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# Quantitative techniques in research

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### Quantitative techniques in research

1. 1. Quantitative Techniques in Research: Statistic in One day Carlo Magno, PhD Lasallian Institute for Development and Educational Research
2. 2. Objectives  Decide on what statistics to use given a set of data  Use appropriate statistics in studies that will be conducted (long term).  Use statistica to conduct some statistical analysis
3. 3. Outline  Considerations in the selection of statistics to use.  List of statistics  Examples in using the statistics
4. 4.  Read the article on CORI
5. 5. Processing  What was the aim of the study?  What is the independent variable in the first study?  What is the dependent variable it the first study?  How many groups were used in the first study?  How many levels of IV was used in the first study?  How was the DV measured?  How was the data analyzed? What statistics was used?  Why do you think this is the appropriate analysis?  What is the difference between study 1 and 2? Would the analysis change?
6. 6.  When we analyzed the use of the statistics in the study by Guthrie et al., what information did we determine first?
7. 7. What determines the use of statistics? Variables Involved •Independent •Dependent How many groups? •Design •Comparison •Correlating •Effect Levels of Measurement of the variables (IV and DV)
8. 8. Identify the IV, DV, and design  Case 1: A study compared males and females. More specifically, the study wanted to determine who is higher in verbal ability between the two groups. A test on verbal ability is given for the two groups and the mean scores were compared.  Case 2: The effect of Project-Based Learning (PBL) on the grades of students was studied among college students. It was hypothesized that students will achieve more in the PBL as compared to a group who received pure lecture. The grades of the students were compared at the end of the term.
9. 9. Identify the IV, DV, and design  Case 3: Writing anxiety, writing metacognition, and topic knowledge was used to predict students writing proficiency. Students essays were scored which served as indicator for their writing proficiency. Scales were used to determine writing anxiety, writing metacognition, and topic knowledge.  Case 4: Neophyte and experienced principals, coordinators, and directors were compared on their degree of transformational leadership. A scale measuring transformational leadership was administered to the administrators across 200 school in NCR.
10. 10. Identify the IV, DV, and design  Case 4: Filipino and Korean high school students were compared on their oral proficiency (TOEFL), vocabulary, and reading comprehension in English (English test).  Case 5: The effect of case study method on students critical thinking was studied. The Watson Glaser Critical Thinking Appraisal (WGCTA) was administered as a pretest then the case study method was implemented for the rest of the term. Towards the end of the term, the WGCTA was administered again.  Case 6: The frequencies of SV agreement errors were counted among high school students in the public and private. The comparison was also done among high and low ability students in these two
11. 11. Levels of Measurement A B C D Type of school Ethnicity Gender Socio-economic status Favorite movie from like to least like Ranking of best science fiction stories Perceived highest to lowest reputable universities in terms of research English Ability Math ability Achievement in Science Motivation Stress Self-esteem Self-efficacy temperature Height of children Weight of first graders Length of travel Width of the table Brightness of light
12. 12. Levels of Measurement Nominal Ordinal Interval Ratio
13. 13. Levels of measurement  Three important properties:  Magnitude--property of “moreness”. Higher score refers to more of something.  Equal intervals--is the difference between any two adjacent numbers referring to the same amount of difference on the attribute?  Absolute zero--does the scale have a zero point that refers to having none of that attribute?
14. 14. Types of Measurement Scales Nominal Scales - there must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other. For example - there are two classes for the variable gender -- males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable. Other Examples: country of origin biