew exactly what are required of them in Mathematics. 173
  • 50 45 40 35 30 25 20 15 10 5 0 agree undecided Disagree Strongly disagree Figure 6.1.8: Perception of Utility Of the sampled population of 68 students, only 1.4 percent (n=1) reported that Mathematics is relevant in their general life compared to 86.7 percent (n=59) who believed that the subject is not relevant to general work and some 12 percent (n=8) who were not sure (‘undecided’). 50 45 40 35 30 25 20 15 10 5 0 strongly agree undecided Disagree Strongly agree disagree Figure 6.1.9: Class environment influence on performance Prior to the introduction of the intervention mechanism, approximately 94 percent (n=64) of the respondents believed that an interactive class environment can influence their performance in the subject compared to 4.4 percent (n=3) who reported that this approach did not make a difference in the learning of Mathematics. 174
  • AFTER INTERVENTION 60 50 40 30 20 10 0 strongly agree agree undecided Disagree Figure 6.1.10: Perception of Ability On completion of the teaching intervention, of the sampled population (n = 68), 76.0 percent (n = 51) indicated that they were undecided about their ability in Mathematics compared to 16.17 percent (n=11) who said their ability was good and 3 percent (n = 2) who reported that their ability was very good, compared to 4.4 percent (n=3) who rated themselves within a poor perspective. (See, Figure 6.1.10). Generally, most of the students change the ratings of themselves from varying degrees of poor to undecided. This perceptual transformation is a gradual change in a higher awareness of their ability to problem-solve mathematical questions. 175
  • 45 40 35 30 25 20 15 10 5 0 agree undecided Disagree Strongly disagree Figure 6.1.11: Self-perception Based on Figure 6.1.11, predominantly (61.8%, n=42) the students disagreed with view that attending Mathematics classes are a waste of time and ‘attending making them nervous’ compared to 1.5 percent who reported that they felt it was a waste of time and that they were nervous before attending Mathematics sessions. 40 35 30 25 20 15 10 5 0 strongly agree agree undecided Figure 6.1.12: Self-perception Approximately 59 percent (n=40) of the students reported that they were very confident in themselves with 38.7 percent (n=27) indicated that they were just confident compared to 1.5 percent (n=1) who reported that they were undecided and none suggested low self- perception after the intervention. (See, Figure 6.1.12) 176
  • 50 45 40 35 30 25 20 15 10 5 0 undecided Disagree Strongly disagree Figure 6.1.13: Perception of Task Generally, (See, Figure 6.1.13), 72.1 percent (n = 49) of the respondents reported that they were unsure of the mathematical task to be performed compared to 20.6 percent (n=14) who indicated that they were ‘undecided’ in regard to the ‘perception of task’. 50 45 40 35 30 25 20 15 10 5 0 agree undecided Disagree Strongly disagree Figure 6.1.14: Perception of Utility Predominantly the students did not see the usefulness of Mathematics to their general environment (86.8 percent, n = 51). Of the 51 respondents who were not able to foresee the uses of Mathematics outside of the actual subject, 16.7 percent (n=11) reported that Mathematics is absolutely irrelevant to their general world compared to 70.6 percent (n=40) who believed that the subject is not relevant, with 10.7 percent (n =7) who were unsure and some 2.9 percent (n=8) who reported a relevance of the subject matter to other areas of their lives (See, Figure 6.1.14). 177
  • 45 40 35 30 25 20 15 10 5 0 strongly agree agree undecided Figure 6.1.15: Class environment influence on performance On completion of the intervention exercise, 94.1 percent (n=64) of the respondents reported that involvement in class and the general integrated class environment influenced their performance in the discipline compared to 5.9 percent (n=4) who were undecided, in comparison to none who reported that the general class environment affected their performance in Mathematics. (See, Figure 6.1.15, above) 178
  • CROSS-TABULATIONS Table 6.1.3(a): Class distribution by gender GENDER Total Male Female CLASS 9(1) 16 (55.2%) 20 (51.3%) 36 (52.9%) 9(2) 13 (44.8%) 19(48.7%) 32 (47.1%) Total 29 39 68 Of 68 students of this sample, 57.4 percent (n=39) were females compared to 42.6 percent (n=29) males. Of the 42.6 percent of the male respondents, 55.2 percent (n=16) were in class one and 44.8 percent (n=13) in class two compared to 51.3 percent (n=20) of females in class one and 48.7 percent (n=19) in class two (See, Table 6.1.3(a)). 179
  • Table 6.1.3(b): Class distribution by age cohorts AGE Total 14 15 16 CLASS Experimental 8 27 1 36 72.7% 49.1% 50.0% 100.0% Controlled 3 28 1 32 27.34% 50.9% 50.0% 100.0% Total 11 55 2 68 Approximately 53 percent (n=36) of the sampled population were in the experimental group in comparison to some 47 percent (n=32) who were within the controlled group. Approximately 81 percent (n=55) of the respondents were 15 years old, of which 50.9 percent (n=28) were in class two (i.e. the controlled group) compared to 49.1 percent who were in class two (i.e. the experimental group). (See, Table 6.1.3(b)). 180
  • Table 6.1.3(c): Pre-test Score by typology of group GROUP TYPE Total experimental group control group RETEST_1 Below 40 % 8 13 21 22.2% 40.6% 30.9% 41 - 59 % 20 10 30 55.6% 31.3% 44.1% 60 - 70 % 4 6 10 11.1% 18.8% 14.7% 71 - 80 % 3 3 6 8.3% 9.4% 8.8% Above 80 % 1 0 1 2.8% .0% 1.5% Total 36 32 68 Table 6.1.3(d): Post-test Score by typology of group GROUP TYPE Total experimental group control group RETEST_2 41 - 59 % 5 16 21 13.9% 50.0% 30.9% 60 - 70 % 8 7 15 22.2% 21.9% 22.1% 71 - 80 % 7 5 12 19.4% 15.6% 17.6% Above 80 % 16 4 20 44.4% 12.5% 29.4% Total 36 32 68 The results reported in Tables 4.1.3 (c) and (d) revealed that prior to the intervention (pre-test – See, Table 6.1.3 c), 30.9 percent (n=30) of the respondents got grades ranging from 0 to less than 40 percent, of which 40.6 percent (n=13) were within the controlled group compared to 22.2 percent (n=8) were in the experimental group. Approximately 2 181
  • percent (n=1) of the sampled population got scores in excess of 80 percent, and the person was from the experimental group. On the other hand, after the student-centred learning approach technique was used by the teacher (post-test scores), none of the students got scores which were lower than 40 percent. (See, Table 6.1.3d). Based on Table 6.1.3(d), 29.4 percent (n=20) of the students got grades higher than 80 %, which represents a 1350 percent increase over Test 1. This was not the only improvement as scores on Test II increased in all categories except scores between 41 and 59 percent (i.e. this was a decline of 100 %). On a point of emphasis, on Test II over Test I, more students within the experimental group was observed excess in scores of 41 to 59%. In addition, after the intervention, 44.4 percent (n=16) of the students within the experimental category (n=36) scores marks higher than 80% compared to only 2.8 percent before the implementation of the intervention strategy by the teacher. 182
  • PAIRED-SAMPLE t TEST: Table 6.1.4: Comparison of Examination I and Examination II Details N Correlation Paired Difference Mean Std. de S.E t Test I 68 0.194 49.22 Test II 68 70.68 -21.46 19.681 2.387 -8.990 Significant (2-tailed) = 0.000 From Table 6.1.3, the paired-sample t test analysis indicates that for the 68 respondents, the mean score on Test II (M = 70.68 %) was significant greater at the ρ value of 0.01 level (note: ρ value = 0.000) than average score on the first test (M= 49.22%). These results also indicate that a positive correlation exist between the two test scores (r = 0.194) representing that those who score high on one of the test tend to score high on the next test. 183
  • INDEPENDENT-SAMPLE t TEST Table 6.1.5: Comparison across the Group by Tests Details N Mean St. Deviation Levine’s Test t-test for Equality of mean Test I: F Sig Sig (2-tailed) Exper group 36 50.31 15.13 2.55 0.115 0.561 Control group 32 48.00 17.42 0.564 Test 2: Exper group 36 76.81 13.48 0.013 0.909 0.000 Control group 32 63.78 13.25 0.000 The independent-sample t test analysis (See, Table 6.1.4) indicates that 36 individuals in the experimental group scored an average of 50.31 percent in the class, the 32 persons within the controlled group had a mean score of 48.0 percent, and the mean difference did not differ significantly at the ρ value of 0.05 (note: ρ value = 0.561). The Levene’s test for Equality of Variance indicates for the experimental and the controlled groups do not differ significantly from each other (note: p=0.115. On the other hand, in respect to typology of groups and second test scores, the mean score for the experimental group was 76.8 percent (n=36) compared to 63.78 percent (n=32) for the controlled group, and that means did differ significantly at the ρ value of 0.05 level (note: p=0.000). The Levene’s test for Equality of Variance indicates for the experimental and the controlled group did not statistical differ (note: ρ value = 0.909). Based on Table 6.1.4, the students who were in the experimental group having been introduced to the student-centred learning approach increased their grade score in Mathematics by approximately 53.0 percent compared to the controlled group whose performance improved by 32.9 percent. 184
  • FACTORS AND THEIR INFLUENCE ON PERFORMANCE Table 6.1.6: Analysis of Factors influence on Test II Scores examssc2 Sum of Squares df Mean Square F Sig. Between Groups 318.025 1 318.025 1.462 .231 Within Groups 14358.857 66 217.558 Total 14676.882 67 Of the sampled population (n=68), for the bivariate analysis of factors on Test II scores, the mean scores between the groups was statistical not significant, ρ value more than 0.05 (note: Ρ value = 0.23136). Based on Table 6.1.6, the factors identified in this study are not statistically explaining variation in performance of students on Test II. Table 6.1.7: Cross-tabulation of Test II scores and Factors Refac_2 Total strongly agree agree retest_2 41 - 59 % 19 (30.2%) 2 (40.0%) 21 (30.9%) 60 - 70 % 12 (19.0%) 3 (60.0%) 15 (22.1%) 71 - 80 % 12 (19.0%) 0 (0.0%) 12 (17.6%) Above 80 % 20 (31.7%) 0 (0.0%) 20 (29.4%) Total 63 5 68 χ2 (3) = 6.207, ρ value = 0.102 Table 4.1.7, further analyses the Test II scores from the perspective that identified factors influences students’ performance and statistically this was not significant (χ 2 (3) = 6.207, 36 The following are reasons why the parameter estimate is not significant – (1) inadequate sample size; (2) type II error, (3) specification error, and (4) restricted variance in the independent variable(s). 185
  • Ρ value = 0.102). Despite the fact that entire sampled population (100%, n=68) either strongly agreed or agreed to the questions on factors, these were not statistically found to contributory factor that influences the change in academic performance. It should be noted that this be a Type II error. In that, the ideal sample size for cross tabulation is in excess of 200 cases with a stipulated minimum of more than 5 responses to a cell, this prerequisite was not the case as the sample size for this study was 68 students. Therefore, the fact that there is not statistical relationship between the examined variables may be as a result of a Type II error (i.e. meaning, statistically indicating that no relationship exist between the factors but in reality a relationship does exists, and the primary reason is due to the relatively small sample size). Table 6.1.8: Bivariate relationship between Student’s Factors and Test II scores Test II Scores Other Total No Yes retest_2 41 - 59 % 15 6 21 29.4% 35.3% 30.9% 60 - 70 % 9 6 15 17.6% 35.3% 22.1% 71 - 80 % 10 2 12 19.6% 11.8% 17.6% Above 80 % 17 3 20 33.3% 17.6% 29.4% Total 51 17 68 χ2 (3) = 3.454, ρ value = 0.327 Students did note that a number of factors contribute to their low academic performance in Mathematics, to which the researcher sought to unearth any merit to this perception. Based on Table 6.1.8, there is not statistical association between the identified factors noted by students and academic performance. (χ2 (3) = 3.454, ρ value = 0.327) Hence, 186
  • collectively, issues such as lighting, resources, and noise and communication barriers were not statistically responsible for improvements in students’ test scores on the second Mathematics examination. Even when the identified factors were disaggregated, none of them was found to contribute to the increased Test II scores (i.e. light: χ2 (3) = 1.298, ρ value = 0.730; communication barriers: χ2 (3) = 2.330, ρvalue = 0.5.07; resources χ2 (3) = 2.126, ρ value = 0.547 and noise: χ2 (3) = 1.169, ρ value = .760). It should be noted that this is a Type II error (See Appendix 2). In that, the ideal sample size for cross tabulation is in excess of 200 cases with a stipulated minimum of more than 5 responses to a cell, this prerequisite was not the case as the sample size for this study was 68 students. Therefore, the fact that there is not statistical relationship between the examined variables may be as a result of a Type II error (i.e. meaning, statistically indicating that no relationship exist between the factors but in reality a relationship does exists, and the primary reason is due to the relatively small sample size). 187
  • CHAPTER 7 Hypothesis 4: General hypothesis – Ho: There is no statistical relationship between expenditure on social programmes (public expenditure on education and health) and levels of development in a country; and H1: There is a statistical association between expenditure on social programmes (i.e. public expenditure on education and health) and levels of development in a country ANALYSES AND INTERPRETATION OF DATA Univariate Analyses Table 7.1.1: Descriptive Statistics - Total Expenditure on Public Health (as percentage of GNP HRD, 1994) TOTAL EXPENDITURE on PUBLIC HEALTH as percentage of GNP (HRD, 1994) Mean 4.6140 Standard deviation 2.1489 Skewness 0.9860 Minimum 0.8000 Maximum 13.3000 From table 7.1.1, the data is trending towards normalcy, as the skewness is 0.9860 and so the distribution is relatively a good statistical measure of the sampled population (see 188
  • figure 1.2 below). A mean of 4.614 shows that approximately 4.614 per cent of the Gross National Production (GNP) is spent on public health ± 2.1489, with a maximum of 13.3% 1990: TOTAL EXPENDITURE ON HEALTH AS PERCENTAGE OF GDP (HDR 1994) 25 20 15 n u q F y c e r 10 5 Mean = 4.614 0 Std. Dev. = 2.1489 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 N = 145 1990: TOTAL EXPENDITURE ON HEALTH AS PERCENTAGE OF GDP (HDR 1994) Figure 7.1.1: Frequency distribution of total expenditure on health as % of GDP 189
  • Table 7.1.2: Descriptive statistics of Expenditure on Public Education (as percentage of GNP, HRD, 1994) PUBLIC EXPENDITURE on PUBLIC EDUCATION as percentage of GNP (HRD, 1994) Mean 4.5340 Standard deviation 1.9058 Skewness 0.1340 Minimum 0.0000 Maximum 10.600 It can be concluded from the data collected and presented in the table above that the data is relatively normally distributed (see Figure 4.2 – skewness is 0.134) and therefore is a good measure of the sample population. The mean amount of public expenditure on public education as a percentage of GNP is 4.534 ± 1.91. This indicates that on an average that approximately of 4.534 per cent of the Gross National Production (GNP) is spent on public education. Figure 4.2: PUBLIC EXPENDITURE ON EDUCATION AS PERCENTAGE OF GNP (HDR 1994) 20 15 10 n u q F y c e r 5 Mean = 4.534 0 Std. Dev. = 1.9058 0.0 2.0 4.0 6.0 8.0 10.0 12.0 N = 115 PUBLIC EXPENDITURE ON EDUCATION AS PERCENTAGE OF GNP (HDR 1994) 190
  • Figure 7.1.2: Frequency distribution of total expenditure on education as % of GNP 191
  • Table 7.1.3: Descriptive statistics of Human Development (proxy for development) HUMAN DEVELOPMENT INDEX Mean 2.0700 Standard deviation 0.7820 Skewness -0.1180 Minimum 1.000 Maximum 3.000 Based on Table 7.1.3 above, the average human development index reads 2.07 ± 0.78, with a negligible skewness of – 0.118. The table shows that the maximum value for human development is 3 with a minimum of 1. 192
  • 1993: HUMAN DEVELOPMENT INDEX IN THREE CATEGORIES: 1 = LOW HUMAN DEVELOPMENT, 2 = MEDIUM HUMAN DEVELOPMENT, 3 = HIGH HUM 100 80 60 n u q F y c e 40 r 20 0 0.5 1 1.5 2 2.5 3 3.5 Mean = 2.07 1993: HUMAN DEVELOPMENT INDEX IN Std. Dev. = 0.782 THREE CATEGORIES: 1 = LOW HUMAN N = 165 DEVELOPMENT, 2 = MEDIUM HUMAN DEVELOPMENT, 3 = HIGH HUM Figure 7.1.3: Frequency distribution of the Human Development Index 193
  • In seeking with the attempt of making this text simple and extensive, I will not only provide an analysis of the generated output from a Pearson statistical test but will illustrate how this should be executed in SPSS. Before we are able to begin the process, let us remind ourselves of the hypothesis: 194
  • H1: There is a statistical association between expenditure on social programmes (i.e. public expenditure on education and health) and levels of development in a country (dependent variable – HDI, which measures levels of development; and independent variables – public expenditure on education, public expenditure on health care). step 1: select analyze Figure 7.1.4: Running SPSS for social expenditure on social programme 195
  • Step 2: Select correlate, then bivariate Figure 7.1.5: Running bivariate correlation for social expenditure on social programme 196
  • This result from step 2 Figure 7.1.6: Running bivariate correlation for social expenditure on social programme 197
  • Step 3: Select the dependent and the independent variables 198
  • Step 4: Select paste then ‘run’ or ok, which then give, Output You would have accomplished a lot from just generating the tables, but the most important aspect is not in the production of the tables but it the analysis of the hypothesis. Hence, I will analyze the results, below. 199
  • 37 PEARSON’S MOMENT CORRELATION: BIVARIATE ANALYSIS Table 7.1.4: Bivariate relationships between dependent and independent variables HUMAN PUBLIC DEVELOPMENT EXPENDITURE INDEX: 0 = 1990: TOTAL ON LOWEST EXPENDITURE EDUCATION HUMAN ON HEALTH AS AS DEVELOPMENT, PERCENTAGE PERCENTAGE 1 = HIGHEST OF GDP (HDR OF GNP (HDR HUMAN 1994) 1994) DEVELOPMENT (HDR, 1997) PUBLIC Pearson 1 .413(**) .435(**) EXPENDITURE Correlation ON EDUCATION Sig. (2- AS . .000 .000 tailed) PERCENTAGE OF GNP (HDR N 115 114 106 1994) HUMAN Pearson .413(**) 1 .395(**) DEVELOPMENT Correlation INDEX: 0 = Sig. (2- LOWEST .000 . .000 tailed) HUMAN DEVELOPMENT, 1 = HIGHEST HUMAN N 114 165 142 DEVELOPMENT (HDR, 1997) 1990: TOTAL Pearson .435(**) .395(**) 1 EXPENDITURE Correlation ON HEALTH AS Sig. (2- PERCENTAGE .000 .000 . tailed) OF GDP (HDR 1994) N 106 142 145 ** Correlation is significant at the 0.01 level (2-tailed). 37 See Appendix IV 200
  • Bivariate relationship between public expenditure on education and human development From Table 7.1.4, the results indicated that there was a statistical relationship between public expenditure on education as a percentage of GNP and levels of human development based on the population sampled. The strength of the relationship is moderate (cc = 0.413 or 41.3 %) and this indicated that there is a positive relationship public expenditure on education as a percentage of GNP and human development. The coefficient of determination indicates that public expenditure on education as a percentage of GNP explains approximately 17.06 percent of the variation in levels of human development of the population sampled. A significant portion of the countries surveyed (82.94%) is not explained in terms of its expenditure on education. Bivariate relationship between total expenditure on health and human development From Table 1.4, the results indicate that there is a statistical relationship between total expenditure on health as a percentage of GDP and levels of human development. The strength of the relationship is moderate which shows that there is a positive relationship total expenditure on health as a percentage of GDP and human development. The coefficient of determination indicates that total expenditure on health as a percentage of GNP explains approximately 15.68 per cent of the proportion of variation in levels of human development of the population sampled. The unexplained variation of 84.32% which indicates that although total expenditure on health explains a particular percent of the variation in development, a significantly larger percent of that variation is not explained by total expenditure on health. 201
  • TABLE 7.1.5: SUMMARY OF HYPOTHESES ANALYSIS VARIABLES COUNT (Ρ value ) Rejected Null Hypotheses (i.e. rejected Ho): TOTAL EXPENDITURE ON HEALTH AND HUMAN DEVELOPMENT 114 (0.001) PUBLIC EXPENDITURE ON HEALTH AND HUMAN DEVELOPMENT 142 (0.001) 202
  • CHAPTER 8 Hypothesis 5: GENERAL HYPOTHESIS: The health care seeking behaviour of Jamaicans is a function of educational level, poverty, union status, illnesses, duration of illnesses, gender, per capita consumption, ownership of health insurance policy, and injuries. [ Health Care Seeking Behaviour = f( educational levels, poverty, union status, illnesses, duration of illnesses, gender, per capita consumption, ownership of health insurance policy, injuries)] DATA INTERPRETATIONS SOCIO-DEMOGRAPHIC INFORMATION Table8.1.1: AGE PROFILE OF RESPONDENTS (N = 16,619) Particulars Years Mean 39.740 Standard deviation 19.052 Skewness 0.717 From table 1 above, the skewness of 0.717 shows that there is a clear indication that the data set is not normal, and so the researcher logged this variable in order to reduce the skewness so that the value will be a relative good statistical measure for the sampled population (n=16,619 respondents). The mean age of the sampled population is 39 years 203
  • and 9 months (39.740 years). Of the population sampled, the minimum age was 15 years and the maximum age was 99 years. The standard deviation (of 19.052) shows a wide spread from the mean of the scatter values of the sampled distribution. Table 8.1.2: LOGGED AGE PROFILE OF RESPONDENTS (N = 16,619) Particulars Years Mean 3.5983 Standard deviation 0.47047 Skewness 0.014 Kurtosis -1.014 From table 8.1.2 above, after the variable was logged (age), the skewness was 0.014 which shows minimal skewness that is a better relative statistical measure for the sampled population (n=16,619 respondents). The sampled population has a mean age of 3 years and 7 months (3.5983 years) with a standard deviation of 0.47047 that shows a narrow spread from the mean of the scatter values of the sampled distribution. Table 8.1.3: HOUSEHOLD SIZE (ALL INDIVIDUALS) OF RESPONDENTS Particular Individuals Mean 4.741 Median 4.000 Standard deviation 2.914 Skewness 1.503 The findings from the sampled population of the Survey of Living Condition (SLC 2002) in table 1 above shows a skewness of 1.503 that is an unambiguous indication that the data set is not close normal and so is not a relative good statistical measure of the measure of central tendency of this population sampled (n=16,619 respondents). Therefore, the researchers use the median, as this is a better measure of central tendency. The median number of individuals within the sampled population is four persons. Of the 204
  • population sampled, the minimum number of individuals with a household was one person and the maximum was 23 people. The standard deviation (of 2.914) shows a relatively close spread from the median of the scatter values of the sampled distribution. Of the sampled population (n=16,619 people beyond and including 15 years), there were 8,078 males (i.e. 48.6 %) and 8,541 females (i.e. 51.4%). Furthermore, 92.1 percent (n=13,339) of the sampled respondents had secondary education and lower [see Table 8.1.] compared with 7.9 percent (n=1142) at the tertiary level. The valid response rate in regards to type of education was 87.1 percent (that is, of the sampled population of sixteen thousand, six hundred and nineteen people). In addition, 14,009 cases were included in the analysis (or 84.3 percent) with 2,610 missing cases (or 15.7 percent). Table 8.1.4: UNION STATUS OF THE SAMPLED POPULATION (N=16,619) Particular Frequency Percent Married 3,907 25.4 Common law 2,608 16.4 Visiting 2,029 12.7 Single 5,638 35.4 None 1,757 11.0 Total 15,939 100.0 Based on the findings of this survey, of the sampled population (n =16,619), the valid response rate to union status was 95 percent. The survey showed that 35.4 percent (n = 5,638) of the sample was single, 25.4 percent (n = 3,907) was married, 16.4 percent (n = 2,608) was in common law union and 11.0 percent (n = 1,757) of the same sample was in no union. Union status was further classified into two (2) main groups; firstly, living together and secondly, not living together. Collectively, 51.9 percent of the respondents (n = 8,272) were not living together and 48.1 percent (n = 7,667) were living together. 205
  • Comparatively, the response rate was 95.9 percent (n = 15,939) to none response rate of 4.1 percent (n = 680). Table 8.1.5: OTHER UNIVARIATE VARIABLES OF THE EXPLANATORY MODEL Particular Frequency Percent Gender Male 8078 48.6 Female 8541 51.4 Dummy educational Level Primary 7294 50.4 Secondary 6045 41.7 Tertiary 1142 7.9 Health Insurance Yes 1919 11.8 No 14292 88.2 Dummy union Status With a partner 8544 53.6 Without a partner 7395 46.4 Poverty Poor 5844 35.2 Middle 6762 40.7 Rich 4013 24.1 From Table 8.1.5, of the sampled population (n=16,619), 51.4 percent (N=8541) were females compared with 48.6 percent (N=8078) males. The findings revealed that were 35.2 percent (5844) poor people compared with 40.7 percent (N=6762) within the middle class with 24.1 percent (N=4013) of the sample in the upper (rich) categorization. With regard to the union status of the sampled group, 53.6 percent (N=8544) had a partner compared with 46.4 percent (7395) who did not have a partner. Furthermore, the educational level of the respondents was 50.4 percent (N=7294) in primary category with 206
  • 41.7 percent (N=6045) in the secondary grouping compared with 7.9 percent (N=1142) in the tertiary categorization. With respect to the issue of availability of health insurance, the findings revealed that 88.2 percent (14,292) of the sampled population did not possess this medium compared with 11.8 percent (1919) that had access. Table 8.1.6: VARIABLES IN THE LOGISTIC EQUATION Particular β S.E Wald df Significant Exp (β) Illnesses 2.336 .075 969.894 1 .000 10.338 Injuries .863 .181 22.655 1 .000 2.370 Poverty 45.938 2 .000 Poverty 1 .127 .056 5.128 1 .024 1.135 Poverty 2 .332 .050 44.601 1 .000 1.394 Per capita .094 .030 10.117 1 .001 1.099 consumption Union status -.169 .040 18.024 1 .000 0.845 Gender .793 .039 418.533 1 .000 2.2210 Health insurance .664 .064 106.383 1 .000 1.942 Age .022 .001 359.375 1 .000 1.022 Levels of .274 .085 10.332 1 .001 1.315 education Constant - 3.024 .319 89.691 1 .000 0.049 Note: If the ρ value ≤ 0.05, then this indicates that the corresponding variable is significantly associated with changes in the baseline odds of not seeking health care. Based on table 8.1.6, illnesses contributes the most (i.e. Exp (β) =10.338) to health seeking behaviour. The relationship between illnesses and health seeking behaviour is significant (Ρ value = 0.000 ≤0.05). Furthermore, positive β values of 2.336 as it relates to illnesses indicate that as people move from no illnesses to illnesses, they will seek more health care. Given that, the logit is positive for illnesses, so we know that being ill increases the odds of seeking health care. The value in table 4 in regards to injuries is not surprising as is inferred from the literature. This variable second ranked (injuries) in contributing to health seeking 207
  • behaviour (i.e. Exp (β) = 2.370) for individuals, ages 15 to 99 years. Furthermore, a positive β value of 0.863 indicates that with the increasing number of injuries, the sampled population sought more health care (or health seeking behaviour increases). With the Ρ value = 0.001 ≤ 0.05, the logit is positive for injuries, and this suggests that being injured increases the odds of seeking health care. As also indicated in table 4, there is a significant relationship between gender and health seeking behaviour (ρ value = 0.000 ≤0.05). Based on the Exp (β) of 2.210, gender is the third largest contributor to the health seeking behaviour. In addition, a positive β value of 0.793 indicates that females sought more health care in comparison to males. Further, a positive logit in relation to gender suggests that being female increases the odds of seeking health care. The findings in table 8.1.6 concur with the literature as it spoke to a positive relationship between possessing health insurance and individual seeking health (ρvalue = 0.000 ≤0.05). Herein, health policy contributes the fourth most to the model of health seeking behaviour (Exp (β) of 1.942). The positive β (of 0.664) suggests that an individual who holds a health policy is more likely to seek health care in contrast to no- health policyholders. In addition, this positive logit of the sampled population infers that having a health insurance increases the odds of seeking health care. The literature review spoke to a direct relationship between moving from lower education to higher education and health seeking behaviour (β of 0.274, ρ value = 0.000 ≤0.05). The positive β reinforced the literature that health seekers are more of a higher educational type. Further, a positive logit in relation to levels of education suggests that being within a higher education type increases the odds of seeking health care. 208
  • In respect to ages of the respondents (15 years ≤ ages ≥99 years), there is a statistical significant relationship between the older one gets and an increase in his/her health seeking behaviour (ρ value = 0.000 ≤0.05). This means that for each additional year that is added to ones life, he/she seeks additional health care. Furthermore, positive logit (based on table 4) suggests that as age increase by each additional year, the odds of seeking health care increases. The information presented in table 4 with regard union status indicates that people who had partner are more likely to seek health care compared with those who do not β (of -0.169) and a ρ value of 0.000 ≤0.05. The reality was that union status contributes the least to the health seeking behaviour (or the model). With a negative logit (from table 4) in regards to union status, this suggests that as union status decrease from living to not living together, the odds of seeking health care decreases. The per capita consumption of the sampled population clearly indicates that a direct significant relationship exists between this variable and dependent variable (health seeking behaviour, ρ value of 0.001 ≤0.05). The Exp (β) of 1.099 values determines that per capita consumption contributes the third least to the model. Furthermore, the positive β indicates that as per capita consumption increases by one additional dollar, health- seeking behaviour increases. Given that, the logit is positive we know that increases in per capita consumption increases the odds of seeking health care. Table 8.1.7: CLASSIFICATION TABLE Predicted Health seeking Percentage behaviour Correct Observed No Yes No 6,452 1.191 84.4 209
  • Yes 3,008 3,358 52.7 Overall percentage 70.0 The literature review perspective was that there were relationships between the dependent and the independent variables, the findings of this survey unanimously support those positions. This means that there were statistical significant relationships between each hypothesis (i.e. ρvalue ≤ 0.05). The variables tested in the model all predict the health seeking behaviour of Jamaicans (of ages 15 to 99 years) but to varied degree (Exp (β). From the model predictor; illnesses, injuries and gender offered the strongest influence. This, therefore, means that people generally tend to seek health care when they are ill or injured and of a particular gender (female). Based on table 5 above, the model correctly predicts 52.7 percent of people in the sample will seek health care. However, the model correctly predicts that 84.4 percent of the will not seek health care. In respect to the overall predictor of the model, 70.0 percent is correctly predicted from the variable chosen of the sample size. The Nagelkerke R square of .284 indicates that, 28.4 percent of the variation in health care seeking behaviour of Jamaicans of ages 15 to 99 years is explained by the nine variables in the model. 210
  • CHAPTER 9 Hypothesis 6: GENERAL HYPOTHESIS There is a negative correlation between access to tertiary level education and poverty controlled for sex, age, area of residence, household size, and educational level of parents (see Appendix III) 211
  • ANALYSES AND INTERPRETATION OF DATA Table 9.1.1: UNIVARIATE ANALYSES Variables Frequency (Percent) Educational Level No formal schooling 118 (0.8) Primary education 6956 (48.1) Secondary education 231 (43.1) Tertiary education 1142 (7.9) Age Mean 40.5 yrs Standard deviation 18.839 Skewness 0.713 Jamaica’s Pop. Quintile Poor 5629 (34.97) Lower Middle Class 3146 (19.5) Upper Middle Class 3400 (21.1) Rich 3957 (24.5) Gender (Sex) Male 7822 (48.5) Female 8310 (51.5) Geographic Locality of Jamaicans Kingston Metropolitan Area (KMA) 3397 (21.1) Other Towns 3046 (18.9) Rural Areas 9689 (61.0) Union Status Married 3906(25.2) Common law 2607 (16.8) Visiting 2017 (13.0) Single 5368(34.6) None 1605 (10.4) Household Size Mean 4.7035 Standard deviation 2.917 Skewness 1.531 Access to Tertiary Education No Access 16422 (89.4) Access 1943 (10.6) Poverty Status Non-poor 10503(65.1) 212
  • Poor 5629 (34.9) 1 The index on access to tertiary level education begins with a of 0.00 to a high of 1.0 Of the sampled population of 16,123 respondents, there are 48.5 percent (n = 7,822) males and 51.5 percent (n = 8310) females. This sample is a derivative of the general sample of 25,007. From table 4(i), above, the incidence of poverty is 34.9 percent (n = 5,629). The findings reveal that 25.2 percent (n = 3906) of the sampled population are married compared to 16.8 percent (n = 2,607) in cohabitant (i.e. common law) relationship, with 13.0 percent (n = 2,017) in visiting unions, compared to 34.6 percent (n = 53) in single relationships, with 10.4 percent (n= 1605) not indicating a union choice. The average number of individuals per household is approximately five (4.7035 ± 2.917) with a standard deviation of approximately three persons. As results in Table 4 (i) indicate, the household size variable has a skewness of 1.5 persons, indicating dispersion away from normality. It is this finding that made the researcher logged the variable in order to remove some degree of the skewness. A preponderance of the sampled population is from the rural zones (i.e. 61.0 percent, n = 9,689) compared to 21.1 percent (n = 3,397) who reside in Kingston Metropolitan Areas, and 18.9 percent from Other Towns. The minimum age for the sampled group is 16 years with an averaged age of 40 years and a standard deviation of 19 years, (40 years 6 months = -18.839). The age variable has a positive skewness of 0.733 to which the researcher logged (natural log) in order to reduce some degree of the variable’s skewness. Despite a preponderance of sample being within the poor categorization (≈35 percent), only 7.9 percent (n=1142) of the sampled population (n=16132) has or is 213
  • pursuing a tertiary level education. In Table 4 (i), the findings reveal that people who have had no formal schooling are less than 1 percent (0.8 percent, n = 118) compared to approximately 48.1 percent (n = 6,956) of people who are pursuing or have not completed primary level education whereas 43.1 percent (n = 6231) are at the secondary level with the formal education system. 214
  • Table 9.1.2: FREQUENCY DISTRIBUTION OF EDUCATIONAL LEVEL BY QUINTILE Jamaica’s Population Quintile Distribution Educational Poor Lower Middle Upper Middle Rich Level Frequency (Percent) No formal 73 (1.4) 12(0.4) 16 (0.5) 17 (0.5) Primary 2,886 (55.9) 1,442(51.3) 1,393 (46.4) 1,235 (35.5) Secondary 2,069 (40.1) 1,248 (44.4) 1,386 (46.2) 1,528 (44.0) Tertiary 135 (2.6) 108 (3.8) 205 (6.8) 694 (20.0) 2 Ρ value = 0.001, χ (9) = 1127.55, Lambda (i.e. λ) = .051 As indicated in Table 9.1.2, there was a statistical relationship between persons within the population quintile and educational level (ρ value = .001 < 0/05, χ2 (9) = 1,127.55). A lambda value of 0.051 indicates that there is a direct relationship between higher levels of educational attainment and affluence. Table 9.1.1 showed that 2.6 percent of the poor has access to tertiary level education compared to 20.0 percent of the rich, and 10.6 percent of the middle class. Approximately 64 percent (64.28 %) less rich person have less than primary school education compared to the poor (see Table 9.1.1, above). In the primary level of education, the poor has more people in this categorization than the other classification (i.e. lower middle/upper middle class and rich). With respect to secondary level educational attainment, the poor have the least number of attendances in the social class stratification (i.e. quintile distribution). 215
  • Table 9.1.3: FREQUENCY DISTRIBUTION OF JAMAICA’S POPULATION BY QUINTILE AND GENDER Gender of Respondents Male Female Pop. Quintile Frequency (%) Frequency (%) Poor 2606 (33.3) 3023 (36.4) Lower Middle Class 1514 (19.4) 1632 (19.6) Upper Middle Class 1643 (21.0) 1757 (21.1) Rich 2059 (26.3) 1898 (22.8) ρ value = 0.001, χ2 (3) = 30.957 When gender is cross tabulated with population quintile, 36.4 percent (n = 3023) of the sampled population who are females are in the poor categorization compared to 33.3 percent males. In the affluence classification, 26.3 percent (n=2059) are males compared to 22.8 (n=1898) being females. From the data (Table 9.1.3), irrespective of a person’s gender, within the middle class groupings, population quintile distribution is the same. This finding reveals that approximately 4 percent more males are richer than females (22.8 %), compared to 3.1 percent more poor females than their male counterparts. It can be safely deduced from the data that poverty is more a female issue (36.4 %) than a male phenomenon (33.3%). 216
  • Table 9.1.4: FREQUENCY DISTRIBUTION OF EDUCATIONAL LEVEL BY QUINTILE Jamaica’s Population Quintile Distribution Union Status Poor Lower Middle Upper Middle Rich Frequency (Percent) Married 1213(22.5) 710 (23.4) 827 (25.3) 1156 (30.4) Common law 972(18.0) 550(18.1) 637 (19.57) 448 (11.8) Visiting 672 (12.4) 358(11.8) 406 (12.4) 581 (15.3) Single 1905 (35.3) 1099 (36.2) 1102(33.7) 1262 (33.2) None 639(11.8) 319 (10.5) 2969(9.1) 351(9.2) 2 Ρ value = 0.001, χ (12) = 187.77 Collectively, 30.4 percent (n=1156) of the sampled population who are affluent (i.e. rich) indicate that they are married compared to 22.5 percent (n=1213) of those who are poor, 23.4 percent (n=710) of those in the lower middle class in comparison to 25.3 percent (n=827) in the upper middle class. Approximately 12 percent (11.8 %) of the rich report that they are in cohabitated relationship compared to 18 percent (n=972) in the poor categorization, and 19.6 percent (n=637) in the upper middle class in contrast to 18.1 percent (n=550) of those in lower middle class. Within the categorization of the single union status, the differences in each quintile are marginal (Table 9.1.4). 217
  • Table 9.1.5: FREQUENCY DISTRIBUTION OF POP. QUINTILE BY HOUSEHOLD SIZE Jamaica’s Population Quintile Distribution Frequency (%) Frequency (%) Frequency (%) Frequency (%) Household size Poor Lower Middle Upper Middle Rich 1 229 (4.11) 149 (4.7) 304 (8.9) 838(21.2) 2 427(7.6) 354(11.3) 507(14.9) 977(24.7) 3 567(10.1) 466(14.8) 614(18.1) 822(20.8) 4 702(12.5) 520(16.5) 631(18.6) 615(15.5) 5 863(15.3) 503(16.0) 499(14.7) 359(9.1) 6 764(13.6) 439(14.0) 311(9.1) 193(4.9) 7 650(11.5) 305(9.7) 260(7.6) 59(1.5) 8 516(9.27) 151(4.8) 133(3.9) 45(1.5) 9 282(5.0) 91(2.9) 36(1.1) 18(0.5) 10 171(3.0) 41(1.3) 44(1.3) 8(0.2) 11 106(1.9) 53(1.7) 26(0.8) 8(0.2) 12 114(2.0) 14(0.4) 9(0.3) 0(0) 13 84(1.5) 9(0.3) 0(0.0) 8(0.2) 14 53(0.9) 7(0.2) 16(0.5) 0(0.0) 15 12(0.2) 17(0.5) 0(0.0) 7(0.2) 16 26(0.50) 8(0.3) 0(0.0) 0(0.0) 17 17(50.0) 0(0.0) 10(0.3) 0(0.0) 18 7(0.1) 8(0.3) 0(00.0) 0(0.0) 19 7(0.1) 11(0.3) 11(0.3) 0(0.0) 21 26(0.5) 0(0.0) 0(0.0) 0(0.0) 23 13(0.2) 0(0.0) 0(0.0) 0(0.0) Ρ value = 0.001, χ2 (60) = 3397.06 The findings in Table 9.1.5 reveal there is a statistical association between population quintile and household size. Even more importantly, 21.2 percent (n=838) of the affluent has a one member household compared to 8.9 percent (n=304) in the upper middle class and 4.7 percent (n=149) of the poor. Comparatively, the rich do not have a 16-member family household or more in comparison to poor, which have household ranging for one- member to 23 members. Collectively the affluent family type has the majority of their household size being between 1 to 4 members compared to the majority of the poor that have household sizes from 4 to 7 members. Table 9.1.6: BIVARIATE ANALYSIS OF ACCESS TO TERTIARY EDU. & POVERTY STATUS Poverty Status Non-poor Poor Access to tertiary education Frequency (%) Frequency (%) 218
  • No Access 8146 (83.3) 5116 (95.3) Access 1631 (16.7) 254 (4.76) ρvalue = 0.001, χ2 (1) = 454.432 The substantive issue of this study is ‘there a relationship between poverty status and access to tertiary level education’ as indicated in Table 8.1.6, there is a statistical association between poverty status and access to tertiary level education. Similarly, 95.3 percent (n=5116) of the poor indicate that they had no access to tertiary level education compared to 8.3 percent (n=8146) of those who are non-poor (i.e. from lower middle class to rich). Some 5 percent (4.76) of the poor reported that they had access to tertiary level education in contrast to 16.7 percent for the non-poor. This finding indicates that a preponderance ( 71.5%) of non-poor had access to tertiary education than the poor. 219
  • Table 9.1.7: BIVARIATE ANALYSIS OF ACCESS TO TERTIARY EDU. & GEOGRAPHIC LOCALITY OF RESIDENTS Access to Geographic Locality of residents tertiary KMA Other Towns Rural Areas education Frequency (%) Frequency (%) Frequency (%) No Access 2348 (76.1) 2446 (85.0) 8468 (92.2) Access 738 (23.9) 430 (15.0) 717 (7.8) 2 Ρ value = 0.001, χ (2) = 570.550 The findings in Table 9.1.7 reveals that 92.2 percent (n=8468) of the residence of rural areas do not have access to tertiary level education compared to 76.1 percent (n=2348) of those who dwell in Kingston Metropolitan Areas and 85.0 percent (n=2446) of those who live in Other Towns. However, 7.8 percent (n=717) of the sampled population who reside in the rural areas have access to tertiary level education followed by 15 percent (n=430) of those who reside in Other Towns have access to post-secondary education compared to 23.9 percent (n=738) of those in Kingston Metropolitan area. 220
  • Table 9.1.8: BIVARIATE ANALYSIS OF GEOGRAPHIC LOCALITY OF RESIDENTS & POVERTY STATUS Poverty Status Non-poor Poor Geographic Locale Frequency (%) Frequency (%) Kingston Metropolitan 2808 (26.7) 589 (17.3) Area(KMA) Other Towns 2139 (20.4) 907 (16.1) Rural Areas 5556 (52.9) 4133 (73.4) Ρ value = 0.001, χ2 (1) = 752.934 According to 73.4 percent (n=1433) of the poor, they live in rural areas in comparison to 52.9 percent (n=5556) of the non-poor. From Table 9.1.8), 17.3 percent of the poor live in Kingston Metropolitan Area compared to 26.7 percent (n=2808) of the non-poor. On the other hand, 20.4 percent (n=2139) of the middle, upper and rich classes live in Other Towns as against the poor. The findings clearly show that poverty is substantially a Rural Area phenomenon as against Other Towns or in urban zones. Statistically, there is a significant association between poverty status and access to tertiary level education (ρvalue = 0.001 < 0.05, χ2 (1) = 752.934). 221
  • Table 9.1.9: BIVARIATE RELATIONSHIP BETWEEN ACCESS TO TERTIARY LEVEL EDUCATION BY GENDER Gender of Respondents Male Female Access to tertiary level ed. Frequency (%) Frequency (%) No Access 6684 (90.2) 6578 (85.1) Access 729 (9.8) 1156(14.9) ρvalue = 0.001, χ2 (1) = 90.812 The findings in Table 9.1.9 reveal that there is a statistical association between gender determining access to post-secondary level education (χ2 (1) = 90.812, ρ value = 0.001<0.05). The sampled population constitutes 90.2 percent (n=6684) males not having access to tertiary level education in comparison to 85.1 percent (n=6578) of females. Using the data in Table 4.7 (ii), approximately 34 percent more females are accessing post-secondary level education than their male counterparts (i.e. 14.9 percent female to 9.8 percent males). 222
  • Table 9.1.10: BIVARIATE RELATIONSHIP BETWEEN ACCESS TO TERTIARY LEVEL EDUCATION BY GENDER CONTROLLED FOR POVERTY STATUS Poverty Status Sex of individual Total male female 0 = Non-poor Access to tertiary 0 = No access Count 4269 3877 8146 education % within Sex of 86.7% 79.9% 83.3% individual 1 = Access Count 657 974 1631 % within Sex of 13.3% 20.1% 16.7% individual Total Count 4926 4851 9777 1 = Poor Access to tertiary 0 = No access Count 2415 2701 5116 education % within Sex of 97.1% 93.7% 95.3% individual 1 = Access Count 72 182 254 % within Sex of 2.9% 6.3% 4.7% individual Total Count 2487 2883 5370 Non-poor: Ρ value = 0.001, χ2 (1) = 79.905; Poor Ρ value = 0.001, χ2 (1) = 34.612 As indicated by Table 9.1.10, gender is a complete explanation for access to post- secondary level education as even when controlled for poverty status, there is still a statistical association (Non-poor: ρ value = 0.001, χ2 (1) = 79.905; Poor Ρ value = 0.001, χ2 (1) = 34.612). According to the data (Table 4.7(iii)) above, 86.7 percent (n=4269) of the males are not able to access post-secondary level education who are with the non- poor categorization compared to 79.9 percent (n=3877) females. In respect to the poor, 97.1 percent (n=2415) are not able to access tertiary level education compared to 93.7 percent. On the contrary, 6.3 percent (n=182) of the females are able to access post- secondary level education despite the social setting of being poor compared to 2.9 percent (n=72) of the males. 223
  • Table 9.1.11: Regression Model Summary Model Model Model Model Model Model Model Model Model Model 1 2 3 4 5 6 7 8 9 10 Dependent variable: Access to Tertiary Level Education Independent: Constant .121 .097 .084 .294 .317 .341 .430 .385 .394 .394 Poverty -.094* -.079* -.077* -.077* -.079* -.076* -.065* -.065* -.065* -.065* Status Dummy .093* .095* .093* .091* .060* .060* .060* .060* .061* KMA Dummy .045* .066* .066* .066* .072* .077* .083* .083* Married Logged -.059* -.060* -.059* -.069* -.056* -.058* -.058* Age Dummy -.038* -.037* -.041* -.043* -.046* -.046* Gender Dummy -.042* -.041* -.041* -.041* -.041* Rural Logged -.033* -.040* -.040* -.040* Household size Dummy .039* .035* .035* child of spouse Dummy -.017* -.016* partner Dummy -.112* helper n 14912 14912 14912 14912 14912 14912 14912 14912 14912 14912 Ρ value .001 .001 .001 .001 .001 .001 .001 .001 .001 .001 R .179 .232 .246 .266 .277 .284 .290 .295 .296 .296 R2 .032 .054 .060 .071 .076 .080 .084 .087 .087 .088 Error term .24577 .24298 .24217 .24083 .24010 .23960 .23915 .23878 .23871 .23867 F statistic 494.98 425.77 319.1 283.84 246.86 217.23 195.00 177.11 158.59 143.31 1 4 6 2 2 4 2 9 ANOVA 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 (sig) Model 1 [ Y= β0 + β1x1 + ei ] - where Y represents Index on Access to Tertiary Education, β0 denotes a constant, ei means error term and β1 indicates the coefficient of poverty x1 represents the variable poverty Model 10 [Y= β0 + β1x1 + …+ βnxn ei] * significant at the two-tailed level of 0.001 224
  • The findings in Table 9.1.11 above reveal that final model (i.e. Model 10) constitutes all the determinants of access to tertiary level education. Model 10 has a Pearson’s Correlation coefficient of 0.296 indicating that the relationship is a weak one. The coefficient of determination, r2, (in Table 9.1.8 from Model 10) is 0.088 representing that a 1 percent change in the determinants of (poverty status, area of residence, union status, age, gender, household size, relationship with head of household) in predictor changes the predictand by 8.8 percent to the sample observation is not a good fit. This means that less that 8.8 percent of the total variation in the Yi is explained by the regression. As shown in Table 9.1.11, Model 10, Testing Ho: β=0, with an α = 0.05, the researcher can conclude that the linear model provides a good fit to the data from a F value of [8.164, 0.057] = 143.319 with a ρ < 0.05. The overall assessment of this causal model climax in Model 10, and so should be disaggregated in order for a comprehensive understand of the phenomenon of poverty and its influence on access to tertiary level education along with other determinants. With all things being constant, access to tertiary level education has a value of 0.394 (i.e. moderate access). From the findings in Table 4.8, poverty status is a negative value of 0.065 indicating that poverty is indirectly related to access to tertiary level education with all other things held constant. On the other hand, there is a direct relationship between person living in the Kingston Metropolitan Area and access to tertiary level education compared to inverse relationship that exists between the rural residents and access to this degree of education. The results in Table 9.1.11 (Model 10) show that inverse association between household size and access to post-secondary level education. This denotes that the larger 225
  • the household size becomes, the less likely that the individuals of that family will access tertiary level education. Hence, household will smaller size means that the people therein are more likely to attend post-secondary education. The data show for the age variable a valuation of -0.058 that this indicates that younger people are more likely to access post- secondary education than older persons. It is found that married people are more likely to access post-secondary education in comparison to people in union status which is single, none, visiting or common-law. In relation to the issue of gender and access to post-secondary level education, a value of negative 0.046 implies that men are less likely to access tertiary level education than their female counterparts. The valuation indicates that women are 0.046 more likely to attend post-secondary education than men. The results in Table 9.1.8 above show helpers are less likely to access post-secondary education in comparison to the child of the spouse. Compared to the child of the spouse concerning access to education, the partner is more likely to acquire a post-secondary level education than the partner. The latter elements are in regard to the question, ‘What is your relationship with the head of the household’? The focus of this text is the provision of materials that make a difference in the analysis of SPSS output, and with this being the aim, one of my responsibility is in assisting with the execution the various SPSS commands, which will generate the necessary output. Hence, I will use an example of some metric variable which are not skewed to produce a regression output. (See Appendix VII) 226
  • CHAPTER 10 Hypothesis 7: There is an association between the introduction of the Inventory Readiness Test and the Performance of Students in Grade 1 ANALYSIS OF FINDINGS Table 10.1.1: Univariate Analysis of Parental Information Description Frequency (Percent) Typology of School: SLB 18 (51.4) KC 17 (48.6) Gender: Male 7 (20) Female 28 ((80) No. of children living at home 0 17 (50) 1 14 (40) 2 2 (5.7) 3 1(7.9) No. of hours spent with child Mean 9.77 hrs Median 2.00 hrs Mode 1.00 hrs Standard deviation 27.0 hrs Of the sampled population (35 respondents), 51.4 percent (n=18) sent their children to SLB compared to 48.6 percent (n=17) who sent them to KC. Approximately eight percent (n=28) were females and 20 percent (n=7) males. Of the total respondents 227
  • interviewed, 50 percent (n=17) reported that they had no children under 6 years old living at home, 40 percent (n=14) had 1 child, 5.7 percent (n=2) two children compared to 7.9 percent (n=1) had 3 children. When asked “how many hours spent with child?” the average hours was approximately 10 ± 27 hours with the most frequent being 1 hour. Table 10.1.2: Descriptive on Parental Involvement Details Frequency (Percent) Educational Involvement Mean 3.77 Median 3.80 Mode 3.6 Standard deviation 0.89 Skewness -0.395 Psychosocial Involvement Mean 3.4 Median 3.4 Mode 3.0 Standard deviation 0.67 Skewness -0.105 From the respondents’ information, they reported that educational involvement was 3.77 (i.e. agree) ± 0.89 with a skewness of -0.395 (i.e. this is negligible negative skewness); psychosocial involvement was 3.4 (i.e. undecided) ± -0.105. 228
  • Table 10.1.3: Univariate Analysis of Teacher’s Information Details Frequency (Percent) Gender: Male 0 (0.0) Female 2 (100) Age 31 to 40 years 1 (50.0) 41 to 50 years 1 (50.0) Educational level Secondary school diploma 1 (50.0) Teacher’s college diploma 1 (50.0) Duration at this school 11 years 1 (50.0) 12 years 1 (50.0) Self-reported Learning Environment Undecided 1 (50.0) Agree 1 (50.0) Of the sampled population (2 teachers), 100 percent (n=2) were females compared to 0 percent males, with 50 percent (n=1) being 31 to 40 years and 50 percent (n=1) 41 to 50 years. The highest level of education was teacher’s college diploma (50%, n=1) followed by secondary school diploma (50%, n=1). The minimum number of years spent at each school is 11 years. When the teachers were asked about the learning environment, 50 percent (n=1) was undecided with 50 percent (n=1) agreeing. 229
  • Table 10.1.4: Univariate Analysis of ECERS-R Profile Details Rating (Averaged score) General (n=35) SLB (n=18) KC (n=18) Space and Furnishings 2.5 2.5 2.38 Personal Care Routines 2.0 1.8 2.17 Language-Reasoning 5.0 5.0 5.25 Activities 4 3.4 4.0 Interaction 5 6.6 5.0 Program Structure 6.0 6.0 6.00 Parents and Staff 5.0 5.17 5.33 From the average score of ECERS-R profile, overall, the space and furnishings in each school was low but this was even lower in KC compared to SLB. With respect to personal care routines offered, generally, it was poor with SLB depicting a lower averaged score than KC. Language reasoning, on the other hand, was high (average of 5 out of 7) with KC showed a marginal higher rating than SLB. Overall, programme structure was received the highest score (6 out of 7) and this was consistent across the two school types. The averaged score received on activities was moderate (4) for KC but weak (3.4) for SLB. On the other hand, interaction in SLB was higher (6.6) compared to KC (5). Parent and staff rating were good in both institutions with KC marginally receiving a better score than SLB. 230
  • Table 10.1.5: Bivariate Analysis of Self-reported Learning Environment and Mastery on Inventory Test Final Report (before Learning Environment grade 1) Final Report (before Pearson Correlation 1 .344 grade 1) Sig. (2-tailed) . .043 N 35 35 Learning Environment Pearson Correlation .344 1 Sig. (2-tailed) .043 . N 35 35 * Correlation is significant at the 0.05 level (2-tailed). From Table 10.1.5, there is a statistical significant relationship between Inventory Test scores of Grade 1 students and their learning environment (ρ value = 0.043 <0.05). The relationship is a weak positive one (Pearson Correlation Coefficient = 0.344 or 34.4 %). This denotes that students’ learning environment explains 34.4 percent of readiness for Grade 1. Statistically, although, this a weak relationship, for any single variable (i.e. learning environment) to explain 34.4 percent of a relationship, the independent variable (learning environment) has a very strong influence on readiness of students. 231
  • Table 10.1.6: Relationship between Educational Involvement, Psychosocial & Environment Involvement and Inventory Test Final Report Educational Psychosocial & (before grade Involvement Environmental 1) Involvement Final Report Pearson 1 .001 .241 (before grade 1) Correlation Sig. (2-tailed) . .995 .162 N 35 35 35 Educational Pearson .001 1 .735 Involvement Correlation Sig. (2-tailed) .995 . .000 N 35 35 35 Psychosocial & Pearson .241 .735 1 Environmental Correlation Involvement Sig. (2-tailed) .162 .000 . N 35 35 35 ** Correlation is significant at the 0.01 level (2-tailed). Of the sampled population (n=35) parents of grade 1 students, no statistical relationship existed between educational (ρ value = 0.995>0.05) psychosocial and environmental involvement (ρ value 0.162>0.05) of parents and students readiness for grade 1. This finding may be due to a Type I error, as the sample size is too small. In that when the sample size was weighted by 6, 10 and so on, a with a new sample size of (i.e. weight 6 = 200, weight 10 = 350), a statistical relationship existed between the independent variable (i.e. educational involvement, psychosocial and environmental involvement) and the dependent variable (i.e. Readiness for grade 1 using the Inventory Readiness Test scores). 232
  • Table 10.1.7: BIVARIATE ANALYSIS OF THE INDEPENDENT VARIABLES AND READINESS FOR GRADE 1 Final Report Personal Language- Activities Interaction Parents and PROGRAM Space and Furniture (before grade Care Reasoning Staff 1) Routines N 35 35 Personal Care Pearson .344 1 Routines Correlation Sig. (2-tailed) .043 N 35 35 35 Language- Pearson .344 1.000 1 Reasoning Correlation Sig. (2-tailed) .043 N 35 35 35 35 Activities Pearson .344 1.000 1.000 1 Correlation Sig. (2-tailed) .043 N 35 35 35 35 35 Interaction Pearson -.344 -1.000 -1.000 -1.000 1 Correlation Sig. (2-tailed) .043 N 35 35 35 35 35 35 35 Parents and Staff Pearson .344 1.000 1.000 1.000 -1.000 1 . Correlation Sig. (2-tailed) .043 .000 N 35 35 35 35 35 35 35 35 PROGRAM Pearson . Correlation Sig. (2-tailed) . N 35 35 35 35 35 35 35 35 Space and Pearson -.344 -1.000 -1.000 -1.000 1.000 -1.000 1 Furniture Correlation Sig. (2-tailed) .043 N 35 35 35 35 35 35 35 35 * Correlation is significant at the 0.05 level (2-tailed). ** Correlation is significant at the 0.01 level (2-tailed). 233
  • From Table 10.1.7, independently each of the following ECERS-R variables (i.e. Parents and Staff, Space and Furnishing, Personal Care Routines, Language-Reasoning, Activities and Interaction) has a statistical (ρ value 0.043 < 0.05) significantly relationship with Readiness of grade 1 pupils. Generally, singly, the weight of each relationship was very strong (i.e. despite Pearson’s Correlation Coefficient value of 0.344). Of the seven ECERS-R profile, programme (i.e. Program) structure is the only one that was not statistically significant, with space and furnishing, and interaction reporting a negative relationship (Pearson’s r = -0.344) and the other with a positive association (Pearson’s Correlation Coefficient = 0.344). A positive association, for example between Parents and staff, and Readiness of Grade 1 pupils, denotes that the greater the parents and staff score the higher the readiness of the child who enters grade 1. On the other hand, a negative score, for example a relationship between interaction and Readiness Test score, a low interaction will produce a high readiness on the Inventory Test. This may be explained by what constitutes interaction, as a low grade was reported for ‘supervision of gross motor activities’ compared to discipline, staff-child interaction, interactions among children and general supervision of children that do not directly influence readiness of a student on an examination. 234
  • Table 10.1.8: School type by Inventory Readiness Score (in %) School Type Total SLB KC Non-mastery 88.9 58.8 74.3 Final Report (before grade 1) Mastery 11.1 41.2 25.7 Total 18 17 35 Χ2 (1) = 4.137, ρ value = 0.049 There is a statistical relationship between type of school attended before grade 1 and score on inventory test (i.e. Χ2 (1) = 4.137, Ρ value = 0.049). Of the 35 students in Grade 1, 88.9 percent of them got non-mastery from SLB compared to 58.8 percent of those who attended KC. Of those who mastery the inventory test (n=9, 25.7%), 41.2 percent attended KC compared to 11.1 percent who attended SLB. Embedded in this finding is the super performance of students who went to KC basic. 235
  • CHAPTER 11 Hypothesis 8: The people who perceived themselves to be in the upper class and middle class are more so than those in the lower (or working) class do strongly believe that acts of incivility are only caused by persons in garrison communities Table 11.1.1: INCIVILITY AND SUBJECTIVE SOCIAL STATUS Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Incivility * Social Status 1728 99.8% 3 .2% 1731 100.0% Column Totals and Totals Incivility * Social Status Crosstabulation Social Status 1=Lower (Working) 2=Middle 3=Upper Class Class Middle Total Incivility 1=Strongly agree Count 296 8 96 400 % within Social Status 37.0% 1.0% 100.0% 23.1% % of Total 17.1% .5% 5.6% 23.1% 2=Agree Count 472 120 0 592 % within Social Status 59.0% 14.4% .0% 34.3% % of Total 27.3% 6.9% .0% 34.3% 3=Disagree Count 32 688 0 720 % within Social Status 4.0% 82.7% .0% 41.7% % of Total 1.9% 39.8% .0% 41.7% 4=Strongly disagree Count 0 8 0 8 % within Social Status .0% 1.0% .0% .5% % of Total .0% .5% .0% .5% 8 Count 0 8 0 8 % within Social Status .0% 1.0% .0% .5% % of Total .0% .5% .0% .5% Total Count 800 832 96 1728 % within Social Status 100.0% 100.0% 100.0% 100.0% % of Total 46.3% 48.1% 5.6% 100.0% 236
  • Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 1425.277a 8 .000 Likelihood Ratio 1629.762 8 .000 Linear-by-Linear 220.288 1 .000 Association N of Valid Cases 1728 a. 6 cells (40.0%) have expected count less than 5. The minimum expected count is .44. Symmetric Measures Value Approx. Sig. Nominal by Nominal Contingency Coefficient .672 .000 N of Valid Cases 1728 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. INTERPRETATION OF INCIVILITY AND SUBJECTIVE SOCIAL STATUS (using the information from Tables 1.1, above) Based on Tables 11.1.1, the results reveal that there is a statistical relationship between‘incivility’ and ‘subjective social class’ (χ2 (8) = 1425.28, Ρ value = 0.001 < 0.05). The findings show that there is a direct association ‘incivility’ and ‘subjective social class’ (i.e. this is based on the positive value of 0.672). The strength of the relationship is moderately strong (cc = 0.672). Approximately 45 % (i.e. cc2 * 100 – 0.672 * 0.672 * 100) of the proportion of variation in ‘incivility’ is explained by an incremental change from one subjective social class to the next (for example, a movement from lower class to middle class or from middle class to upper class). 237
  • Of the respondents who had indicated ‘strongly agree’ (n=400, 23.1%), 37.0% percent of them (n=296) were from the ‘lower class’ while 1.0 % (n=8) were from ‘middle class’ compared to 100 % (n=96) who classified themselves as being in the ‘upper class’. Of those responded ‘Agree’ (n=592, 34.3%), 59.0% (n=472) of them were within the ‘lower class’, 14.4% (n=120) in the ‘middle class’ and 0.0% (n=0) from the ‘upper class’. While of those who ‘disagree[d]’ with ‘incivility’ (41.7%, n=720), 4.0 % (n=32) were ranked in the ‘lower class’, 82.7% (n=688) from the ‘middle class’ and 0% (n=0) within the ‘upper class’. Ergo, we accept the H1 (alternative hypothesis) and by so doing reject the Ho (i.e. the null hypothesis). Let us assume that within the ‘Symmetric measure’ the ‘approximate significant’ (i.e. the Ρ value) was greater than 0.05 (for example 0.256), the analysis would read: The results in Tables 1.1 above, indicate that there is no statistical relationship between the ‘incivility’ and ‘subjective social class’ (χ 2(8) = 0.256, p>0.05) of the population sampled. This implies that perception on ‘incivility’ is not associated (or related) in no statistical way with ones classification of him/herself within the social strata of society. Thus, we reject the H1 (alternative hypothesis) or fail to reject the Ho (i.e. the null hypothesis). (Note briefly – this none relationship must be explained and/or justified using empirical data or the result may argue that this is due to a Type II Error – See Appendix II). Type II Errors occur, when the statistical correlation reveals no relationship but in reality an association does exist. This may be as a (i) the sample size is ‘too’ small; (ii) ‘too’ many of the cells in the cross tabulations have less than ‘5’ respondents; (iii) errors exist in the data collection process and (iv) issues relating to validity and/or reliability. 238
  • CHAPTER 12 Table 12.1.1: Do you believe that corruption is a serious problem in Jamaica? Valid Cumulative Frequency Percent Percent Percent Valid Not a serious 35 3.1 3.2 3.2 problem Somewhat 185 16.2 16.7 19.9 serious Very serious 886 77.7 80.1 100.0 Total 1106 97.0 100.0 Missing -99.00 24 2.1 -98.00 2 .2 -88.00 8 .7 Total 34 3.0 Total 1140 100.0 As shown in Table? majority of the respondents indicated that corruption is a very serious problem in Jamaica (80.1%, n=886), with approximately 17% (n=185) ‘somewhat serious’ compared to 3.2% (n=35) who remarked it was ‘not a serious problem. Table 12.1.2: Have you or someone in your family known of an act of corruption in the last 12 months? Valid Cumulative Frequency Percent Percent Percent Valid Yes 406 35.6 40.1 40.1 No 606 53.2 59.9 100.0 Total 1012 88.8 100.0 Missin -99.00 26 2.3 g -98.00 96 8.4 -88.00 6 .5 Total 128 11.2 Total 1140 100.0 239
  • Of the sampled population (n=1140), 88.8% (n=1012) responded to this question. The results indicated that approximately 60% (n=606) of the respondents believed ‘No’ compared to 40% (n=406) who remarked ‘Yes’. Table 12.1.3: Gender of Respondent Valid Cumulative Frequency Percent Percent Percent Valid Male 511 44.8 46.8 46.8 Female 581 51.0 53.2 100.0 Total 1092 95.8 100.0 Missing -99.00 43 3.8 -88.00 5 .4 Total 48 4.2 Total 1140 100.0 Of the sampled population (n=1140), approximately 45 percent (n=511) were males compared to 51 percent (n=581) who were females. The non-response rate was approximately 4 percent. 240
  • Table 12.1.4: In what Parish do you live? Valid Cumulative Frequency Percent Percent Percent Valid Clarendon 105 9.2 9.3 9.3 Hanover 59 5.2 5.2 14.6 Kingston 112 9.8 9.9 24.5 Manchester 122 10.7 10.8 35.3 Portland 95 8.3 8.4 43.8 Saint 18 1.6 1.6 45.4 Andrew Saint Ann 70 6.1 6.2 51.6 Saint 143 12.5 12.7 64.3 Catherine Saint 77 6.8 6.8 71.1 Elizabeth Saint James 106 9.3 9.4 80.6 Saint Mary 30 2.6 2.7 83.2 Saint 74 6.5 6.6 89.8 Thomas Trelawny 52 4.6 4.6 94.4 Westmorela 63 5.5 5.6 100.0 nd Total 1126 98.8 100.0 Missing -99.00 14 1.2 Total 1140 100.0 241
  • Table 12.1.5: Suppose that you, or someone close to you, have been a victim of a crime. What would you do...? Valid Cumulative Frequency Percent Percent Percent Valid Report it to an influential 89 7.8 8.3 8.3 neighbour or don Settle the matter 72 6.3 6.7 14.9 yourself Report it to a private security 48 4.2 4.5 19.4 company Report the crime to the 802 70.4 74.5 93.9 police Do nothing 35 3.1 3.2 97.1 Other 31 2.7 2.9 100.0 Total 1077 94.5 100.0 Missing -99.00 46 4.0 -98.00 17 1.5 Total 63 5.5 Total 1140 100.0 Generally, 74.5% (n=802) of the sampled population (n=1140) reported that they would inform the police in the event that someone that they know has been victimized by another. On the other hand, approximately 8% (n=89) indicated that they would use an influential community member or a ‘Don’, with some 7% (n=72) stating they would ‘settle matter themselves’. 242
  • Table 12.1.6: What is your highest level of education? Valid Cumulative Frequency Percent Percent Percent Valid No formal 17 1.5 1.5 1.5 education Primary/Prep 51 4.5 4.6 6.1 school All-Age school or some 172 15.1 15.4 21.5 Secondary education Completed secondary 319 28.0 28.6 50.2 school Vocational/Skill 188 16.5 16.9 67.1 s training University graduate 250 21.9 22.4 89.5 (Undergraduate) Some professional 69 6.1 6.2 95.7 training beyond university Graduate degree (MSc, MA, PhD 48 4.2 4.3 100.0 etc) Total 1114 97.7 100.0 Missing -99.00 20 1.8 -98.00 2 .2 -88.00 4 .4 Total 26 2.3 Total 1140 100.0 Most of the sampled population had attained at completed secondary (i.e. high) school education (28%, n=319); with 21.9% (n=250) an undergraduate level, 16.5% (n=188) a vocational level education, 15.1% (n=172) and 6.1% professional. The non-response rate was approximately 2% (n=26) 243
  • Table 12.1.7: In terms of work, which of these best describes your present situation? Valid Cumulative Frequency Percent Percent Percent Valid Employed, Full- 497 43.6 43.9 43.9 Time job Employed, Part- 69 6.1 6.1 50.0 Time job Seasonally 49 4.3 4.3 54.3 employed Temporarily 50 4.4 4.4 58.7 employed Self-employed 186 16.3 16.4 75.2 Unemployed, 91 8.0 8.0 83.2 out of work Retired 32 2.8 2.8 86.0 Housewife 17 1.5 1.5 87.5 Student 116 10.2 10.2 97.8 Sick/Disabled 25 2.2 2.2 100.0 Total 1132 99.3 100.0 Missing -99.00 6 .5 -98.00 2 .2 Total 8 .7 Total 1140 100.0 Of the surveyed population (n=1140), the response rate, for this question, was 99.3% (n=1132). Approximately 44% (n=497) of the sampled population were full-time employees, 16.4% (n=186) self-employed, 10.2 % (n=116) were students, 6.1% (n=69) part-time employees, 4.3 % (n=49) seasonally employed, 4.4% (n=50) temporarily employed, 2.8% (n=32) retirees, 2.2 % (n=25) physically challenged and 1.5 % (n=17) were housewives. 244
  • Table 12.1.8: Which best represents your present position in Jamaica society? Valid Cumulative Frequency Percent Percent Percent Valid Working 562 49.3 50.9 50.9 (lower) class Middle class 421 36.9 38.1 89.0 Upper-middle 70 6.1 6.3 95.3 class upper class 52 4.6 4.7 100.0 Total 1105 96.9 100.0 Missing -99.00 27 2.4 -98.00 1 .1 -88.00 7 .6 Total 35 3.1 Total 1140 100.0 Of the population surveyed (n=1140), the response rate was 96.9% (n=1105). Some 50.9 percent (n=562) perceived themselves to be within the working-class categorization, 38.1 percent (n=421) middle-class, 6.3 percent (n=70) within the upper-middle class compared to 4.7 percent (n=52) who said upper class. Table 12.1.9: Age on your last birthday? N Valid 1058 Missing 82 Mean 35.6805 Std. Deviation 13.25951 Skewness .710 Std. Error of Skewness .075 The average age of the sampled population (n=1140) is 35 years and 8 months ± 13 years and 3 months. The non-response rate was 7 percent. 245
  • Table 12.1.10: Age Categorization of respondents Valid Cumulative Frequency Percent Percent Percent Valid 1= Young (less 289 25.4 27.3 27.3 than 26 yrs) 2= middle-aged (between 25 717 62.9 67.8 95.1 and 60 yrs) 3= seniors (older than or 52 4.6 4.9 100.0 equal to 60 yrs) Total 1058 92.8 100.0 Missing System 82 7.2 Total 1140 100.0 The sampled population (n=1140) was predominately of people within the middle-aged categorization (67.8%, n=717) with 27.3 % (n=289) being young people compared to 4.9% (n=52) seniors. 246
  • Table 12.1.11: Suppose that you, or someone close to you, have been a victim of a crime. What would you do... * Gender of Respondent Cross tabulation Gender of Respondent Total Male Female Suppose that you, Report it to an Count or someone close to influential you, have been a neighbour or don 43 43 86 victim of a crime. What would you do % within Gender of 8.9% 7.9% 8.3% Respondent Settle the matter Count 39 33 72 yourself % within Gender of 8.0% 6.0% 7.0% Respondent Report it to a Count private security 21 22 43 company % within Gender of 4.3% 4.0% 4.2% Respondent Report the crime to Count 356 413 769 the police % within Gender of 73.4% 75.6% 74.6% Respondent Do nothing Count 15 17 32 % within Gender of 3.1% 3.1% 3.1% Respondent Other Count 11 18 29 % within Gender of 2.3% 3.3% 2.8% Respondent Total Count 485 546 1031 % within Gender of 100.0% 100.0% 100.0% Respondent Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 2.964(a) 5 .706 Likelihood Ratio 2.973 5 .704 Linear-by-Linear 2.043 1 .153 Association N of Valid Cases 1031 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 13.64. There is not statistical relationship that was found between the two variables. 247
  • Table 12.1.12: If involved in a dispute with neighbour and repeated discussions have not made a difference, would you...? * Gender of Respondent Cross tabulation Gender of Respondent Total Male Female If involved in a Report it to an Count dispute with influential neighbour neighbour and or don repeated discussions 58 66 124 have not made a difference, would you...? % within Gender of 12.1% 12.1% 12.1% Respondent Settle the matter Count 68 36 104 yourself % within Gender of 14.2% 6.6% 10.2% Respondent Report it to a private Count 12 13 25 security company % within Gender of 2.5% 2.4% 2.4% Respondent Report the crime to Count 303 382 685 the police % within Gender of 63.4% 70.0% 66.9% Respondent Do nothing Count 15 24 39 % within Gender of 3.1% 4.4% 3.8% Respondent Other Count 22 25 47 % within Gender of 4.6% 4.6% 4.6% Respondent Total Count 478 546 1024 % within Gender of 100.0% 100.0% 100.0% Respondent 248
  • Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 17.342(a) 5 .004 Likelihood Ratio 17.464 5 .004 Linear-by-Linear 4.666 1 .031 Association N of Valid Cases 1024 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 11.67. When the respondents’ answers for “If involved in a dispute with neighbour and repeated discussions have not made a difference, would you...?” was cross tabulated with ‘gender’, a significant statistical association was found (χ2 (5) = 17.342, Ρ value =.004< 0.05). Some 12% (n=124) of the respondents indicated that they would address the matter(s) through an influential individual within the community or a don. Furthermore analysis revealed that both males and females (12%) would use the same source – influential community member or ‘don’. With regard to addressing the matter personally, approximately twice the number of males (14.2%, n=68) would do this compared to females (6.6%, n=36). On the other hand, marginally more females (70%, n=382) than males (63.4%, n=303) would inform the police, and a similar situation existed in respect to ‘doing nothings and using ‘other’ approaches – females (4.4%, n=24) and 3.1% (n=15) for males and females (4.6%, n=22) and 4.6% (n=25) for males respectively. 249
  • Table 12.1.13: Do you believe that corruption is a serious problem in Jamaica? * Gender of Respondent Cross tabulation Gender of Respondent Total Male Female Do you believe that Not a serious problem Count corruption is a serious 17 16 33 problem in Jamaica? % within Do you believe that 51.5% 48.5% 100.0% corruption is a serious problem in Jamaica? Somewhat serious Count 91 82 173 % within Do you believe that 52.6% 47.4% 100.0% corruption is a serious problem in Jamaica? Very serious Count 388 468 856 % within Do you believe that 45.3% 54.7% 100.0% corruption is a serious problem in Jamaica? Total Count 496 566 1062 % within Do you believe that 46.7% 53.3% 100.0% corruption is a serious problem in Jamaica? Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 3.376(a) 2 .185 Likelihood Ratio 3.369 2 .186 Linear-by-Linear Association 2.859 1 .091 N of Valid Cases 1062 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 15.41. From Table, no statistical relationship exists between ‘Do you believe that corruption is a serious problem in Jamaica’ and the Gender of the Respondents. 250
  • Table 12.1.14: Have you or someone in your family known of an act of corruption in the last 12 months? * Gender of Respondent Cross tabulation Gender of Respondent Total Male Female Have you or Yes Count someone in your family known of an act 192 198 390 of corruption in the last 12 months? % within Have you or someone in your family known of an act 49.2% 50.8% 100.0% of corruption in the last 12 months? No Count 257 321 578 % within Have you or someone in your family known of an act 44.5% 55.5% 100.0% of corruption in the last 12 months? % within Have you or someone in your family known of an act 46.4% 53.6% 100.0% of corruption in the last 12 months? 251
  • Chi-Square Tests Asymp. Sig. Exact Sig. Exact Sig. Value df (2-sided) (2-sided) (1-sided) Pearson Chi-Square 2.128(b) 1 .145 Continuity 1.941 1 .164 Correction(a) Likelihood Ratio 2.127 1 .145 Fisher's Exact Test .149 .082 Linear-by-Linear 2.126 1 .145 Association N of Valid Cases 968 a Computed only for a 2x2 table b 0 cells (.0%) have expected count less than 5. The minimum expected count is 180.90. Based on the findings in Table, there is no statistical association between responses garnered from “Have you or someone in your family known of an act of corruption in the last 12 months?” tabulated by Gender of Respondent. 252
  • CHAPTER 13 Hypothesis 10: There is no statistical difference between the typology of workers in the construction industry and how they view 10-most top productivity outcomes SOCIODEMOGRAPHIC CHARACTERISTICS Categorization of respondents 50 45 40 45.9 35 30 33.8 25 20 15 10 13.5 6.8 5 0 Superintendent Field workforce President, VP) manager Project Executive (CEO, Field Figure13.1.1: Categories that describe respondents’ position Of the sampled population (n=80), the non-response rate was 7.5% (n=6). Approximately 45.9% of the respondents (n=34) were from ‘Field workforce’, 33.8% (n=25) ‘Field Superintendent’, 13.5% (n=10) ‘Project manager’ compared to 6.8% (n=5) ‘Executive’. 253
  • COMPANY’S ANNUAL WORK VOLUME 45 40 42.1 35 30 25 26.3 20 21.1 15 10 5 10.5 0 Under 25 dollars Over 100 million 26 - 50 51 - 100 dollars million dollars million dollars million Figure13.1.2: Company’s annual work volume Based on Figure 1.2, 42.1% of the respondents (n=16) remarked that their company’s annual work volume in dollars was ‘Over 100 million’, 26.3% between ’51 and 100 million’, 21.1% ’26 to 50 millions’ compared to 10.5% ‘under 25 million. 254
  • LABOUR FORCE – ‘ON AN AVERAGE PER YEAR’ 50 45 48.7 40 35 30 25 28.2 20 23.1 15 10 5 0 Over 250 Under 50 50 - 249 Figure13.1.3: Company’s Labour Force – ‘On an average per year’ Of the sampled population (n=80), using Figure 1.3, approximately 49% of the respondents (n=19) said that their companies employed ’50 to 249’ employers per annum per average, with some 28% remarked ‘over 250’ employees compared to 23% who said ‘under 50’ employees. 255
  • MAIN AREA OF CONSTRUCTION WORK 35 30 32.5 32.5 25 20 20.0 15 12.5 10 5 2.5 0 Highway Residential Other Public Commercial Works Figure13.1.4: Respondents’ main area of construction work Based on Figure 1.4, 50% of the respondents (n=40) responded to this question. Of the respondents (n=40), approximately33% said ‘Commercial and Residential, 20% remarked ‘Highways’, 2.5% ‘Public Works’ and 12.5% said ‘Other’. 256
  • SELF-PERFORMED IN CONTRAST TO SUB-CONTRACTED 35 30 32.6 25 23.3 20 20.9 15 11.6 10 11.6 5 0 1 -10 % 26 - 50 % 51 - 75 % 11 - 25 % 76 - 100 % Figure13.1.5: Percentage of work ‘Self-performed’ in contrast to ‘Sub-contracted’ Of the sampled population (n=80), the non-response rate was 46.2% (n=37). Of the respondents (n=43), 11.6 % indicated that between ‘1 and 10%’ of their work was ‘Self- performed’ compared to ‘Sub-contracted’, with 20.9% said between ’11 to 25%’, 32.6% revealed ’51 to 75%’, with 23.3% make mention that it was between ’26 and 50%, compared to 11.6% who mentioned ’76 – 100%. 257
  • AGE COHORT OF RESPONDENTS 40 35 37.8 30 25 21.6 25.7 20 15 10 14.9 5 0 Over 45 yrs 35 - 44 yrs 18 - 24 yrs 25 - 34 yrs Figure13.1.6: Percentage of work ‘Self-performed’ in contrast to ‘Sub-contracted’ Figure 1.6 revealed that the modal age (37.8%, n=28) group was 25 – 34 years. Approximately 22% of the respondents were older than 45 years with 14.9% between the age cohort of ’18-24’ years and another 25.7% being ’35 to 44’ years. 258
  • YEARS OF EXPERIENCE IN CONSTRUCTION INDUSTRY 40 35 30 35.1 25 24.3 17.6 20 23 15 10 5 0 Under 5 yrs Over 20 yrs 5 - 9 yrs 10 -19 yrs Figure13.1.7: Years of Experience in Construction Industry 259
  • PRIMARY AREA OF EMPLOYMENT 40 35 30 35.1 25 20 24.3 23 15 10 5 0 Kingston (combine a Coast North Andrew and St. Migratory and b) Figure13.1.8: Geographical Area of Employment 260
  • DURATION IN PRESENT EMPLOYMENT 50 45 40 35 30 25 20 15 10 5 0 Less than 2 2 - 5 yrs 6 - 9 yrs Over 10 yrs yrs Figure13.1.9: Duration of service with current employer When asked “How long have you been with your present employer?” 90 % of the respondents (n=72) answered this question. Most of the respondents (50%, n=36) indicated less than 2 years, with 22.2% (n=16) mentioned 2-5 years, 8.3% (n=6) said 6-9 years compared to 19.4% (n=14) saying over 10 years 9(see Figure 1.9). 261
  • PRODUCTIVITY CHANGES IN THE PAST FIVE YEARS 50 47.7 45 40 35 32.3 30 25 20 15 10.8 10 6.2 3.1 5 0 substantially Significantly changed Improved Decreased Has not decreased slightly Improved slightly Figure13.1.10: Productivity changes over the past five years Of the sampled population (n=80), the response rate was 81.3% (n=65). Of the respondents (n=65), approximately 48% indicated that their company had ‘Improved slightly’, with 32% mentioned ‘Improved substantially’, and some 11% remarked ‘Has not changed’ compared to 3.1% who said ‘Decreased slightly’, with 6.2% mentioned ‘Significantly decreased’. 262
  • SELF-RATED PERCEPTION of PRODUCTIVITY IN CONSTRUCTION SECTOR 1 2 3 4 5 Mean Mod Median e 1 Work force skill and experience? 4.45 5.00 5.00 1 1 Workers’ motivation? 4.25 5.00 4.00 2 1 Frequency of breaks? 3.55 3.00 3.00 3 1 Absenteeism and turnover? 4.00 5.00 4.00 4 1 Poor use of turnover? 3.77 4.00 4.00 5 1 Pay increases and bonuses? 4.10 5.00 4.00 6 1 Better management? 4.15 5.00 4.00 7 1 Job planning? 4.36 5.00 5.00 8 Lack of pre-task planning? 4.04 4.00 4.00 1 9 2 Lack of work force training? 4.11 5.00 4.00 0 2 Internal delay (crew interfacing)? 3.65 3.00 4.00 1 2 Waiting for instructions? 3.57 4.00 4.00 2 263
  • 2 Management’s resistance of change 3.70 4.00 4.00 3 2 Supervision delays? 3.60 3.00 4.00 4 2 Safety (near misses and accidents)? 3.68 5.00 4.00 5 2 Poor construction methods? 4.03 5.00 4.00 6 2 Weather conditions? 3.89 5.00 4.00 7 2 Shortage of skilled labour? 4.06 5.00 4.00 8 2 Lack of proper tools and equipment? 4.18 5.00 4.50 9 3 Incentives that reward maintenance of status quo or that reward unproductive 3.62 3.00 4.00 0 employees As well as productive ones SCALE: 1 = No impact; 2 =Low importance; 3 = Moderate; 4 = Important; 5 = Very important’ N/A = Not applicable SELF-RATED PERCEPTION of PRODUCTIVITY IN CONSTRUCTION SECTOR (con’td) 1 2 3 4 5 Mean Mode Median 3 Ignoring or not asking for employers input? 3.48 4.00 4.00 1 3 Lack of quality control? 4.03 4.00 4.00 264
  • 2 3 Equipment breakdown? 3.93 4.00 4.00 3 3 Lack of material? 4.13 5.00 4.00 4 3 Late material fabrication and delivery? 3.69 4.00 4.00 5 3 Congested work areas? 3.34 4.00 4.00 6 3 Poor drawing or specification? 3.94 5.00 4.00 7 3 Change orders and rework? 3.68 3.00 4.00 8 Regulatory burdens? 3.46 3.00 3.00 3 9 4 Inspection delays? 3.38 3.00 3.00 0 4 Local union and politics? 3.80 4.00 4.00 1 4 Poor communication between office and field? 4.33 4.00 4.00 2 4 Project uniqueness (size and complexity)? 3.03 3.00 3.00 3 4 Theft of material and equipment? 3.86 5.00 4.00 4 4 Extortion? 3.52 5.00 3.00 5 SCALE: 1 = No impact; 2 =Low importance; 3 = Moderate; 4 = Important; 5 = Very important’ N/A = Not applicable 265
  • THE 10 MOST IMPORTANT SELF-RATED PERCEPTION INDICATORS OF PRODUCTIVITY IN CONSTRUCTION SECTOR 1 2 3 4 5 Mean Mode Median 1 Work force skill and experience (Ques11) 4.45 5.00 5.00 2 Job planning (Ques18) 4.36 5.00 5.00 3 Poor communication between office and field 4.33 4.00 4.00 (Ques42) 4 Workers’ motivation (Ques12) 4.25 5.00 4.00 5 Lack of proper tools and equipment (Ques29) 4.18 5.00 4.50 6 Better management (Ques17) 4.15 5.00 4.00 7 Lack of material (Ques34) 4.13 5.00 4.00 8 Lack of work force training (Ques20) 4.11 5.00 4.00 9 Pay increases and bonuses (Ques16) 4.10 4.00 5.00 10 Shortage of skilled labour (Ques28) 4.06 5.00 4.00 TOTAL SCALE: 1 = No impact; 2 =Low importance; 3 = Moderate; 4 = Important; 5 = Very important’ N/A = Not applicable 266
  • Table 13.1.1: RESEARCH QUESTION # 1: Spearman’s rho ques01 ques11 ques12 ques16 ques17 ques18 ques20 ques28 ques34 ques29 ques42 ques01 Correlation Coefficient 1.000 .140 .108 -.073 .137 .270(*) .158 .081 -.030 -.025 .062 Sig. (2-tailed) . .236 .361 .541 .256 .022 .208 .499 .801 .838 .614 N 74 74 73 72 71 72 65 72 72 72 69 ques11 Correlation Coefficient .140 1.000 .544(**) .173 .348(**) .212 .372(**) .297(*) .169 .421(**) .069 Sig. (2-tailed) .236 . .000 .145 .003 .074 .002 .011 .157 .000 .573 N 74 74 73 72 71 72 65 72 72 72 69 ques12 Correlation Coefficient .108 .544(**) 1.000 -.040 .134 .032 .109 .278(*) .254(*) .388(**) -.024 Sig. (2-tailed) .361 .000 . .739 .268 .793 .387 .018 .032 .001 .843 N 73 73 73 71 70 71 65 72 71 71 68 ques16 Correlation Coefficient -.073 .173 -.040 1.000 .194 .143 -.005 -.127 -.013 -.087 -.044 Sig. (2-tailed) .541 .145 .739 . .111 .236 .966 .296 .914 .465 .721 N 72 72 71 72 69 70 64 70 70 72 68 ques17 Correlation Coefficient .137 .348(**) .134 .194 1.000 .517(**) .196 .192 .144 .140 .396(**) Sig. (2-tailed) .256 .003 .268 .111 . .000 .120 .114 .237 .250 .001 N 71 71 70 69 71 70 64 69 69 69 67 ques18 Correlation Coefficient .270(*) .212 .032 .143 .517(**) 1.000 .220 .238(*) .151 -.027 .345(**) Sig. (2-tailed) .022 .074 .793 .236 .000 . .079 .047 .212 .821 .004 N 72 72 71 70 70 72 65 70 70 70 67 ques20 Correlation Coefficient .158 .372(**) .109 -.005 .196 .220 1.000 .319(*) .225 .361(**) .355(**) Sig. (2-tailed) .208 .002 .387 .966 .120 .079 . .010 .077 .003 .005 N 65 65 65 64 64 65 65 64 63 64 62 ques28 Correlation Coefficient .081 .297(*) .278(*) -.127 .192 .238(*) .319(*) 1.000 .575(**) .695(**) .277(*) Sig. (2-tailed) .499 .011 .018 .296 .114 .047 .010 . .000 .000 .022 N 72 72 72 70 69 70 64 72 70 70 68 ques34 Correlation Coefficient -.030 .169 .254(*) -.013 .144 .151 .225 .575(**) 1.000 .556(**) .454(**) Sig. (2-tailed) .801 .157 .032 .914 .237 .212 .077 .000 . .000 .000 N 72 72 71 70 69 70 63 70 72 70 67 * Correlation is significant at the 0.05 level (2-tailed). ** Correlation is significant at the 0.01 level (2-tailed). 267
  • Based on the statistical test (Spearman rho) which was performed on ‘The 10 most important self-rated perception indicators of? productivity in construction sector’, the findings revealed that only ‘Job planning’ and ‘Categorization of position was statistically related. This implies that, hierarchal level that one holds within the construction level is positively related to ‘Job planning’ (cc= 0.27, Ρ value < 0.05), and not any of the other characteristics identified in the ‘Top 10’ indicators. Based on the contingency coefficient (0.27 or 27%), the association is a moderately weak one. 268
  • RESEARCH QUESTION # 2 The statistical test revealed that irrespective of the respondents’ area of specialization in the construction industry, the ‘Top 10 indicators’ are the same. This can have been caused by the sample size (Type II Error – See Appendix II). RESEARCH QUESTION # 3 The statistical test revealed that irrespective of the respondents’ location of employment in the construction industry, the ‘Top 10 indicators’ remain the same. This can have been caused by the sample size (Type II Error). ESEARCH QUESTION # 4 The statistical test revealed that irrespective of the respondents’ years of experience in the construction industry, the ‘Top 10 indicators’ remain the same. This can have been caused by the sample size (Type II Error – see Appendix II).
  • CHAPTER 14 Hypothesis 11: Determinants of the academic performance of students SOCIO-DEMOGRAPHIC VARIABLES guardian 19% parent 81% Figure 14.1.1: Characteristic of Sampled Population Of the sampled population (n=100), 81 percent (n=81) were parents (i.e. biological parents) compared to 19 percent (n=19) were guardians. (See, Figure 14.1.1) Predominantly the sampled population was single individuals (45 %, n=45) compared to 39 percent who were married, 12 percent divorced and 4 percent who were remarried people (See, Table 14.1.1). Table 14.1.1: Marital Status of Respondents Detail Frequency Percent Single 45 45 Married 39 39 Divorced 12 12 Remarried 4 4 Total 100 100 270
  • Table 14.1.2: Marital Status of Respondents by Gender gender of respondents Total Marital status male female 5 40 45 single 21.7% 51.9% 45.0% married 10 29 39 43.5% 37.7% 39.0% divorced 7 5 12 30.4% 6.5% 12.0% remarried 1 3 4 4.3% 3.9% 4.0% Total 23 77 100 Based on Table 14.1.2, 77 percent (n=77) of the respondents were females, of which 51.9 percent (n=40) were single mothers compared to 37.7 percent (29) who were married, 6.5 percent divorced and 3.9 percent (n=3) who had got remarried. Only 23 percent (n=23) of the sampled population were males, of which approximately 44 percent (n=10) were married men compared to some 22 percent (n=5) who were single, 30.4 percent (n=7) divorced and 4.3 percent (n=1) were remarried fathers. 271
  • Table 14.1.3: Marital Status by Gender by Age Cohort Age Age Age Gender Marital Status 20 – 30 Yrs 31 – 40 Yrs Above 40 Yrs Single 0 (0.0%) 1 (16.7%) 4(26.7%) Male Married 1 (50.0%) 3 (50.0%) 6(40.0%) Divorced 1 (50.0%) 2 (33.3%) 4(26.7%) Remarried 0 (0.0%) 0 (0.0%) 1(6.7%) Single 5 (71.4%) 22 (68.8%) 13(34.2%) Female Married 2 (28.6%) 8 (25.0%) 19(50.0%) Divorced 0(0.0%) 2 (6.3%) 3(7.9%) Remarried 0 (0.0%) 0 (0.0%) 3(7.9%) Generally the sampled population was from beyond 40 years (53 %, n=53), of which 72 percent (n=38) were females. Of the respondents who were older than 40 years, they were primarily married men (40%, n=6) and married females (50%, n=19). Only 9 percent of the respondents were younger than 30 years with 71.4 percent (n=5) being single females compared to no single male of the same age cohort. Approximately 28 percent (n=2) of the respondents who were younger than 30 years were married compared to 50 percent (n=1) of males (See, Table 14.1.3). employed unemployed 80% 20% Figure 14.1.2: Employment Status of Respondents Generally the sampled population was employed (80%, n=80). 272
  • Table 14.1.4: Marital Status by Gender by Age Cohort Age Age Age Gender Marital Status 20 – 30 Yrs 31 – 40 Yrs Above 40 Yrs Male Employed 2(1000%) 4 (66.7%) 14(93.3%) Unemployed 0 (0.0%) 2 (33.3%) 1(6.7%) Female Employed 5 (71.4%) 21(65.6%) 34(89.5%) Unemployed 2(28.6%) 11 (34.4%) 4(10.5%) Of the 80 percent (n=80) of the sampled population who were employed, 90.6 percent (n=48) were beyond age 40 years, or which 89.5 percent (n=34) were females compared to 93.3 percent (n=14) who were males. However, only 77.8 percent (n=7) of the people younger than 31 years were employed with 71 percent being females compared to all the males being employed (100%, n=2). In regard to the people who were 31 to 40 years at their last birthday, the employment rate was 65.8 percent. Approximately 66 percent (n=21) of that age cohort was female compared to 68 percent (n=4) male. 273
  • Table 14.1.5 Educational Level by gender by age cohorts Age Age Age Gender Marital Status 20 – 30 Yrs 31 – 40 Yrs Above 40 Yrs None 0 (0.0%) 0 (0.0%) 1 (6.7%) Male Primary 0 (0.0%) 1 (16.7%) 4 (26.7%) High 1 (50.0%) 4 (66.7%) 2(13.3%) College 0 (0.0%) 0 (0.0%) 2(13.3%) Tertiary 1 (50.0%) 1 (16.7%) 6 (40.0%) Female None 0 (0.0%) 3 (9.4%) 0 (0.0%) Primary 2 (28.6%) 8 (25.0%) 6(15.8%) High 3(42.9%) 15 (15.6%) 16(42.1%) College 0(0.0%) 5 (15.6%) 7 (18.4%) Tertiary 2 (28.7) 4(12.5%) 9 (23.7%) The highest level of educational attainment of the sampled population (n=100) was tertiary with 23 percent (n=23) compared to 38 percent (n=38) who had completed high/secondary level education, 21.0 percent (n=21) primary, 14 percent (n=14) college and only 4 percent (n=4) of who had no formal education. Of the seventy-seven percent (n=77) of the sampled females, the most frequently highest level of formal education had was secondary (40.3%, n=31) compared to university for the males (34.8%, n=8). Only 4 percent (n=4) of the sampled respondents did not have any formal education, and of this total, 3.9 percent (n=3) were females compared to 4.3 percent (n=1) of males. Based on Table 14.1.5, of the 53 percent (n=53) of the sampled who were older than 40 years, 28.3 percent (n=15) had completed university level education, 17.0 percent (n=9) college, 34.0 percent (n=18) high/secondary, 18.9 percent (10) primary and 1 percent had no formal education. Generally, in the age cohort 20 to 30 years, males had a higher rate of completion of high/secondary level school and university level education (50% and 274
  • 50% respectively) compared to females (high - 42.9% and secondary -28.6%). On the other hand, females had higher completion rate than males in respect to college level (i.e. people beyond 40 years) and primary (i.e. for people whose ages range from 31 to 40 years). Table 14.1.6: Income distribution of respondents Income (in $) Frequency Percent less than 20,000 20 20.0 20,000 - 39,999 20 20.0 40,000 - 59,999 18 18.0 60,000 - 79,999 8 8.0 80,000 - 99,999 10 10.0 100,000 - 119,999 5 5.0 120,000 19 19.0 Less than 69 percent (n=68) of the respondents received income that was lower than $60,000 per month, with 20 percent (n=20) of them receiving less than $20,000 monthly and same percent were earning between $20,000 and $39,999 monthly. The median wage for the sample was between $40,000 to $59,999 with less than 25 percent of the respondents received incomes which were higher than $100,000 on an average each month (See, Table 14.1.6) 275
  • PARENT ATTITUDE TOWARD SCHOOL Table 14.1.7: Parental Attitude toward School Detail Frequency Percent Strongly Disagree 45 45 Disagree 39 39 Undecided 12 12 Agree 4 4 Strongly Agree 5 5.0 Total 100 100 Parental attitude toward the school was generally extraordinarily poor. Based on Table 14.1.7, approximately 84 percent (n=84) of the respondents reported a negative attitude in respect to the school. Of the 100 respondents, 45 percent viewed the school in an extremely negative manner compared to 5 percent who reported on the positive extreme. Only 9 percent (n=9) of the interviewees saw the school in a positive light, with 12 percent (n=12) being unsure (“undecided”). 276
  • PARENT INVOLVING SELF Table 14.1.8: Parent Involving Self Detail Frequency Percent Strongly Disagree 1 1 Disagree 21 21 Undecided 47 47 Agree 4 4 Strongly Agree 31 31 Total 100 100 From the findings in Table 14.1.8, 31.0 percent (n=31) of the respondents reported that they were involved themselves in the educational well-being of their children. A startling finding was the high percent of sampled population who indicated that they were “unsure” of an involvement of self in Parent Teacher Association meetings, assisting their children with assignment, communicating with their children on school work and other educational activities. Twenty-two percent (n=22) of the respondents indicated that they were not involved in the educational development of their children, with 1 percent reporting that they were absolutely not personally not involvement in the educational development of their children. 277
  • SCHOOL INVOLVING PARENT Table 14.1.9: School Involving Parent Detail Frequency Percent Strongly Disagree 8 8 Disagree 45 45 Undecided 33 33 Agree 14 14 Strongly Agree 0 0 Total 100 100 When the respondents were asked about the schooling involving them in school activities, 53 percent (n=53) reported no with 8 percent (n=8) of them indicating an absolute no. Only 14 percent (n=14) of the sampled population cited that they were invited to be involved in the school’s apparatus with 33 percent (n=33) being unsure of any such demand. Generally, the sampled population (53%) is reporting that there is a gap between themselves and the school, with the school requesting little of their involvement in the educational process of their children. 278
  • MODEL Table 14.1.8: Regression Model Summary Details Beta Coefficient Constant 68.751 Dummy Primary School Level Education -22.747* Dummy High School Level Education -19.995* Dummy University Level Education. -5.488* Dummy Income less than $20,000 -12.430* Dummy Income (1= $40K - $59,999) 7.20* Dummy Income (1=>$120,000) -6.038* Dummy Gender (0= males) -4.969* Dummy Remarried (0= other) -6.009* Dummy Parent Attitude toward 8.737* School ( 0= negative) Dummy School involving parents -5.183 School ( 0= low) n 195 R .686 R2 .471 Standard Error 10.19 F statistic 16.378 ANOVA (sign.) 0.000 Model [ Y= β0 + β1x1 +…+ ei ] - where Y represents Academic Performance of the students, β0 denotes a constant, ei means error term and β1 indicates the coefficient of dummy primary level education * x1 where represents the variable primary level of education to βi and xi * Significant at the two-tailed level of 0.05 (see Appendix V) The findings in Table 14.1.8 (see above) revealed that primary, high and university level education, gender of respondents, parent attitude towards school, school involving parents, low income (i.e. income below $20,000), income in excess of $120,000 along with being remarried are determinants of students’ academic performance. The relationship between the independent variables (i.e. the determinants) and the dependent variable (i.e. academic performance) is a statistical one (as the ρ value was less than 0.05). The causal relationship was a relatively strong one (i.e. Pearson’s Correlation Coefficient = 0.686). Furthermore, approximately 47 percent of the variation in students’ 279
  • academic performance is explained by a 1 percent change in the determinants. This means that the regression model explains 47 percent of the total variation in students’ academic performance. As shown in Table 14.1.8, the regression model, Testing Ho: β=0, with an α = 0.05, indicates that the linear model provides a good fit to the data based on the F value of (1,700.74, 103.85) 16.378 with a p < 0.05 (p = 0.000). Generally, without the determinants being held constant, a student will score 68.75 percent on his/her examination. However, if the student’s parent had only completed primary level education he/she score will decline by 22.75 percent, and if the parent had completed high/secondary school his/her child score will reduce by 20 percent compared to a decrease of 5.5 marks if the parent had completed university level education. Embedded within this finding is the contribution of parents with university level education compared to other levels of education on a child’s academic performance. Issues such as income, gender, remarried guardians/parents and school involving the parents were discovered to decrease students’ performance. From Table 14.1.8, with all other things being held constant, a child’s academic score will decrease by 6 percent if his/her parent/guardian is remarried, a 5 percent fall in student’s score if school involves the parents, a reduced score if the parent income is more than $120,000 or less than $20,000 per month. Another reduction in a child’s score is attributable to the guardian/parent being female (i.e. approximately 5%). Subsumed in this finding is that the students with a male parent/guardian score 5% more than children with female parents/guardians. 280
  • The findings further revealed that students’ whose parents have a positive attitude toward school will score approximately 9% more compared to parent who have a negative attitude toward the school. Concurrently, a child whose parent/guardian received between $40,000 and $60,000 per month will score 8.7 % more than students whose parents/guardians’ income is more $60,000 or less than $40,000. It should be noted that parents whose incomes are high or lower than $40,000 score approximately 100 % less than children who guardian received $40,000 to $59,999 monthly. In addition to those variables which were found to be statistically significant (i.e. ρ value less than 0.05), some issues that initially were entered into the regression model were discovered to be statistically not significant (i.e. ρ value > 0.05). These factors are employment status; college trained parents; parents with no formal education; parents whose income were $20,000 to $39,999, $40,000 to $59,999, $100,000 to $119,999; divorced, married and single parents and parents involving themselves in their children educational programme. Hence, the determinants of students’ academic performance of this sample reads: Students’ Scores = 68.751 + (-22.7) * Parents’ Primary Level Education + (-20.0) * Parents’ Secondary Level Education + (-5.5) * Parents’ University Level Education + (-6) * Parent who are remarried + (-5.2) * School Involved Parents (0=low involvement) + (8.8) * Parent Attitude toward school (0=Negative) + (-12.4) * Parent whose income (less $20,000) + (7.3) * Parent whose income ($40, 000 - $59,999) + (-6.0 ) * Parent whose income (beyond $120,000) + (-5.0) * Dummy gender (0= males). 281
  • CHAPTER 15 Hypothesis 12: People who perceived themselves to be of the lower social status (i.c. class) are more likely to be in-civil than those of the upper class. Based on the level of measurement of the variables – dependent (DV), ordinal and the independent (IV), ordinal. The social researcher has the option of using either (1) Spearman rho or (2) Cross-tabulations – Chi Square Analysis. Table 15.1.1: Correlations Social Status Incivility Spearman's rho Social Status Correlation 1.000 Coefficient Sig. (2-tailed) . N 216 Incivility Correlation .512(**) 1.000 Coefficient Sig. (2-tailed) .000 N 216 216 ** Correlation is significant at the 0.01 level (2-tailed). Based on Table 15.1.1, there is a statistical association between incivility and ones perceived social status (using correlation coefficient of 0.512, Ρ value = 0.001< 0.05). Furthermore, a positive correlation coefficient, 0.512, indicates that a direct relationship exists between the DV and the IV. This implies that the higher one goes up the ranked- ordered social class, the more likely that the individual is less uncivil, which can be simply put as those within the lower social status are more ‘uncivil’ than those further up the social ladder. This statistical association is a moderate one using Cohen and 282
  • Holliday’s classifications of statistical relationships (Cohen and Holliday 1982). In addition, 26.214% (i.e. cc2 * 100 – 0.512 * .0152 * 100) of the variation in the DV, incivility, is explained by a change in ones social status. This could have been analyzed using Chi-Square instead of Spearman’s rho, based on Chapter 1. Thus, using the former gives this set of analysis. Table 15.1.2: Cross Tabulation between incivility and social status Incivility * Social Status Crosstabulation Social Status 1=Lower (Working) 2=Middle 3=Upper Class Class Middle Total Incivility 1=Strongly agree Count 37 1 12 50 % within Incivility 74.0% 2.0% 24.0% 100.0% % within Social Status 37.0% 1.0% 100.0% 23.1% % of Total 17.1% .5% 5.6% 23.1% 2=Agree Count 59 15 0 74 % within Incivility 79.7% 20.3% .0% 100.0% % within Social Status 59.0% 14.4% .0% 34.3% % of Total 27.3% 6.9% .0% 34.3% 3=Disagree Count 4 86 0 90 % within Incivility 4.4% 95.6% .0% 100.0% % within Social Status 4.0% 82.7% .0% 41.7% % of Total 1.9% 39.8% .0% 41.7% 4=Strongly disagree Count 0 1 0 1 % within Incivility .0% 100.0% .0% 100.0% % within Social Status .0% 1.0% .0% .5% % of Total .0% .5% .0% .5% 8 Count 0 1 0 1 % within Incivility .0% 100.0% .0% 100.0% % within Social Status .0% 1.0% .0% .5% % of Total .0% .5% .0% .5% Total Count 100 104 12 216 % within Incivility 46.3% 48.1% 5.6% 100.0% % within Social Status 100.0% 100.0% 100.0% 100.0% % of Total 46.3% 48.1% 5.6% 100.0% 283
  • Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 178.160a 8 .000 Likelihood Ratio 203.720 8 .000 Linear-by-Linear 27.424 1 .000 Association N of Valid Cases 216 a. 8 cells (53.3%) have expected count less than 5. The minimum expected count is .06. Symmetric Measures Asymp. a b Value Std. Error Approx. T Approx. Sig. Nominal by Nominal Contingency Coefficient .672 .000 Ordinal by Ordinal Gamma .620 .089 7.662 .000 Spearman Correlation c .512 .078 8.709 .000 Interval by Interval Pearson's R .357 .082 5.594 .000c N of Valid Cases 216 a. Not assuming the null hypothesis. b. Using the asymptotic standard error assuming the null hypothesis. c. Based on normal approximation. From the Chi-Square Tests table above, there is a statistical association between incivility (DV) and the perceived social class (IV) of respondents (χ2 (8) = 178.16, ρ value = 0.001< 0.05). In order to establish strength, direction and magnitude of the relationship, we need to use the Symmetric Measures Table. Based on this Table, given that the variables are Ordinal, DV and Ordinal, IV, the statistical value which should be used is the Gamma valuation, 0.620. This value denotes (1) a positive relationship between the DV and IV; (2) the associate is a moderate one using Cohen and Holliday’s38,39 figures, and (3) 38.44% of the variation in incivility is explained a by change in ones perceived social class. 38 Very low, < 0.19; Low, 0.20 – 0.39; Moderate, 0.40 – 0.69; High 0.70 – 0.89; Very High 0.9 – 1.0. 39 Bryman and Cramer modified Cohen and Holliday’s work by using Very weak, < 0.19; Weak, 0.20 – 0.39; Moderate, 0.40 – 0.69; Strong 0.70 – 0.89; Very Strong 0.9 – 1.0 (Bryman and Cramer 2005, 219. 284
  • 16. Data Transformation In order for me to provide an integrative understanding of how the following are possible: Recoding Dummying variables Averaging Scores Reverse coding I will use the Questionnaire below 285
  • QUESTIONNAIRE ADVANCED LEVEL ACCOUNTING SURVEY 2004 SECTION 1 CHARACTERISTICS (for all persons) 1.1 Is …male or female? 1.6 What is your mother’s highest О Male О Female level of education? 1.2 What is your….at last birthday? О No formal education О Primary/Preparatory school 1.3 Where do you live? ____________ О All-Age school 1.4 In response to Q1.3, Is the home О Secondary school О Owned О Rented О Vocational/skill training О Leased О Unsure О Other(specify) ________ О Some professional training 1.5 What is your father’s highest level О Tertiary (Undergraduate) of education? О Tertiary (Post-graduate О No formal education О Primary/Preparatory school 1.7. What is your perception of your parent(s)/guardian(s) social О All-Age school class? О Secondary school О Lower class О Vocational/skill training О Lower middle class О Some professional training О Middle middle class О Tertiary (Undergraduate) О Upper middle class О Tertiary (Post-graduate О Upper class 286
  • 1.8 Are you currently living with? 1.11 If you answer to Q1.10 is YES, О Mother only how often in the last six (6) months? О Mother and father О Always (4-6 months) О Father only О Sometimes (2-3 months) О Mother and Step-father О Occasionally (1 month) О Father and Step-mother О Rarely (0 to <4 weeks) О Other О Never (0 week) ___________________ 1.12 Do any of your close family 1.9 Which of the following affect you? member(s) suffering from a major illness? О Migraine О Arthritis О Yes О No О Psychosis О Anxiety 1.13 If your response to Q1.12 is Yes, О Sickle cell Are you close this family О Diabetes member? О Asthma О Heart disease О Yes О No О not really О Hard drug addiction – marijuana, heroine, crack, 1.14 If your response to Q1.12 is Yes, etc. How frequently in the last three О depression (3) months? О hypertension О fit (epilepsy) О Always (11/2 - 3months) О numbness of the hand(s) О Sometimes (< 3 weeks but > 5weeks) О None ОUnsure О Other ________________ О Occasionally (less than two weeks) О Never 1.10 If you answer to Q6.1 is YES, how often in the last three (3) months? О Always (7-12 weeks) О Sometimes (3-6 weeks) О Occasionally (1-2 weeks) О Rarely (0 to <1 week) О Never (0 week) 287
  • SECTION 2 QUALIFICATION 2.1 What were your grades in the following course(s), specify: tick appropriate response Subject CXC - Grade O’Level Grade A/O Grade General English N/A N/A Language English N/A N/A Literature Mathematics General Paper or Communication N/A N/A N/A N/A Studies Principles of Accounts N/A N/A
  • SECTION 3 ACADEMIC PERFORMANCE 3.1 In Advanced Level, what were your last two (2) tests scores over the past six (6) months? (1) _______________________ (2) _______________________ 3.2 In A’ Level Accounting, what were your last two (2) assignments scores over the past six (6) months. (1) _______________________ (2) _______________________ 3.3 What was your lowest score on an Advanced Level Accounting test in the last three (3) months? (1) __________________________ 3.4 Comparing this term to last term, How was your academic performance in A’ Level Accounting О Better О Same О Worse
  • SECTION 4 CLASS ATTENDANCE Read each of the following options, then you are to select the numbered response that best express your choice. KEY 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree 1 2 3 4 5 4.1 I enjoy attending A’ Level Accounting classes 4.2 A’ Level Accounting classes are boring so why should I attend as this as will destroy my psyche for the other classes 4.3 My Accounts teacher knows nothing so I do not attend 4.4 I attend all the A’ Level Accounts classes in the past because the teacher uses techniques that allow us to grasp the principles of the subject matter 4.5 Whenever its time for A’ Level Accounts classes I become nauseous so I go home 4.6 I wished all the other disciplines, courses, were taught like that of the accounts, I like being there 4.7 I oftentimes wished the A’ Level Accounts classes never end 4.8 My A’ Level Accounts teacher has impacted positively on my self concept 4.9 The physical layout of the classroom in which A’ Level Accounts is taught turns me off, so I do not attend 4.10 I will not waste precious time attending A’ Level Accounts classes, when I can spend this time on other subject(s)
  • SECTION 5 DIETARY INTAKE 5.1 How often do you consume the following per week? Tick your choices Frequency Breakfast Lunch Dinner Seven times Six times Five times Four times Three times Two times One time Never SECTION 6 DAILY FOOD INTAKE 6.1 What is your normal food intake for each day; tick your choice(s)? ITEM(S) Pineapple/orange/banana Chicken and parts Apple/beat root/ Fish, other meats Grape Carrot Butter/margarine Cabbage/water Pear Sweet sop/soar sop Coconut Turnip/salad/tomatoes Ackee String beans/string peas/ green Rice/oats peas/broad beans/gongo - PEAS Peanuts/cashew Flour/ wheat bread/ wheat biscuits Milk/eggs Cornmeal/wheat/corn Yam Green bananas Irish/sweet potato(es) Dasheen
  • SECTION 7 INSTRUCTIONAL RESOURCES Read each of the following options, then you are to select the numbered response that best express your choice. KEY 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree 1 2 3 4 5 7.1 I will not buy an A’ Level Accounting text 7.2 I have a minimum of two (2) of the prescribed reading materials in Accountings 7.3 I am very aware of the required texts needed for the examination in Accounting but I have none 7.4 I visit the library at least once a week in order to borrow resource materials in Accounting 7.5 The libraries provide pertinent textbooks and journal in Accounting that I use in my preparation of the subject 7.6 My teacher provides little notes on each topic which cannot be used to problem-solve examinations questions 7.7 I have Examiners’ Reports on Advanced level Accounting 7.8 I have never read an Examiners’ Report on Advanced Level Accounting 7.9 Generally, I revise my notes daily 7.10 I have a copy of the Advanced Level Accounting syllabus 7.11 In the last six (6) months, I have not read the Advanced Level Accounting Syllabus 7.12 Generally, my teacher provides all the solutions to practiced papers and other questions solved in class 7.13 Generally, I frequently use my textbooks in problem-solving questions 7.14 I am not comfortable using a calculator
  • SECTION 8 SELF-CONCEPT Read each of the following options, then you are to select the numbered response that best express your choice. KEY 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree 1 2 3 4 5 8.1 I am proud of my present body weight 8.2 I am glad to know I look this good/attractive 8.3 I would like to take plastic surgery to alter a few aspects of by body 8.4 I am always upset at the accomplishment of others 8.5 I am never angry in being around someone who 8.6 speaks highly of himself/herself 8.7 I am proud of my present body weight 8.8 I am glad to know I look good 8.9 I would like to take plastic surgery to alter a few aspects of by body 8.10
  • SECTION 9 PHYSICAL EXERCISE Read each of the following options, then you are to select the numbered response that best express your choice. KEY 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree 1 2 3 4 5 8.1 I enjoy working out (i.e. physical exercise) at least once per week 8.2 I do not understand why someone would want to become sweaty by exercising 8.3 I just enjoy being physically active 8.4 I do not see the importance of participating in any form of physical exercise, as other activities appear more important Physical exercising is a crucial aspect of my health programme 8.6 Although physical exercise is good for the Human body, I do not participate because On completion I want to sleep Now that we have come to the end of this exercise, I would like to expend my deepest appreciation for your co-operation and involvement in this data gathering process – THANK YOU!
  • RECODING A VARIABLE From the Questionnaire, I will be recoding – Question 4 “What is your mother’s highest level of education?” In SPSS, Question 4 was coded as 1= Primary/All Age 2=Junior High 3=Secondary/High 4=Technical high 5=Vocational 6=Tertiary 7=None In order to know how the variables were coded, we need to use the variable view window
  • Instead of the seven categories, I would like to have – 5 categorization – 1=No formal Education; 2= Primary to Junior High (including All Age); 3=Secondary (including Technical High schools): 4= vocational and 5=Tertiary. Step 3: select Into Different variables Step 1: Step 2: select Transform select Recode
  • Step 4: Identify the variable, in this case Education of parents Use the arrow to take this variable into Input Variable
  • This results from Step4: q4 is now the variable selected to be recoded
  • Step5 Use whatever you want to identify the variable by
  • Step 6: Select change, which gives this dialogues box ‘Recode into Different Variables:
  • In order for the process to be effective, we need to know the old codes following by ‘how we would like the new codes to be. Thus, see the example here: Old Codes 1= Primary/All Age 2=Junior High 3=Secondary/High 4=Technical high 5=Vocational 6=Tertiary 7=None New Codes 1= None 2=Primary/All Age - Junior High 3=Secondary/High to Technical high 4=Vocational 5=Tertiary In order to convert the variables, place the value for the old variable on the Left-hand-side followed by the new value on the right-hand-side, then add (see below)
  • To convert the old 7 to 1, then select add to complete this stage
  • To convert a range of values (for example 1 and 2) – see below Step 3: Place the new value here Then, do not forget to choose add Step 2: Place the lowest value first To convert a range followed by the of values; step 1: last value select range
  • This is the result, and then
  • Having selected continue, this is what results, then choose OK or Paste
  • The next step, is to label the variables
  • Select variable view, then: Select the left of the values for the recoded variable
  • Step1: Place the new value here, for example 1 Step 2: Place 1, then equal, followed by the label of
  • This is ‘what it looks like’
  • Select OK
  • This is to verify what has been done:
  • Dummying a Variable. Creating a dummy variable apply this rule (k – 1), where k denotes the number of categories. Hence, for this case (2 – 1), which means that we can only dummy once. Where one of the two (males or females) will be given 1 and the other 0. Initially, these are the code
  • Use a label, which will be used identify the dummy variable
  • Select label, this gives ‘compute variable Type and Label
  • Identify the variable you seek to label 1, and implied 0 is not stated
  • Step 3: this results Step 2: Use the arrow to take it across Step 1: Select the variable to be dummied, e.g. gender
  • Step 4: Select =, then 2, which we want to be saying I and males 0 Choose either OK or Paste
  • Following the OK or the Paste, this results
  • Now, let use see if this process was done and if it as we intended (Descriptive statistics for the dummy variable gender):
  • Before dummying the variable, e.g. gender, in which we will make 1=female
  • After the process to dummy the variable gender:
  • Dummying a variable that has more that two categories The example that we will use here is educational level, which has four categories – (1) No formal education; (2) Primary or Preparatory level education,; (3) Secondary level education and (4) Tertiary (or post-secondary) level education. Step 1 – In order to know the number of dummy variables that are likely to result from this initial variable (educational level), we need to use the formula – k -1. In the formula, k represents the number of categories that constitute the variable education. In this example, if there are categories. Thus, (k-1 = 4-1=3), the number of dummy categories that are possible are 3. It should be noted here, that one of the category which constitute the initial variable educational level will be used as the reference group. The referent unit will be determined based on literature. Step 2: In this, let us assume that we are seeking to the relationship between educational level of respondents and their wellbeing. Wellbeing is a continuous variable and so, in order to include education within the linear regression model it must be a dummy measure. Therefore, this is what it should like: Educational level Edulevel1 1=Primary, 0=Other or Otherwise Edulevel2 1=Secondary, 0=Other or Otherwise Edulevel3 1=Tertiary, 0=Other or Otherwise The reference group is ‘no formal education. The rationale for this choice is the literature that has established that people with more education have a greater wellbeing. As such, the group that is best suited to be the referent group is ‘no formal education. (Would you like to see how this is done in SPSS? See, below)
  • Reverse Coding Sometimes within the research process, as is the case in the Questionnaire above - using Section 9, the researcher may want to create a single variable, for example in this case Physical Exercise, from a number of sub-questions around a particular topic. However, he/she is hindered by the differences in direction, for example take Q8.1 – this is a positive statement whereas Q8.2 is negative, thus they cannot be summed as they are not compatible. What is done in such instance is called reverse coding. The researcher will decide of the two directions, which he/she is more comfortable working with. In this case, I will choose the positive, which include Q8.1; Q8.3; Q8.4 with Q8.2; Q8.5; and Q8.6 being negative. Having decided to work with the positive, I must now reverse the codes for Q8.2; Q8.5; and Q8.6, in an effort to attain compatibility. (see the process below, the SPSS approach) SECTION 9 PHYSICAL EXERCISE Read each of the following options, then you are to select the numbered response that best express your choice. KEY 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree 1 2 3 4 5 8.1 I enjoy working out (i.e. physical exercise) at least once per week 8.2 I do not understand why someone would want to become sweaty by exercising 8.3 I just enjoy being physically active 8.4 I do not see the importance of participating in any form of physical exercise, as other activities appear more important Physical exercising is a crucial aspect of my health programme 8.6 Although physical exercise is good for the Human body, I do not participate because On completion I want to sleep
  • Step 1: select – Transform, Recode, and Into Different Variables
  • Step 2: Select the variables, which are needed for reverse coding – (the eg here, q8.2; q8.5, q8.6
  • Step 3: Rename the new variable Step 5: Step 4: Then, select change, each time in step 4 State what will be done – reverse afterq8.2; q8.5, and coding for q8.2, etc. q8.6
  • Following the completion of this (step 5) the process will look like this Step 6: Select Old and New values
  • In order for the researcher to complete the process, he/she needs to know ‘how the variables were coded, initially’ – for example 1- Strongly Disagree; 2 – Disagree; 3 – Neutral; 4 – Agree; 5 – Strongly Agree. Reverse coding means that Old values New values 1= Strongly Disagree 5=strongly disagree 2 – Disagree 4=disagree 3 – Neutral 3 = Neutral 4 – Agree 2=Agree 5 – Strongly Agree 1= strongly agree (See how this is done in SPSS, below)
  • Select continue Step 8: Step 7: Select the old value 1 (this is place in the left-hand window; then write the new value 5, in new value; repeat this process for each base on the old and new values, which are written above is executed each time a convert Add is selected,
  • Step9: Select OK or Paste
  • SUMMING CASES: The issue of summing variables must meet two conditions: (1) Variables must be similar, and (2) If they are not, then use reverses coding Note: Having reversed the codes for q8.2, q8.5 and q8.6; it now follows that all 6 questions (q8.1 to q8.6) are positive. (see the SPSS steps below) 1 2 3 4 5 8.1 I enjoy working out (i.e. physical exercise) at least once per week 8.2 I do not understand why someone would want to become sweaty by exercising 8.3 I just enjoy being physically active 8.4 I do not see the importance of participating in any form of physical exercise, as other activities appear more important Physical exercising is a crucial aspect of my health programme 8.6 Although physical exercise is good for the Human body, I do not participate because On completion I want to sleep
  • Summing cases in SPSS (Note in order to sum the cases, we should use those cases such as q8.1, q8.3 and q8.4, which were not reversed along with the reversed once) Step 1: Select – Transform, and then Compute
  • On carrying out step1, this dialogue box appears
  • Step 2: Type a word or phrase that will represent the combined variable (in this case Total_ ph) Step 4: Select continue to move to the next process Step 3: Write the label for the event
  • Step 5: look for the mathematical operation, sum Step 6: Select the Step 6, takes it into the arrow Numeric Expression box (see that output in Step 7, below
  • Step 7: Having select the arrow, it goes to Numeric Expression - SUM(?,?) The question mark should be replaced by each variable, followed by a comma. Note no comma should be placed after the last variable
  • Step 9: Choose those variables that were reversed coded, and are needed for the composite variable Step 8: Select those variables, which were not recoded in the first class but are apart of the computation of the new composite Step 10: variable select either OK or Paste
  • This is the final product of step 10
  • What should be done, now is to ‘run’ the frequency (i.e. the descriptive statistics for this new variable, Index of Physical Exercise) This is the newly created variable, Index of Physical Exercise from the summing and reverse coding processes What the researcher has created in an index (or a metric variable), which can be reduced by recoding
  • DATA REDUCTION (USING A SUMMED VARIABLE) The researcher should note that there were five categorizations, from 1= strongly disagree to 5=strongly agree. Thus, to reduce the Index (the summed variable) into five groupings, we should – do a count of the number of values, which constitute the Index. The example here is 16. The approach that I prefer is to divide the 16 by 5, which gives 3.2. This 3.2 indicates that each category should contain a minimum of three values, with one group housing more than three. Before this process can be executed, the researcher should be aware of what constitutes the least value and the largest number. Based on this case, the standard that should be applied is now the values were coded, using the positive coding (i.e. 1= strongly disagree, 2= disagree, 3=neutral, 4= agree and 5=strongly agree). This means that from 5 to 13 would be 1 or strongly disagree in keeping with the coding scheme; 14 to 16, 2 – disagree; hence, 17 to 19, is 3 i.e.– neutral; from 20 to 22 is 4 or agree and strongly agree would have the following numbers – 23, 24, 25, and 27. (see the SPSS process below).
  • DATA REDUCTION (Having computed by hand the categories, use SPSS to recode the new categorization – this will see the variable remaining as Ordinal) To recode, the calculate values – Step 1: select - Transform, Recode, and Into Different Variables
  • Step 3: Select this arrow, to have the variable placed into the box marked input variable –Output variable box Step 2: Look for the composite variable, which is in the left-hand side dialogue box
  • step 4: write a word for the new variable step 5: optional – describe for labeling step 7: purposes select old and new step 6: values, for the select recoding exercise change
  • Step 8: Select range
  • Step 10: Select 1 as the new value, which represent strongly disagree Step 11: Having selected the step 9: old and new values, Based on the index, the old then select add to value from the calculation complete the process would be from 5 to 13, etc. each time
  • step 13: Select continue step 12: Do the same process for all other values, system missing after the last category (5= 23 to 27)
  • step 14: go to variable view, in order to label the new variable, then values, followed by the labeling in the Values Label box
  • step 15: select OK
  • Final stage: Run the descriptive statistics for the new ordinal variable
  • GOLSSORY Bivariate r – Bivariate correlation and regression assess the degree of association between two continuous variables (i.e. one independent, continuous and a continuous dependent) Concept – This is an abstraction that is based on characteristics of a perceived reality Conceptual (or nominal) definition – this means a statement that encapsulates the particular meaning of a word or concept in a research Correlation - “Correlation is basically a measure of relationship between two variables (Downie and Heath 1970, 86) Correlation - “Correlation is use to measure the association between variables” (Tabachnick and Fidell 2001, 53) Dependent variable – this is the variable with which the study seeks to explain Eta – This is a measure of correlation between two variables; in which one of the variables is discrete. Explanation – This denotes relating variation in the dependent variable to variation in the independent variable Homoscedasticity – Homoscedasticity is a term which is usually related to normality, because when the assumption of normality is attained, in multiple regressions, the association variables are said to be homoscedastic. “For ungrouped data, the assumption of homoscedasticity is that the variability in scores for one continuous variable is roughly the same at all values of another continuous variable” (Tabachnick and Fidell 2001, 79) Hypothesis – This is a testable statement of relationship, which is derived from a theory Independent variable – This is the variable that is used explain the dependent variable. Linearity – This speaks to a straight line relationship between two variables. The issue of linearity holds in Pearson’s Product-Moment Correlation Coefficient, and in multiple linear regressions. In the case of Pearson’s r, linearity is denoted by an oval shaped scatter plot between the DV and the IV. Thus, if any of the variables is non-normal, the scatter plot fails to be oval shaped. Whereas for linear regression, standardized residual when plotted against predicted values, if non-linearity is indicated whenever most of the data-points of the residuals are above the zero line or below the zero line.
  • Logistic Regression – This allows for the prediction of group membership when predictors are continuous, discrete, or a combination of the two. It is used in cases when the dependent variable (DV) is discrete dichotomous variable. Multiple Regression – “Multiple correlation assess the degree to which one continuous variable (the dependent) is related to a set of other (usually) continuous variables (the independent) that have been combined to create a new composite variable” (Tabachnick and Fidell 2001, 18). Furthermore, it should be noted that multiple regression emphasizes the predictability of the dependent variable from a set of independent variables whereas bivariate correlation speaks to the degree of association between the dependent and the independent variable. Nonparametric test – A statistical test that requires either no assumptions or very few assumptions about the population distribution. Operational definition – A specification of a process by which a concept is measured or the measuring rob for a concept Parameter – A specified number of variables to be found within a population. Parametric test – A hypothesis testing that is based on assumptions about the parameter values of the population Pearson’s Product-Moment Correlation, r. -“The Pearson product-moment correlation, r, is easily the most frequently used measure of association and the basis of many multivariate calculations” (Tabachnick and Fidell 2001, 53). Reliability – This denotes the extent to which a measurement procedure consistently evaluates whatever it is to measure 5% level of significance - “With the use of multivariate statistical technique, complex interrelationship among variables are revealed and assessed in statistical inference. Further, it is possible to keep the overall Type I Error rate at, say 5%, no matter how many variables are tested” (Tabachnick and Fidell 2001, 3) Null Hypothesis – Speaks of no statistical relationship (or association) between the variables (i.e. dependent and independent variables) that are being tested in a hypothesis. Validity – this is the extent to which a measurement procedure measures (or evaluates) what it is intended to meaure Variation – speaks to differences within a set of measurements of a variable
  • REFERENCES Aitken, A. C. 1952. Statistical Mathematics, 7th ed. New York: Oliver and Boyd. Alleyne, Sylvan and Benn, Suzette L. 1989. Data collection and presentation in social surveys with special reference to the Caribbean Kingston: Institute of Social and Economic Research. Babbie, Earl, Halley, Fred, and Zaino, Jeanne. 2003. Adventures in Social Research: Data Analysis Using SPSS 11.0/11.5 for Windows, 5th. London: Pine Forge Press. Babbie, Earl. 2001. The Practice of Social Research, 9th. New York, U.S.A.: Wadsworth. Behren, Laurence, Rosen, Leonard J., and Beedles, Bonnie. 2002. A Sequence for Academic Writing. New York, U.S.A.: Longman. Bobko, Philip. 2001. Correlation and Regression: Applications for Industrial Organizational Psychology and Management, 2nd. London, England: SAGE Publications. Boxill, Ian, Chambers, Claudia M., and Wint, Eleanor. 1997. Introduction to Social Research with Applications to the Caribbean. Kingston, Jamaica: Canoe Press. Bryman, Alan and Cramer, Duncan. 2005. Quantitative Data Analysis with SPSS with 12 and 13: A Guide for Social Scientists. East London, England: Routledge. Burnham, Peter; Gilland, Karin; Grant, Wyn, and Loyton-Henry, Zig. 2004. Research Methods in Politics. New York, U.S.A.: Palgrave MacMillan. Chicago University. 2003. The Chicago Manual of Style: The Essential Guide for Writers, Editors, and Publishers, 15th. U.S.A.: Chicago University Press. Chou, Ya-lun. 1969. Statistical Analysis with Business and Economic Applications. U.S.A.: Holt, Rinehart and Winston. Clarke, G. M. and Cooke, D. 2004. A basic course in Statistics, 5 th ed. New York: Oxford University Press Cohen, Jacob and Cohen, Patricia. 1983. Applied Multiple Regression/Correlation Analysis of the Behavioral Sciences, 2nd. New Jersey, U.S.A.: Lawrence Erlbaum Associates. Cohen, L. and Holliday, M. 1982. Statistics for Social Sciences. London, England: Harper and Row. In Bryman, Alan and Cramer, Duncan. 2005. Quantitative Data Analysis with SPSS with 12 and 13: A Guide for Social Scientists. East London, England: Routledge. Corbett, Michael and Le Roy, Michael. 2003. Research Methods in Political Science: An Corston, Rob and Colman , Andrew. 2000. A Crash Course in SPSS for Windows. Crawford, J., and Chamber, J. 1994. A Concise Course in A-Level Statistics with worked Examples, 3rd. London, England: Stanley Thornes. Crotty, Michael. 2003. The Foundations of Social Research: Meaning and Perspective in the Research Process. London, England: SAGE Publications. Dale, Angela, Arber, Sara and Procter, Michael. 1988. Contemporary Social Research. Doing Secondary Analysis. London, England: Unwin Hyman. Daniel, Wayne, W. 1987. Biostatistics: A foundation for analysis in the health sciences, 4th ed. New York: John Wiley.
  • Dawson, Catherine. 2002. Practical Research Methods: A User-friendly guide to mastering research techniques and projects. Oxford, United Kingdom: How to Books. de Vaus, David. 2002. Analyzing Social Science Data. London, England: SAGE Publications. Evans, Omri I. 1992. Statistics made Simple for Students of Social Sciences and management, 2nd. Kingston, Jamaica: Packer-Evans and Associates. Flick, Uwe. 2006. An introduction to qualitative research, 3rd. London, England: SAGE Publications. Francis, A. 1995. Business Mathematics and statistics. London: DP Publications. Freeman, Lincoln. 1965. Elementary applied statistics. New York: John Wiley. Furlong, Nancy, Lovelace, Eugene, and Lovelace, Kristen. 2000. Research Methods and Statistics: An Integrated Approach. U.S.A.: Harcourt College Publishers. George, Darren, and Mallery, Paul. 2003. SPSS for Windows Step by Step: A Simple Guide and Reference 11.0 Update, 4th. U.S.A.: Pearson Education. Goode, W. J. and Hatt, P.K. 1952. Methods in social research. New York: McGraw-Hill. Hair, Joseph F. Jr., Anderson, Rolph E., Tatham, Ronald L., Black, William C. 1998. Multivariate Data Analysis, 5th. New Jersey, U.S.A.: Prentice Hill. Hakim, Catherine. 1987. Research design. Strategies and choices in the desgn of social research. London: Unwin Hyman. Hill, R. Carter, Griffiths, William E., Judge, George G. 2001. Undergraduate Econometrics, 2nd. U.S.A.: John Wiley and Sons. Hogg, Robert V., and Tanis, Elliot A. 2006. Probability and Statistical Inference, 7th ed. New York: Upper Saddle River. Hult, Christine A. 1996. Research and writing in the Social Sciences. U.S.A.: Allyn and Bacon, Pearson Education. Jackson, Barbara B. 1983. Multivariate Data Analysis: An Introduction. U.S.A.: Richard D. Irwin. Kendall, Philip C., Butcher, James N., Holmbeck, Grayson N. 1999. U.S.A.: John Wiley and Sons. King, G., Keohane, R., and Verba, S. 1994. Designing Social Inquiry: Scientific Inference in Qualitative Research. Princeton, New Jersey, U.S.A.: Princeton University Press. Kish, Leslie. 1965. Survey Sampling. U.S.A.: John Wiley and Son. Klecka, William R. 1980. Discriminant analysis. London: Sage. Kleinbaum, David G., Kupper, Lawrence L., Muller, Keith E. 1988. Applied regression analysis and Other Multivariable Methods, 2nd. Boston, U.S.A.: PWS-KENT Publishing. Larson, Ron, and Farber, Betsy. 2003. Elementary statistics. Picturing the world, 2nd ed. New Jersey: Prentice-Hall. Lee, Eun S., Forthofer, Ronald N., and Lorimor, Roanld J. 1989. Analyzing Complex Survey Data. U.S.A.: SAGE Publications. Lewis-Beck, Michael S. 1980. Applied Regression: An Introduction. London, England: SAGE Publications. Magidson, Jay ed. 1978. Analyzing Qualitative/Categorical Data: Log-Linear Models and Latent Structure Analysis, 3rd. Massachusetts, U.S.A.: Abt Associates.
  • Marsh, Catherine. 1988. Exploring data: An Introduction to data Analysis for Social Scientists. Oxford, United Kingdom: Polity Press and Basil Blackwell. Maxwell, A. E. 1970. Basic statistics in behavioural research. London: Penguin Education. McClave, James T., Benson, P. George, and Sincich, Terry. 2001. Statistics for Business and Economics, 8th. New Jersey, U.S.A.: Prentice Hall. McDaniel, Samuel A. 1999. Your Statistics: The Easy Way. Kingston, Jamaica: Samuel A. McDaniel. McNabb, David E. 2004. Research Methods for political Science: Quantitative and Qualitative Methods. London, England: M.E. Sharpe. Miller, Delbert C. 1970. Handbook of research design and social measurement. New York: David McKay . Miller, Scott A. 1998. Developmental research methods, 2nd. New Jersey, U.S.A.: Prentice-Hall. Moser, C. A. and Kalton, G. 1971. Survey methods in social investigation. London: Heinemann Educational Books. Nachmais, David and Nachmias, Chava. 1987. Research Methods in the Social Sciences, 3rd. U.S.A.: St. Martin’s Press. Neuman, William L. 2003. Social Research methods Qualitative and Quantitative Approahes, 5th. U.S.A.: Allyn and Bacon. Neuman, William L. 2003. Social Research methods Qualitative and Quantitative Approaches, 5th. U.S.A.: Allyn and Bacon. Neuman, William L. 2006. Social Research methods Qualitative and Quantitative Approaches, 6th. U.S.A.: Pearson Education. Norušis, Maria J. 1988. The SPSS Guide to Data Analysis for SPSS/PC+. Chicago, U.S.A.: SPSS Inc. . Powell, Lawrence A., Bourne, Paul, and Waller, Lloyd. 2007. Probing Jamaica’s Political Culture: Main Trends in the July-August 2006 Leadership and Governance Survey, Volume 1. Kingston, Jamaica: Centre for Leadership and Governance. Ramjeesingh, D. H. 1990. Introduction to probability theory, 2 nd ed. Kingston: CFM publications. Ross, Sheldon M. 1996. Introductory statistics. U.S.A.: McGraw-Hill. Roundtree, Kathryn and Laing, Tricia. 1996. Writing by Degrees: A Practical Guide to Writing Thesis and Research Papers. Auckland, New Zealand: Addison Wesley Longman New Zealand. Rubin, Donald. 1987. Multiple Imputation for Nonresponse in Survey. New York, U.S.A.: Wiley and Sons. Rummel, Rudolph J. 1970. Applied Factor Analysis. Evanston, U.S.A.: Northwestern University Press. Runyon, Richard P., Haber, Audrey, Pittenger, David J., and Coleman, Kay. 1996. Fundamentals of Behavioral Statistics, 8th. New York, U.S.A.: McGraw-Hill. Stacy, Margaret. 1969. Methods of social research? Pergamon Press. Stevens, James. 1996. Applied Multivariate Statistics for the Social Sciences, 3rd. Mahwah, New Jersey, U.S.A.: Lawrence Erlbaum Associates.
  • Stevens, James. 1999. SPSS for Windows 8.0 supplement for Applied Multivariate Statistics for the Social Sciences, 3rd. New Jersey.: Lawrence Erlbaum Associates. Stevens, Stanley S. 1946. “On the Theory of scales of measurement”. Science, 103: 670-680. Stevens, Stanley S. 1958. “Measurement and Man.” Science, 127: 383-389. Stevens, Stanley S. 1968. “Measurement, Statistics, and Chemapiric view”. Science, 161: 845-856. Tabachnick, Barbara G., and Fidell, Linda S. 2001. Using Multivariate Statistics, 4th. MA., U.S.A.: Pearson Education. Thirkettle, G.L. 1988. Weldon’s Business Statistics and Statistical Method, 9th. London, England: Pitman. Thirkettle, G.L. 1988. Weldon’s Business Statistics and Statistical Method, 9th. London, England: Pitman. Watson, Collin J., Billingsley, Patrick, Croft, D.J., and Hutsberger, David, V. 1993. Statistics for management and Economics, 5th. MA., U.S.A.: Allyn and Bacon. Welkowitz, Joan, Ewen, Robert B., and Cohen, Jacob. Introductory Statistics for the Behavioral Sciences, 5th. U.S.A.: Harcourt Brace College. Wilhoit, Stephen W. 2004. A brief guide to Writing from reading, 3rd. U.S.A.: Pearson Willemsen, Eleanor W. 1974. Understanding statistical reasoning. San Francisco, U.S.A.: W. H. Freeman. Yamane, Taro. 1973. Statistics, An Introductory Analysis, 3rd. New York, U.S.A.: Harper and Row.
  • APPENDIX I: LABELING NON-RESONPONSES This may be addressed in any of the two ways: i) In the event that the variable is a single-digit, the following holds – For ‘don’t know’ use ‘8’ or ‘-8’ In the case the respondent refused to answer, use ‘9’ or ‘-9’ If the interviewee used ‘not applicable’ or NAP, use 97 or ‘-97’ ii) In the event that the variable is two-digit, the following holds – For ‘don’t know’ use ‘98’ or ‘-98’ In the case the respondent refused to answer, use ‘99’ or ‘-99’ If the interviewee used ‘not applicable’ or NAP, use 97 or ‘-97’
  • APPENDIX II: ERRORS IN DATA This table should be used in order to establish correctness of a statistical decision Table: Have We Made the Correct Statistical Decision STATISTICAL RESEARCHED OUTCOME Reject Ho Fail to reject Ho REALITY: Type I Error40 Correct Decision (α ) ( 1- α) Ho – True (in the population) Ho - False Correct Decision Type II Error41 (using the population information) ( 1- β) (β ) (See for example de Vaus 2002; Bobko 2001; Tabachnick and Fidell 2001; Willemsen 1974). Social researcher unlike natural scientists (for example, medical practitioners, chemists) may not understand the severity and importance of not making a Type II error because their may not result in physical injury or mortality, but this is equally significant in social sciences. When a social scientist (for example a pollster) make prediction of say 40 Type I error, α, is the probability of rejecting the null hypothesis when it is true (see for example Steven 1996, 3) 41 Type II error, β, denotes the probability of accepting the Ho, when it is false (see for example, Steven 1996, 7)
  • a particular party winning an election based on Type I error, this may be embarrassing, when in actuality of the election proves him/her otherwise. On the other hand, if he/she we to fail to predict the results based on the findings, failing to reject Ho, then this is equally disenchanting for the statistician. Type I error may be as a result of (1) unreasonable sample size, and/or (2) the level of the significance, α. Thus, it may be prudent for the researcher to change α from 0.05 (5%) to 0.10 or 0.15, when the sample size is small (n ≤ 20). It should be noted that, whenever we increase α, we reduce β and vice versa. With such a possibility, it is in the researcher’s best interest to achieve the right balance, α and β. Because a Type II error is so severe, if the researcher knows what this is, then can establish the statistical power ( 1 – β), which is the probability of accepting the H , 1 when the H0 is false. This is simply, the power of making the right decision. Furthermore, there is an indirect relationship between the sample size and the power. Thus, a small sample size is associated with a low power (i.e. probability of being correct), whereas a large sample size ( n ≥ 100), relates to a high power (1 – β).
  • APPENDIX III: This research, a negative correlation between access to tertiary level education and poverty status controlled for sex, age, union status, area of residence, household size, and relationship with head of household, is primarily seeking to determine access to tertiary level education based on poverty, sex, age of respondents, area of residence, household size and educational level of ones parents. As such, the positivists’ paradigm is the most suitable and preferred methodology. Furthermore, the study will test a number of hypotheses by first carefully analyzing the data through cross tabulation – to establish relationship, and then, secondly, by removing all confounding variables. After which, the researcher will use model building in order to finalize a causal model. Hence, the positivist paradigm is the appropriate choice. The positivists’ paradigm assumes objectivity, impersonality, causal laws, and rationality. This construct encapsulates scientific method, precise measurement, deductive and analytical division of social realities. From this standpoint, the objective of the researcher is to provide internal validity of the study, which, will rely totally on the scientific methods, precise measurement, value free sociology and impersonality. The study will design its approach similar to that of the natural science by using logical empiricism. This will be done by precise measurement through statistics (chi- square and modeling – logistic regression). By using hypotheses testing, value free sociology, logical empiricism, cause-and-effect relationships, precise measurement through the use of statistics and survey and deductive logical with precise observation,
  • this study could not have used the interpretivists paradigm. As the latter seeks to understand, how people within their social setting construct meaning in their natural setting which is subjective rather than the position taken in this research – an objective stance. Conversely, this study does not intend to transform peoples’ social reality by way of empowerment but is primarily concerned with unearthing a truth that is out there and as such, that was the reason for the non-selection of the Critical Social Scientist paradigm. METHODS A secondary data set (Jamaica Survey of Living Conditions – JSLC) from the Planning Institute of Jamaica and Statistical Institute of Jamaica was used for the analysis of the variables. Data were analyze using SPSS (Statistical Packages for the Social Sciences) 12.0. Firstly, prior to the bivariate analyses that were done, univariate frequency distributions were done so as to pursue the quality of the specified variables. Some variables were not used because, the non-response rate was high (i.e. >20%) or the response rate was low (i.e. < 80%). In addition, before a number of variables were further used in multivariate analysis, because they were skewed, first, they were logged to attain normality. Secondly, the researcher selected ages that were greater than or equal to 17 years, because this is the minimum age at which colleges and university accept entrants. Thirdly, the independent variables were chosen based on their statistical significance from a bivariate analysis testing and on the literature. Next, logistic
  • regression analysis was performed in order to identify the determinants of access to education of poor Jamaicans. Chi-square analysis is used in determining whether any meaningful association exist between choiced variables so that will be to construct a model in regard to the poor’s ability to access tertiary level education. Variables that are found significant will be used in the regression modeling equation. Table 4.(i) and 4 (ii) provides an overview of the variable under discussion, after which cross-tabulations are presented in setting a premise for the model in Table 4.0. CONCEPTUAL DEFINITION Access – According to UNESCO “Access means ensuring equitable access to tertiary education institutions based on merit, capacity, efforts and perseverance”. For this study, the variable of access to post-secondary education is conceptualized as the number of persons beyond age 16 years who are attending and have attended universities and colleges, highest level of examination passes of post 16 year-olds, number of schooling years attending of people who are older than 16 years, and approval of loans from the Students’ Loan Bureau (SLB). Hence, Access to tertiary education will be measured based on: (1) one half of the highest level of examination passed and one half of the school attending. The primary reason behind this is due to the number of missing cases or valid responses for persons who are applied to the loans from SLB. Where less than 1 percent of the sampled population has received grants from SLB, or no more than 5 percent applied for SLB grants or loans.
  • GENERAL HYPOTHESIS There is a negative correlation between access to tertiary level education and poverty controlled for sex, age, area of residence, household size, and educational level of parents SPECIFIC HYPOTHESES  Ho: Reduction in poverty does not result in greater access to tertiary level education; Ha: Reduction in poverty results in greater access to tertiary level education;  Ho: If one is poor, gender does not influence access to tertiary level education; Ha: If one is poor, gender influences access to tertiary level education;  Ho: Poor people who reside in rural zones have less access to tertiary level education than those in urban zones ; Ha: Poor people who reside in urban zones have greater access to tertiary level education than those in rural zones;  Ho: there is a positive association between age of respondents and access to tertiary level education; Ha: there is a negative association between age of poor respondents and access to tertiary level education;  Ho: there is a positive association between typologies of relationship with head of household and access to tertiary level education; Ha: there is a positive association between typologies of relationship with head of household and access to tertiary level education;
  •  Ho: there is a direct relationship between increasing household size and access to tertiary level education; Ha: there is an indirect relationship between increasing household size and access to tertiary level education; OPERATIONALIZATION AND DATA TRANSFORMATION DEPENDENT VARIABLE Access to tertiary level education: First, two variables are used to construct this variable (i.e. highest examination passed, b24, and school attending, b21). Secondly, highest examination passed is transformed into two categories – (1) access - 3+ CXC passes and beyond are considered to be matriculation requirement for some tertiary level institution, and (2) no access. School attending is categorized into (i) none tertiary (i.e. secondary level and below) and (ii) tertiary (i.e. vocational institutions, other colleges and universities. Thirdly, a summative function is used to convert the two named variables and then finding one half of each. Finally, the indexing technique is used to finalize the variable, access to tertiary level education. Despite the importance of grants from Students’ Loan Bureau (SLB), the response rate is less than 6 percent, d10b8, in one instance and in another less than 2 percent, d10b8. With this being the case, loans and-or grant from the SLB are not used in this study because of the non-response rate of in excess of 94 and-or 98 percent.
  • INDEPENDENT VARIABLES:  Part B, question 21 “What type of school did… [Name] ….last attends. This is an ordinal variable which when recoded was given a value of “0” for primary education, “1” for secondary and a value of “2” for tertiary level education;  Popquint: This ordinal variable dealt with the five (5) quintiles; poverty is recoded as Poor for quintiles 1 and 2, Lower Middle Class for quintiles 3, Upper Middle Class 4, and Rich for quintile 5. Following this, these are dummied for the regression analysis;  The variable Union Status is a nominal variable, given to question 7 on the Household Roster; it is grouped as was (see Appendix I) in addition to none being included as apart of single. After which each option is dummied for the purpose of the linear regression modeling;  Household size is logged in order to remove some degree of its skewness for regression;  Area: Initially this variable is a nominal one which reads: Kingston Metropolitan Area, Other Towns, Rural and 4 and 5. First, from the frequency distribution there were two categories 4 and 5 that are that the researcher placed into Kingston Metropolitan Area (group 1). Following this process, each of the response was dummied in order for appropriateness in the regression model. Where for KMA “1” denotes KMA and “0” other localities; for Other Towns, “1” represents Other Towns and “0” indicates any other area of residence; for Rural – “1” means rural zones and “0” implies residence outside of the rural classification;  From the Household roster, Round 16, the question, Sex, dichotomous variable) (1) Male, (2) Female, was recoded as Gender, (0) Female (1) Male;  The variable relationship to head of household is a nominal variable with the following categorization: Head, spouse, child of spouse, great grand child, parent of head/spouse, other relative, helper/domestic and other not relative. The variable relationship to head of household, relatn, is dummied for the reason of the regression analysis. The dummy is for each category- where for example i) head of household – “1” for head and “0” for not head; ii) spouse – “1” for spouse and “0” for not spouse; iii) child of spouse – “1” for child of spouse and “0” for not; iv) great grand child – “1” for great grand child and “0” for not; v) parent of head/spouse – “1” parent of head/spouse and “0” for not; vi) helper/domestic – “1” for helper and “0” for not; vii) other not relative – “1” for other not relative and “0” for not.
  •  Age: From the age restriction of tertiary institution on its entrants, the researcher selects the minimum age of 16 years in order to construct an access model of tertiary education. With this complete, the variable is logged because of its skewness. The age variable is people’s ages from 16 years onwards.  The interval variable, Age, located on the Household Roster, is logged (i.e. natural log) in order to reduce its skewness for the multiple linear regression model.
  • APPENDIX IV: EXAMPLE OF AN ANALYSIS PLAN The Statistical Packages for the Social Sciences (SPSS) was used to analyze the data. Cross tabulations was be used to ascertain the relationship between the dependent and the independent variables. The method of analyses was Pearson’s correlation testing that determine if any relationship existed between the variables. Contingency coefficient was be used to determine the strength of any relationship that may exist between variables. The level of significance used is alpha=0.05, at the 95 percent confidence level (CI).
  • APPENDIX V: ASSUMPTIONS IN REGRESSION Regression Model: Parameter (population)  Yi = α + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6+ …+ βnXn + Єi Statistic (sample)  Yi = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + b6X6+ …+ bnXn + ei In order to use ‘a’ and ‘bs’ to accurately infer of the true population values, α, β, the following assumptions will be made of ‘a’ and ‘bs’: (Note: α or a denotes a constant; β1 … βn – where B1 refers to the coefficient of the variable X1 and like). Assumptions of regression 1 No specification error (a) the relationship between Xi and Yi is linear; (b) no germane independent variables are exclusive from the model; (c) no irrelevant independent variables were included 2 No measurement error – the IVs and DV are accurately measured; 3 Assumptions in regard the error term:  zero mean E(Єi) = 0 – the expected value of the error term E(Єi), for each observation, is zero;  Homoskedasticity E(Є2i) = 62 – the variance of the error term is construct for all values of xi;  no autocorrelation E(Єi Єj) = 0, (i≠j) – the error terms are uncorrelated;  the independent variable is uncorrelated with the error term E(Єi Xi) = 0;  normality – the error term, Єi, is normally distributed
  • (See for example, Lewis-Beck 1980; Stevens 1996; Bryman and Cramer 2005; Blaikie 2003; Tabachnick and Fidell 2001; Kleinbaum, Kupper and Muller 1988) APPENDIX VI: STEPS IN ‘RUNNING’ CROSSTABULATIONS STEP TWELVE STEP Analyze the ELEVEN output select paste or ok STEP ONE Assume bivariate STEP TEN STEP TWO in percentage, select – row, Select Analyze column and total STEP NINE HOW TO STEP THREE select cells RUN CROSS Select TABULATIONS descriptive in SPSS? statistics STEP EIGHT STEP FOUR select x2, contingency coefficient and Phi select crosstabs STEP FIVE STEP SEVEN in row place select statistics STEP SIX either DV or IV in column vice versa to Step 5 Figure: Appendix VI
  • In order to illustrate the steps in Figure Appendix VI, I will use the hypothesis, “There is a statistical association between ones state of general happiness and the gender of the respondents” (The variables are general happiness, dependent, and gender, independent) Step 1: Select analyze
  • Step 2: Select ‘Descriptive statistics’
  • Step 3: Select Crosstabs…
  • On selecting Step 3, this dialogue box will open
  • Step 4: From the left-hand side, select the variable that you would like to be in the row(s), I prefer the dependent in this section but there is no rule as to where this should go
  • Step 5: From the left-hand side, select the variable that you would like to be in the column(s), I prefer the independent in this section but there is no rule as to where this should go. However, if the independent variable is place in the row, then the independent goes in the column Step 6: Select ‘Statistics’ – this is where the statistical tests are for crosstabs…
  • On selecting Step 6, this dialogue box opens Step 8: Select continue, then ‘cell’- (i.e. which is at the end of the dialogue box Step 7: Choose the appropriate ‘statistics’ – based on the types of variables, and the number of categories of within each variable
  • Step 10: Select ‘continue’, and either ‘OK’ or ‘Paste’ from Crosstabs dialogue box- Step 9: There is no rule embedded in stone that you should select ‘row’, ‘column’ and ‘total’ as this is dependent on the researcher. Some researcher chooses what is needed; and this is based on where the independent variable is. If the independent variable is placed in the column, then what are really needed are the column and total percentages. On the other hand, if it is in the ‘row’ then row and total percentages are need and nothing else.
  • Final Output – this is on completion of the ten steps above. (See the entire ‘Final Output, below
  • FINAL OUTPUT Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent General Happiness * Respondent's Sex 1504 99.1% 13 .9% 1517 100.0% General Happiness * Respondent's Sex Cross tabulation Respondent's Sex Total Male Female General Very Happy Count 206 261 467 Happiness % within General 44.1% 55.9% 100.0% Happiness % within Respondent's 32.5% 30.0% 31.1% Sex % of Total 13.7% 17.4% 31.1% Pretty Happy Count 374 498 872 % within General 42.9% 57.1% 100.0% Happiness % within Respondent's 59.1% 57.2% 58.0% Sex % of Total 24.9% 33.1% 58.0% Not Too Happy Count 53 112 165 % within General 32.1% 67.9% 100.0% Happiness % within Respondent's 8.4% 12.9% 11.0% Sex % of Total 3.5% 7.4% 11.0% Total Count 633 871 1504 % within General 42.1% 57.9% 100.0% Happiness % within Respondent's 100.0% 100.0% 100.0% Sex % of Total 42.1% 57.9% 100.0%
  • Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 7.739(a) 2 .021 Likelihood Ratio 7.936 2 .019 χ2 = 7.739 Linear-by-Linear 4.812 1 .028 Association N of Valid Cases 1504 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 69.44. n = 1,504, the number of cases used for the cross tabulation Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .072 .021 Cramer's V .072 .021 Contingency .072 .021 Coefficient N of Valid Cases 1504 a Not assuming the null hypothesis. b Using the asymptotic standard error assuming the null hypothesis. Ρ value = 0.021 (The social researcher having got the output from the Cross Tabulations, see above, needs to know the figures which are appropriate for his/her usage. I have said already that we will always analyze with the independent variables, which means: NOTE: χ value is 7.739 (it is taken from the chi-square test table); df (degree of freedom) is 2 (in the chi-square test table); ρ value , 0.021, is taken from the Symmetric measure table and it is the Approx. sig). The case processing summary has a number of vital information: (1) Total sampled population (that is, the number of people interviewed for this study) 1,517 whereas the number of cases which are used for this cross tabulation is 1,504 (i.e. the valid cases) I have been emphasizing that we use the independent values for the analysis of the cross tabulations. See below (using the information in the cross tabulation
  • APPENDIX VII – Appendix 7- Steps in running a trivariate cross tabulation run the SPSS The command hypothesis select the Identify necessary variables from percentage hypothesis select the appropriate conceptualize statistics each variable place independent variables in operationalize column each variable place dependent determine variable in the row determine the dependent independent variables
  • There is a positive relationship between ones perceived social status and income, and that this does not differ based on gender? Step 1 – identification of the variables with the hypothesis – social status, income and gender (note that there are three variables for this hypothesis unlike if it were social status and income, thus this question is a trivariate cross tabulation) Step 2 – define and conceptualize each variable (for this purpose, I will assume that the variables are already conceptualized and operationalized, hence the substantive issue is the ‘running of the cross tabulation’ Step 3 – determine the dependent and the independent variables (dependent – social status; independent variables – income and gender) Step 4 – End – ‘Running the cross tabulations’ – (see illustrations below)
  • Select ‘Analyze’
  • Select ‘analyze’ then ‘descriptive statistics’
  • Having selected ‘analyze’ and ‘descriptive statistics’, then you choose ‘crosstabs..’
  • For this purpose, I will begin with entering the dependent variable first (i.e. entering this with the row space)
  • After which, I will enter the independent variable second (i.e. entering this with the column space) When has just occurred is called, bivariate analysis, using cross tabulations. To continue this into a trivariate relationship, I will enter the third (control variable) in the final entry box. (see example, below)
  • This process illustrates what is referred to trivariate analysis, using cross tabulations (see final steps below)
  • Selecting the Appropriate statistical test
  • Selecting the necessary cell values42 42 In the spaces below the percentage, there is absolutely no need to select ‘row’, ‘column’ and ‘total’ as the appropriateness of this lies in which position the independent variable is placed. Thus, if the independent variable is placed in the column, then what is needed is the column percentage; and if the independent variable is in the row, then we need the ‘row percentage’. Hence, I have only chosen all three because of formatily.
  • The Final Selection, before ‘running the SPSS’ command Gender is the control variable, hence, this becomes trivariate analysis
  • FINAL OUTPUT IN SPSS, PART I Number of cases used for the association Output: Summary of the association
  • FINAL OUTPUT IN SPSS, PART II ‘df’ is the degree of freedom χ2 = 150.00 Ρ value for Ρ value for female, 0.003 male, 0.000
  • APPENDIX VIII – WHAT IS PLACED IN A CROSSTABULATION TABLE, USING THE ABOVE SPSS OUTPUT? Bivariate relationships between general happiness and gender (n= 1,504) GENDER χ 2 = 7.739 Male Female Ρ value Number (Percent) Number (Percent) 0.021 GENERAL HAPPINESS: Very Happy 206 (32.5) 261 (30.0) Pretty Happy 374 (59.1) 498 (27.2) Not Too Happy 53 (8.4) 112 (12.9) Ρ value = 0.021 < 0.05
  • APPENDIX IX– How to run a regression in SPSS?43 STEP TWELVE STEP ELEVEN Analyze the STEP ONE output select paste or Identify all the ok variables STEP TEN STEP TWO select Z RESID determine the for Y; and Z DV and the IVS PRED for X STEP NINE HOW TO STEP THREE select plots RUN A REGRESSION Select analyze MODEL STEP EIGHT STEP FOUR choose select descriptive, regression, then collinearity linear diagnostics STEP FIVE STEP SEVEN place the DV in STEP SIX the space select statistics place the IVs in marked the space for dependent marked Indepenent(s) 43 Before we are able to run a linear regression, ensure that the metric variables are not skewed. Note a linear regression can also be done without using all metric variables. You could dummy, some. The rule for dummy a variable is K – 1. It should be noted that k denotes the number of categories within the stated variable.
  • APPENDIX X– RUNNING REGRESSION IN SPSS Assume that the hypothesis is “Public expenditure on education and health determines level of development” – variables – public expenditure on education; public expenditure on health, and levels of development (which is measured using HDI). For this example, the dependent variable is levels of development (using HDI) and the independent variables are (1) public expenditure on education and (2) public expenditure on health. Select Analyze
  • Step 3: Select Linear Step 2: Select Regression Step 1: Select Analyze
  • Step 5: Select Dependent variable , Human Development Step 4: Select Dependent variable, from the list of variables
  • Step 7: Select Independent variable(s) - Public Exp. on Edu Step 6: Select Independent variable(s), from the list of variables
  • Select Public Exp. on Health
  • Step 9: Select – ‘descriptive’ … Step 8: Select statistics
  • FINAL OUTPUT Correlations Correlations HUMAN DEVELOPM ENT INDEX: 0 = LOWEST PUBLIC HUMAN EXPENDITU DEVELOPM 1990: TOTAL RE ON ENT, 1 = EXPENDITU EDUCATION HIGHEST RE ON AS HUMAN HEALTH AS PERCENTA DEVELOPM PERCENTA GE OF GNP ENT (HDR, GE OF GDP (HDR 1994) 1997) (HDR 1994) PUBLIC EXPENDITURE Pearson Correlation 1 .413** .435** ON EDUCATION AS Sig. (2-tailed) . .000 .000 PERCENTAGE OF GNP (HDR 1994) N 115 114 106 HUMAN DEVELOPMENT Pearson Correlation .413** 1 .395** INDEX: 0 = LOWEST Sig. (2-tailed) HUMAN DEVELOPMENT, .000 . .000 1 = HIGHEST HUMAN DEVELOPMENT (HDR, N 1997) 114 165 142 1990: TOTAL Pearson Correlation .435** .395** 1 EXPENDITURE ON Sig. (2-tailed) .000 .000 . HEALTH AS N PERCENTAGE OF GDP (HDR 1994) 106 142 145 **. Correlation is significant at the 0.01 level (2-tailed). This is the Pearson Level of significance Moment Correlation (Ρ value = 0.000, which is written as Coefficient (0.395) 0.001)
  • Variables Entered/Removedb Variables Variables Model Entered Removed Method 1 1990: TOTAL EXPENDIT URE ON HEALTH AS PERCENT AGE OF GDP (HDR 1994), . Enter PUBLIC EXPENDIT URE ON EDUCATIO N AS PERCENT AGE OF GNP (HDR a 1994) a. All requested variables entered. b. Dependent Variable: HUMAN DEVELOPMENT INDEX: 0 = LOWEST HUMAN DEVELOPMENT, 1 = HIGHEST HUMAN DEVELOPMENT (HDR, 1997) Model Summaryb Adjusted Std. Error of Model R R Square R Square the Estimate 1 .490a .240 .225 .213970 a. Predictors: (Constant), 1990: TOTAL EXPENDITURE ON HEALTH AS PERCENTAGE OF GDP (HDR 1994), PUBLIC EXPENDITURE ON EDUCATION AS PERCENTAGE OF GNP (HDR 1994) b. Dependent Variable: HUMAN DEVELOPMENT INDEX: 0 = LOWEST HUMAN DEVELOPMENT, 1 = HIGHEST HUMAN DEVELOPMENT (HDR, 1997) Coefficient of determination (R2 = 0.240)
  • ANOVA, analysis of variance, with an F test that is significant 0.000 ANOVAb Sum of Model Squares df Mean Square F Sig. 1 Regression 1.472 2 .736 16.072 .000a Residual 4.670 102 .046 Total 6.141 104 a. Predictors: (Constant), 1990: TOTAL EXPENDITURE ON HEALTH AS PERCENTAGE OF GDP (HDR 1994), PUBLIC EXPENDITURE ON EDUCATION AS PERCENTAGE OF GNP (HDR 1994) b. Dependent Variable: HUMAN DEVELOPMENT INDEX: 0 = LOWEST HUMANb2, coefficient of X2, i.e. DEVELOPMENT, 1 = HIGHEST HUMAN DEVELOPMENT (HDR, 1997) Public Exp. on Health, is 0.033 Coefficientsa Unstandardized Standardized Coefficients Coefficients Collinearity Statistics Model B Std. Error Beta t Sig. Tolerance VIF 1 (Constant) .351 .060 5.811 .000 PUBLIC EXPENDITURE ON EDUCATION AS .033 .012 .257 2.707 .008 .825 1.212 PERCENTAGE OF GNP (HDR 1994) 1990: TOTAL EXPENDITURE ON HEALTH AS .033 .010 .322 3.392 .001 .825 1.212 PERCENTAGE OF GDP (HDR 1994) a. Dependent Variable: HUMAN DEVELOPMENT INDEX: 0 = LOWEST HUMAN DEVELOPMENT, 1 = HIGHEST HUMAN DEVELOPMENT (HDR, 1997) Constant, a, 0.351 b1, coefficient of X1, i.e. Public Exp. on Edu. is 0.033 Linear Multiple Regression formula - Y44 = a + b1 X1 + b2X2 + ei (Levels of Development = 0.351 + 0.033* Public Exp on Edu. + 0.033 * Public Exp. on Health) 44 where Y is the dependent variable, and X1 to X2 are the independent variables; with b1 and b2 being coefficients of each variable
  • Scatterplot Dependent Variable: HUMAN DEVELOPMENT INDEX: 0 = LOWEST HUMAN DEVELOPMENT, 1 = HIGHEST HUMAN DEVELOPMENT (HDR, 1997) 2 1 0 -1 -2 R S u d n o g a s e z r t l i -3 -4 -2 0 2 4 Regression Standardized Predicted Value This aspect of the textbook was only to show how a linear regression in SPSS is done, but in order for us to analysis this, this is already done above.
  • APPENDIX XIa – INTERPRETING STRENGTH OF ASSOCIATION This section is not universally standardized, and as such, the student should be cognizant that this should not be construed as such. Thus, what I have sought to do is to provide some guide as to the interpretation of the value for Phi, or Cramer’s V, or Contingency Coefficient just to name a few: Interpreting Phi, Lambda, Cramer’s V, Contingency Coefficient, et al. Very weak: Weak: Moderate: Strong: Very strong: 0.00 – 0.19 0.20 - 0.39 0.40 – 0.69 0.70 – 0.89 0.90 – 1.00
  • APPENDIX XIb – INTERPRETING STRENGTH OF ASSOCIATION Over the years, I have come to the realization that the aforementioned valuations on the strength of statistical correlations can be modified to: Interpreting Phi, Lambda, Cramer’s V, Contingency Coefficient, et al. Weak: Moderate: Strong: 0.00 – 0.39 0.40 - 0.69 0.70 – 1.00
  • APPENDIX XII – SELECTING CASES Sometimes a researcher may need information on a specific variable. The example here is, let us say I need information on only males. I could select cases for males. In this case 1=males, so
  • Step 1: select data Step 2: choose – select cases
  • Step 3: select if
  • Step 5: Take this here Step 4: select gender select arrow Step 5:
  • step 6: Choose =, then the value for the which you need to select, in this case 1, which is for males
  • Step 7: select continue
  • Step 8: select OK or Paste
  • The result will be something that looks like this, where the select cases are marked (meaning information for only males It should be noted that having selected cases for males, any information that is forthcoming would be those for only males, the selected cases. To undo this process (see below)
  • APPENDIX XIII – ‘UNDO’ SELECTING CASES Step 2: Step 1: Choose select cases select data
  • Step 4: select all cases
  • Final step Choose OK or Paste, which then remove the markers
  • APPENDIX XIV – WEIGHTING CASES Sometimes within your research, you may decide to weight the cases owing to sampling issues or insufficient cases to name a few examples. See below for this process: The example here is we have decided to weight the cases by 10 (see Illustration below). Step 1: select Step 10: Transform Step 2: place the weight in the select section marked compute Frequency var. Step 9: Step 3: In the Target choose weight variable, write cases by, on the the word right hand side weight Weighting cases Step 8: Step 4: select the word, In the numeric weight in expression, weight cases type 10 (i.e. the section weight value) Step 7: Step 5: select weight Step 6: select OK or cases Paste select data
  • Step 1& 2: select Compute, then Transform
  • Steps 4 &5: In the Target variable, write the word weigh
  • Step 6: Type the value for the weight, in this case 10. Step 7: select either OK or Paste
  • Following Step 7, it takes you here
  • With this box, observe what I will do with the weight
  • Step 8: Select weight cases by
  • This is referred to as the arrow
  • The dataset is now weighted by 10
  • APPENDIX XV – ‘UNDO’ WEIGHTING CASES Step 1: select data and then weight cases
  • step 2: look for the word weight on the left hand side, window
  • This is what would have existed from the process of weighting the cases, so in order to undo this, see the final set below
  • Final step: select Do not weight cases, then either OK or Paste
  • In the event, the researcher wants to calculate the average or the mean value of say a group of variables. In this case, I would like the find the average score for two test scores. (Variables to be used are – Questions 3.1 In Advanced Level, what were your last two (2) tests scores over the past six (6) months? (1) _______________________ (2) _______________________ Step 1: Select Transform Step 2: Select Compute
  • Use a phrase or word to identify the averaged score Detailed the variable, which is used to identify the variable
  • Select the mean, which is used to calculate the average score for number of variables
  • select, the arrow, which results in
  • Step 2: Separate each variable that will be used by a comma Step 3: Select OK or Paste Step 1: Select each variable from this section, then use the arrow
  • The following will be done to ‘run’ the descriptive statistics for the new variable, called averaged scores
  • APPENDIX XV – Statistical and/or mathematical Symbolism µ - mu – Population mean α - alpha – level of significant; probability of Type I error θ - sigma - β - beta - probability of Type II error 1-β - power Σ - summation – total of a set of observation (i.e. data points) Ν - population (i.e. parameter) – total of all observations of a population n - sample (i.e. statistic) – total of all observations of a sub-set of a population Φ - phi - statistical test, which is used in the event of dichotomous variable Ŷ - predictor of Y ± - plus and/or minus < - less than > - greater than γ - gamma ≤ - less than or equal to ≥ - greater than or equal to ≠ - not equal to ≈ - approximately equal to H1 - alternative hypothesis (i.e. Ha) H0 - null hypothesis r - Pearson’s moment correlation coefficient r2 - coefficient of determination (i.e. strength of a linear relationship) λ - lambda Δ - delta (i.e. incremental change) η - eta ρ - rho χ2 - chi-square
  • APPENDIX XVI – Converting ‘string’ data into ‘numeric’ data Sometimes a researcher may not have entered the data him/herself, and so the data entry operator may use ‘string’ to enter the data in SPSS instead of numeric. From entering the data as ‘string’ it prevents further manipulation of the as the data are not considered as numbers but rather letter (see example below). Before the researcher begins with any form of data analysis he/she should check to ensure that the data are entered as ‘numeric’ and not ‘string data. This is found in the ‘variable view’ window to the end of the SPSS window (see below)
  • Having established that data were entered as ‘string’ data, the researcher can use any of the following options: Apparatus One (i) Use – for example ‘a20’ on each occasion that the variable will be used for any form of analysis (see Figure 1); or Apparatus Two (ii) Convert the ‘string’ into ‘numeric’ data (see Figure 2). In the forthcoming pages, I will seek to provide detailed information on how the processes of converting ‘string’ into ‘numeric’ data’ are achieved using option II.
  • CONVERTING FROM ‘STRING’ TO ‘NUMERIC’ DATA45 END, HERE. STARTING POINT Then, select the right-hand side View the Variable View - to the ‘string’ which is at the the option bottom of the SPSS ‘numeric’. Then – Data Editor OK. Window? Return to Pursue the Data ‘Variable View, to View’, and then establish ‘how go to the data were variable in entered?’ question … If the data were entered as, numbers but the researcher selected ‘string’ Figure 1: CONVERTING FROM ‘STRING’ TO ‘NUMERIC’ DATA: When the data were entered as numbers, only. (See illustration below, the SPSS form) 45 There are instances, when the researcher uses a combination of ‘letters and ‘numbers’. In this case we use Figure 2 instead of Figure 1(See figure 2, below).
  • APPARATUS ONE Step 1 select to the right- hand side of this box
  • Step 2: Having selected the right-hand side to the string for the variable, it produces this dialogue box. Remove the mark from ‘string’ to numeric. (See illustration, below).
  • By select ‘Numeric’, we have deselected ‘string’ Step 3: To execute the command, we select ‘OK’ (Note: The process that has just ended is an illustration of how we address converting ‘string’ data to ‘numeric’ data, if the initially data were entered as number but the data entry clerk had selected ‘string’ in Type instead of ‘Numeric’. (See below, how the combination is handled).
  • CONVERTING FROM ‘STRING’ TO ‘NUMERIC’ DATA END START T In old value type View the the ‘letter’, in Variable View - New value type which is at the the number, then bottom of the OK. SPSS – Data Leave all the Pursue the numeric values, Data View, to and then select the letter in the establish ‘how form it was type data were – SEE END entered?’ If the data were entered as, Select ‘Old and numbers and letters but the researcher New Values’ selected ‘STRING’ Select ‘Transform’, ‘Recode’, then go to ‘Into same variable’ Figure 2: CONVERTING FROM ‘STRING’ TO ‘NUMERIC’ DATA: When the data were entered as numbers and letters.
  • APPPARATUS TWO Step 1: Run the frequency for the variable labeled ‘string’. In this case, the variable is a20.
  • Note: From all indications, the clerk entered 1, 2, 3, 4, 5, and N in the data view. This is the reason for this output. Thus, this ‘string’ can be converted to numeric by (see illustration below).
  • Steps 1 to 3: Select ‘Transform’, ‘Recode’, and ‘Into Same Variables…’
  • Step 4 and 5: Identify the variable on the left- hand side (i.e. the dialogue box), then use the arrow to take it into the space marked ‘Variable’
  • This is the result from executing steps 4 and 5. Step 6: Now the next step is to select ‘Old and New Values…’
  • The researcher needs to understand that the conversion is not for the numeric variables that are present within the data set but for the letter ‘N’, as this was mistakenly recorded by the data-entry clerk. Thus, we are seeking to correct the error. (See below). Step 8: Initially, what the clerk should have been entered was 2; instead he/she used N. Thus, now, we select New Value and type the number 2. Step 9: In order that this command can be recorded, we need to select ‘Add’, which takes it into the dialogue box marked Step 7: ‘Old→New’. On completion, you should select ‘continue’ then The mistake was using capital ‘n’ instead of ‘OK’ which will then execute the no, which was coded as two. Note whatever is command. used in the first instance must be entered herein. (See page 399, N).
  • This is the output for the variable that had a combination of ‘string’ and ‘numeric’ data pre the conversion exercise. On completion of the steps carried out earlier, this is the result of what the variable looks like post the exercise. There is no more ‘N’ of 44 case, it is now in two, which has increased by 44 cases (i.e. the frequency of two was 464, with the additional 44 cases it becomes 508. Having used the steps above, the researcher will then perform the final step by converting the variable from ‘string’ to ‘numeric’ data. using Apparatus One.
  • APPENDIX XVII – Running Spearman Step 1: Step 1: Select Analyze Select Analyze →→ correlate correlate → bivariate → bivariate Step 4: Step 2: Use either OK or In order to run a an ordinal against an paste to execute ordinal variable, you the command Steps in running should deselect chosen in step 3 Spearman rho Pearson and choose Spearman Step 3: Highlight and Highlight and choosethethe ordinal choose variablesordinal variables from the left-hand-side, then use the arrow between left-hand and from the left- right-hand side to select the variables hand-side, then in the dialoguethe on the right hand box arrow use side that between left-hand was empty Figure: Steps to following to performing Spearman’s ranked ordered Correlation
  • Step 1: Select analyze, then correlate and followed by bivariate…
  • Step 2: By default the computer shows Pearson, in order to run a an ordinal against an ordinal variable, you should deselect Pearson and choose Spearman
  • Step 3: Highlight and choose the ordinal variables from the left- hand-side, then use the arrow between left-hand and right- hand side to select the variables in the dialogue box on the right hand side that was empty Step 4: Use either OK or paste to execute the command chosen in step 3
  • Final Output from the entire step executed above Given that there is no relationship from a noted sig. ( 2- tailed) that is more than 0.05, correlation coefficient is not used as there is no The sig. (2-tailed) of 0.704 is association to used to state whether a establish strength relationship exists at the 0.05 and/or direction level of significance
  • APPENDIX XVIII – Running Pearson Step 1: Step 1: Select Analyze Select Analyze →→ Correlate correlate → bivariate → Bivariate Step 4: Step 2: Use either OK or paste to execute Select a set of metric variables, which are the command Steps in running normally distributed chosen in step 3 Pearson Step 3: Highlight and Highlight and choose the metric choose the variablesordinal variables from the left-hand-side, then use the arrow between left-hand and from the left- right-hand side to select the variables hand-side, then in the dialoguethe on the right hand box arrow use side that between left-hand was empty Figure: Steps to following to performing Pearson’s Product moment Correlation
  • Step 1: Select analyze, then correlate and followed by bivariate…
  • Step 2: By default, the computer shows Pearson, this should be left alone
  • Age Income ∙
  • Pearson Age Income
  • APPENDIX XIX – CALCULATING sampling errors from sample sizes Students should be aware that despite the scientificness of statistics, the discipline recognizes that by seeking to predict events (behavioural or otherwise), there is a possibility of making an error. This is equally so when deciding on a particular sample size. se = z√ [(p %( 100-p %)] √s Symbols and their meanings: se = sampling error (i.e. the percentage of error that the researcher is prepared to accept or tolerate) s = sample size (or n) z = the number relating to the degree of confidence you wish to have in the result: (note 95% CI, z= 1.96; 99% CI, z=2.58; and 90% CI, z=1.64) p = an estimated percentage of people who are into the group in which you are interested in the population In order to illustrate the usage of the above formula, we will give an example. Here for example, assume that from a sample of 500 respondents (s or n), 20% of people will vote for the PNP/JLP in the upcoming elections (p – percentage or proportion). What is the sampling error, using a 95% confidence level? se = 1.96√(20(80)) √ 500 Interpretation of the results: The result from the formula is 3.5% (this can either be positive or negative). The value denotes, ergo, that based on a sample of 500 Jamaicans, we can be 95% sure that the true measure (e.g. voting behaviour) among the whole population from which the sample was drawn will be within +/-3.5% of 20% i.e. between 16.5% and 23.5%.
  • APPENDIX XX – CALCULATING sample size from sampling error(s) One of the fundamental requirements of executing social (or natural science) research is selecting a sample. The researcher must decide on how many people (or subjects or participant) that she/he would like to survey, interview or speak with in regard a particular subject matter. In quantitative studies, the researcher must select from a population (i.e.) a subpopulation (sample) with which s/he is interesting to garner germane information. There are two formulae that are available to the researcher. Formula One n = (z / e) times 2 Symbols and their interpretations: n = the sample size z = the value for the level confidence level. Researchers frequently use a 95% confidence level, but this is not carved in stone. Other confidence levels can be used such as 99% and its ‘z’ is 2.58; 95% confidence with a ‘z’ value of 1.96; ‘z’ = 1.64 for 90% confidence and 1.28 for 80% confidence. e = the error you are prepared to accept, measured as a proportion of the standard deviation (accuracy) For a better understanding of this situation, we will use an illustration. The example here is, assume that we are estimating mean weight of a women in Lucea, Hanover, and that we wish to identify what sample size to aim for in order that we can be 95% confident in our result. Continuing, let us assume that we are prepared to accept an error of 10% of the population standard deviation (previous research might have shown the standard deviation of income to be 8000 and we might be prepared to accept an error of 800 (10%)), we would do the following calculation: n = 2(1.96 / 0.1) Therefore s = 384.16. As such, we should use 385 people. Because we interviewed a sample and not the whole population (if we had done this we could be 100% confident in our results), we have to be prepared to be less confident and because we based our sample size calculation on the 95% confidence level, we can be confident that amongst the whole population there is a 95% chance that the mean is
  • inside our acceptable error limit. There is of course a 5% chance that the measure is outside this limit. If we wanted to be more confident, we would base our sample size calculation on a 99% confidence level and if we were prepared to accept a lower level of confidence, we would base our calculation on the 90% confidence level.` Formula Two n = z2 (p (1-p)) e2 Symbols and their interpretations: n = the sample size z = the number relating to the degree of confidence p = an estimate of the proportion of people falling into the group in which you are interested in of the population e = the proportion of error that the researcher decides to accept We will use a hypothetical case of voters to illustrate the use of this formula, which is different from Formula One. If we assume that we wish to be 99% confident of the result i.e. z = 2.85 and that we will allow for errors in the region of +/-3% i.e. e = 0.03. But in terms of an estimate of the proportion of the population who would vote for the PNP/JLP candidate (p – proportion and not party abbreviation), if a previous survey had been carried out, we could use the percentage from that survey as an estimate. However, if this were the first survey, we would assume that 50% (i.e. p = 0.05) of people would vote for candidate X and 50% would not. Choosing 50% will provide the most conservative estimate of sample size. If the true percentage were 10%, we will still have an accurate estimate; we will simply have sampled more people than was absolutely necessary. The reverse situation, not having enough data to make reliable estimates, is much less desirable. In the example: s = 2.582(0.5*0.5) = 1,849 0.032 This rather large sample was necessary because we wanted to be 99% sure of the result and desired and desired a very narrow (+/-3%) margin of error. It does, however reveal why many political polls tend to interview between 1,000 and 2,000 people.
  • APPENDIX XXI – Sample sizes and their sampling errors One thing that must be kept in mind when doing research that there is truth that errors are ever present with sampling or for that matter equally existing in census data. With this recognition, the researcher must now plan what is an acceptable sampling error that she/he wants from a certain sample size. Thus, the choice of a sample size should not be arbitrary but it should be based on – (i) the degree of accuracy that is required from the selected sample size, and (ii) the extent with which there is a variation in the population with regard to the principal features of the study. We will now provide a listing of sample sizes and their appropriate sampling error, assuming that we are using the 95% level of confidence (i.e. confidence level - CI). Table 1: Sample errors and their appropriate sample sizes, using a CI of 95%46 Sample Error (in %) Sample Size Sample Error (in %) Sample Size 1.0 10000 6.0 277 1.5 4500 6.5 237 2.0 2500 7.0 204 2.5 1600 7.5 178 3.0 1100 8.0 156 3.5 816 8.5 138 4.0 625 9.0 123 4.5 494 9.5 110 5.0 400 10.0 100 5.5 330 Interpretation: This is simple, do not be scared, as 1.0% which is beneath sample error corresponds to a sample size of 10,000 respondents (or subject or participants or interviewed). Continuing, if one were to select a sample size of 277 participants for a survey, using 95% confidence level, then she/he is expected to have a sample error 6.0%. It should be noted that Table 1 above, assumes a 50/50 split for the sample size (i.e. this should be used if the researcher is unsure what the proportion of population might be that she/he intends to study). 46 In attempting to make this text simple, we have sought to provide the easy way to understand complex materials. Thus, the calculation of Table above can be done by inputting the figures (the sample size 10,000 and 50% sample proportion in space provided on (http://www.dssresearch.com/toolkit/secalc/error.asp), and no figure should be placed in total population, because this is in keeping with the assumption that the researcher does not know this. Note 50% produces the largest likely variation.
  • APPENDIX XXII – Sample sizes and their sampling errors Table 1: Sample errors and their appropriate sample sizes, using a CI of 95% Sample Error (in %) Sample Size47 Sample Error (in %) Sample Size 0.6 10000 3.4 277 0.8 4500 3.6 237 1.1 2500 3.9 204 1.4 1600 3.9 200 1.7 1100 4.2 178 2.0 816 4.5 156 2.2 625 4.8 138 2.5 494 5.0 123 2.8 400 5.3 110 3.1 330 5.6 100 Factors which are used in determining a sample size 1) the degree of accuracy required for the sample; and 2) the extent to which there is variation in the population concerning the key characteristics of the study 47 Table 1 above, assumes a 90/10 split for the sample size (i.e. we are assuming that the sample represents a 10% of the population - the proportion of population is 10%). 475
  • APPENDIX XXIII – If conditions In order that we will be able to make to grasp the understanding of this ‘If conditionalities’ in research, we will present a frequency tables of tow univariate factors – (i) gender and (ii) age of the sampled group. Table 1: Gender of the respondents Frequ Cumulative ency Percent Valid Percent Percent Valid MALE 59 43.4 43.4 43.4 FEMALE 77 56.6 56.6 100.0 Total 136 100.0 100.0 Table 2: The age distribution of the sampled population Cumulative Frequency Percent Valid Percent Percent Valid 16 25 18.4 18.5 18.5 17 51 37.5 37.8 56.3 18 40 29.4 29.6 85.9 19 13 9.6 9.6 95.6 20 3 2.2 2.2 97.8 21 1 .7 .7 98.5 22 1 .7 .7 99.3 25 1 .7 .7 100.0 Total 135 99.3 100.0 Missing System 1 .7 Total 136 100.0 To effectively reduce this to micro simplicity, we will be seeking to carryout a command, which is to ascertain young adults (i.e. respondents who are at most 16 years at their last birthday). 476
  • If conditionality (or If condition) are a set of mathematical formulae with which the researcher will write as a programme that upon completion, the computer (using SPSS) will generate the commands which were given it. In order to bridge the challenge of this apparatus to you the reader, we will perform the task through a serious of step. Steps 1 → Go to the SPSS menu bar, where you will see a number of words including ‘File’. Select the ‘File’ by ‘clicking’ on that option 477
  • Steps 2 → Now you would be within the ‘File’ menu bar, and so your next step is to select ‘New’ followed by the word ‘syntax’. It is through this widow that the mathematical formula will be store and manipulated. 478
  • Steps 3 → Because you have selected ‘New’ and ‘syntax’, a program will that is called the ‘syntax’ will now appear (see display below) 479
  • Steps 4 → Note that our objective is to construct a program with which the computer on the given instruction will create a variable called young adults (i.e. respondents who are at most 16 years of age at their last birthday). In order to understand why we have written these jargons, you need to know the end objective. This is a variable which denotes young adults (<or = 16 yrs.). With this in mind, the next step is to write If (the variable which houses gender - i.e. q1 and the value for male – i.e. 1 then and (or &) which is the symbol that speaks to the desire overlap between being young and male) followed by the name of the new variable – i.e. young adults, equals a value which represents young men. On completion of each expression, a period should follow – ‘.’ The same process is carried out for the young female, with a few modifications. These changes are necessary as 2 is the valuation for the female within q1. The next adjustment is the valuation for ‘Young adults’ which must be different from the value given to the males. Hence, this is the why it was called 2 indicate the new label. The final command that is used is the now ‘execute’ followed by period. If you are to highlight and ‘run’ this expression the computer will give you a table with young male ‘1’ and females ‘2’. 480
  • Running the Command 481
  • Comparing the result to ascertain the truthfulness of the operation Table 3: Young_Adults_1 Cumulative Frequency Percent Valid Percent Percent Valid 1.00 16 11.8 64.0 64.0 2.00 9 7.4 36.0 100.0 Total 25 19.1 100.0 Missing System 111 80.9 Total 136 100.0 Note carefully- using the age distribution that only 25 respondents are approximately 16 yrs. old. Table: Age at last birthday Cumulative Frequency Percent Valid Percent Percent Valid 16 25 18.4 18.5 18.5 17 51 37.5 37.8 56.3 18 40 29.4 29.6 85.9 19 13 9.6 9.6 95.6 20 3 2.2 2.2 97.8 21 1 .7 .7 98.5 22 1 .7 .7 99.3 25 1 .7 .7 100.0 Total 135 99.3 100.0 Missing System 1 .7 Total 136 100.0 482
  • Students should be cognizant that cross tabulation can be used to verify the authenticity of the mathematical formula (see below) 483
  • APPENDIX XXIV – The meaning of the ρ value The ρ value speaks to the likelihood that a particular outcome may have occurred by chance. Thus, ρ = 0.01 level of significance, means that there is a 1 in 100 probability that the result may have happened by chance or a 99 in 100 probability that the outcome is a reliable finding. Furthermore, ρ = 0.05 is a 1 in 20 probability (or 5 in 100) probability that the observed results may have appear by chance. Another matter is that a significance level of 0.05 to 0.10, indicates a marginal significance. Social scientists have generally used the rule of thumb of 0.05 level of significance to indicated statistical significance. Thus, when the level of significance falls below 0.05 (e.g. 0.01, 0.001, 0.0001, etc), the smaller the numeric value the greater the confidence of the researcher in speaking about his/her findings (i.e. the findings are valid). I would like for reader to note here that in the social environment (i.e. in particular social sciences), nothing is ever “proved”. This position is not the same in the natural sciences (or physical sciences) as phenomena can be “proved” but in the social space, it can be demonstrated or supported at a certain level of significance (or likelihood). Again, the smaller the ρ value, the greater is the likelihood that the findings are valid. 484
  • APPENDIX XXV – Explaining Kurtosis and Skewness Skewness is a statistically measure that is used by statisticians and researchers to evaluate the distribution of a data. It measures the degree of a distribution of values divide the symmetry around the mean. The value for skewness may be more than zero (i.e. 0) or less than zero; where a value of zero (0) indicates a symmetric or evenly balanced distribution. A value of zero is ideal and in social sciences the realistic values will more likely be ± 1, ±2 or ± ≥3; and a skewness value between ±1 is considered excellent for most social scientists, but some argue that a value between ±2 is also acceptable. The issue of acceptability speaks of value without which no modification is required as it can be used as indicating normality. However, in this text we will use between ±1; and any value more 1 or less than negative 1 is unacceptable as this indicates high skewness. Kurtosis evaluates the “peakness” or the “flatness” of a frequency distribution (or frequency curve). Kurtosis’ value is indicate a similarly to skewness as zero (0) means normality. However, this is idealistic and so the acceptable reality is between ±1, which is considered an excellent mark of normality, and so social scientists cite that this can be between ±2. Nevertheless, in this text we will use between ±1; and any value more 1 or less than negative 1 is unacceptable as this indicates high skewness. 485
  • APPENDIX XXVI – Sampled Research Paper I Health Determinants: Using Secondary Data to Model Predictors of Wellbeing of Jamaicans Paul Andrew Bourne48 Department of Community Health and Psychiatry, Faculty of Medical Sciences The University of the West Indies at Mona, Jamaica Brief synopsis This study broadens the operational definition of wellbeing from physical functioning (or health conditions) to include material resources and income. Secondly, it seeks to provide a detail listing of predisposed variables and their degree of influence (or lack of) on general wellbeing. 48 Correspondence concerning this article can be by email: paulbourne1@yahoo.com or by telephoning (876) – 841-4931 or by mail to Department of Community Health and Psychiatry, Faculty of Medical Sciences, The University of the West Indies, Mona-Jamaica. 486
  • Abstract Objective. During 1880-1882 life expectancy for Jamaican males was 37.02 years and 39.80 for their female counterparts and 100 years later, the figures have increased to 69.03 for males and 72.37 for females. Despite the achievements in increased of life expectancies of the general populace and the postponement of death, non-communicable diseases are on the rise. Hence, this means that prolonged life does not signify better quality life. Thus, this study seeks to examine the quality of life of Jamaicans by broadening the measure of wellbeing from the biomedical to the biopsychosocial and ecological model Method. Secondary data was used for this study. It is a nationally representative sample collected by the Statistical Institute of Jamaica and the Planning Institute of Jamaica in 2002. The total sample is 25,018 respondents of which the model used 1,147. Data was stored and analysed using the Statistical Packages for the Social Sciences (SPSS). Multivariate regression was used to test the general hypothesis that wellbeing is a function of psychosocial, biological, environmental and demographic variables. Results. The model explains 39.3 percentage of the variance in wellbeing (adjusted r2). Among those 10, the 5 most significant determinants of wellbeing in descending order are average number of persons per room (β = -0.254, ρ < 0.001); area of residence (1=KMA), (β = -0.223, ρ < 0.001); area of residence (1=Other Towns), (β = -0.209, ρ < 0.001); and lastly age of respondents (β = -0.207, ρ < 0.001). Those five variables accounted for 27.2 percentage of the model, with average occupancy and area of residence (being KMA) accounted for 7 percentages each. Conclusion. This study has shown that wellbeing is indeed a multidimensional concept. The paper has proven that the determinants of wellbeing include psychosocial, environmental and demographic variables. 487
  • Introduction Many scholars such as Erber (1), Brannon and Feist (2) have forwarded the idea that it is germane and timely for us to use a biopsychosocial construct for the measurement of quality of life. But neither Erber nor Brannon and Feist have proposed a mathematical model that can be used to evaluate this worded construct. This is also similar to and in keeping with the broad definition given by the WHO in 1946 (3), and later promulgated by Dr. George Engel (4-8). However, in 1972, Grossman (9) filled this gap in the econometric analysis to formulate a measurement for health. This was later expanded by Smith and Kington (10,11). Despite the premise set by Grossman, Smith and Kington used physical functioning in their definition of health, which again is a narrow approach to the concept of health and wellbeing. Grossman’s model which was further enhanced by Smith and Kington did not provide us with the relative contribution of each of the determinants of wellbeing. On the other hand, a study by Hambleton et al (12) in Barbados, decomposed the predictors of self-reported health conditions, and found that 38.2% of the variation in health status can be explained by some predisposed variables. Of the variation explained, ‘current health status’ account for 24.5%, lifestyle risk factors, 5.8%, current socioeconomic factors, 2.5% and historical conditions, 5.4%. The composition of the aforementioned groups were (i) Historical indicators – education, occupation, childhood economic situation, childhood nutrition, childhood health, number of childhood diseases; (ii) Current socioeconomic indicators – income, household crowding, currently married, living alone; (iii) Lifestyle risk factors – body mass index, waist circumference, categories of diseases, smoking, exercise and (iv) current Disease indicators – number of illness, number of symptoms, geriatric depression, number of nights in hospitals, number of medical contacts in 4-month period. Again, while Hambleton et al’s work provided explanations that determinants of 488
  • wellbeing expand beyond ‘current disease conditions’ to lifestyle practices and socioeconomic factors using ‘physical functioning’ (i.e. health conditions) in conceptualizing health. This is not in keeping with the WHO expanded definition (3). Such an approach focuses on the mechanistic result of the exposure to certain pathogen which results in ‘disease-causing conditions’. The WHO’s definition has been widely criticized for being elusive and immeasurable because the concept is too broad. On the other hand, the traditional view of the Western culture is such that health means the ‘absence of diseases’ (Papas, Belar & Rosensky (13). However, in the 1950, a psychiatrist, Dr. Engel (4-8), began promoting what he referred to as the biopsychosocial model. He believed that the treatment of mental health must be from the perspective of the body (i.e. biological conditions), mind (i.e. psychological) and sociological conditions. Engel believed that the psychological, biological and social factors are primarily responsible for human functioning. He forwarded the thought that these are interlinked system in the treatment of health care, which is compared to the interconnectivity of the various parts of the human body. Engel believed that when a patient visits the doctor, for example, for a mental disorder, the problem is a symptom not only of actual sickness (biomedical), but also of social and the psychological conditions. He, therefore, campaigned for years that physicians should use the biopsychosocial model for the treatment of patient’s complaints, as there is an interrelationship among the mind, the body and the environment. He believed so much in the model that it would help in understanding sickness and provides healing that he introduced it to the curriculum of Rochester Medical School (14, 15). Medical psychology and psychopathology was the course that Engel introduced into the curriculum for first year medical students at the University of Rochester. This approach to the study and practice of medicine was an alternative paradigm to the biomedical model that was popular in the 1980s and 1990s, and is still popular in 489
  • Jamaica in 2007. In writing about wellness and wellbeing, there are no studies in Jamaica that can definitely state that these are the determinants of wellbeing, or quality of life. Dr. Pauline Milbourn Lynch (16), Director of Child and Adolescent Mental Health in the Ministry of Health in 2003, argued that wellness is “a balance among the physical, spiritual, social, cultural, intellectual, emotional and environmental aspects of life” but, there is no research that put all of these conditions together, and show their relationship with wellbeing. As such, a model was constructed which will be in keeping with the concept of the biopsychological model. This study seeks to examine the quality of life of Jamaicans by broadening the measure of wellbeing and to ascertain possible factors that can be used to predict wellbeing from a biopsychosocial and environmental approach as against the traditional biomedical model (i.e. biological conditions or the absence of pathogens). Theoretical Framework The overarching theoretical framework that is adopted in this study is an econometric model that was developed by Grossman (9), quoted in Smith and Kington (10), which reads: Ht = ƒ (Ht-1, Go, Bt, MCt, ED) ……………………………………… (2) In which the Ht – current health in time period t, stock of health (Ht-1) in previous period, Bt – smoking and excessive drinking, and good personal health behaviours (including exercise – Go), MCt,- use of medical care, education of each family member (ED), and all sources of household income (including current income)- (see Smith and Kington 1997, 159-160). Grossman’s model further expanded upon by Smith and Kington to include socioeconomic variables (see Equation 3). Ht = H* (Ht-1, Pmc, Po, ED, Et, Rt, At, Go) …. ……………………… (3) 490
  • Equation (i.e. Eq.) (2) expresses current health status Ht as a function of stock of health (Ht-1), price of medical care Pmc, the price of other inputs Po, education of each family member (ED), all sources of household income (Et), family background or genetic endowments (Go), retirement related income (Rt ), asset income (At,) Among the limitations in the use of the biopsychology model that is use by Smith and Kington are psychological conditions and ecological variables. This study is equally limited by many of the variable used in Eq. (2) because data from this study is based Jamaica Survey of Living Conditions (JSLC) and Labour Force Survey (LFS) were not primarily intended for this purpose. The JSLC is a national cross-sectional study which collects data for general policy formulation and so we will not be able to track the individuals over time in order to establish a former health status (17). The updated JSLC and LFS do have information – such as preventative lifestyle behaviour – exercise, family background, and not-smoking. The JSLC, on the other hand, collects data on crime and victimization, environment conditions and household size, room occupancy, gender and age of respondents, which were all important for this modified model from that use by Smith and Kington in Equation 3. W=ƒ ( Pmc , ED, Ai , En, G, M, AR, P, N, O, Ht, T, V,S, HS) ………… (4) Wellbeing of Jamaican W, is the result of the cost of medical care (Pmc), the educational level of the individual, ED, age of the respondents, the environment (En), gender of the respondents (G), marital status (M), area of residents (AR), positive affective conditions (P), negative affective conditions (N), average number of occupancy per room (O), home tenure, (Ht), land ownership(proxy paying property taxes), T, crime and victimization, V, social support, S, seeking health services, HS. Method and Data 491
  • This research uses secondary data [JSLC, 2002)] that is a joint publication of the Planning Institute of Jamaica (PIOJ) and the Statistical Institute of Jamaica (STATIN). Its purpose is to divulge the efficiency of public policy on the Jamaican economy. The survey was carried out between June-October, 2002; it is a subset of the Labour Force Survey (i.e. ten percent). Of a population of 9,656 households, the sample size used for the JSLC was 6,976 households. The instrument (i.e. questionnaire) was categorized based on demographic char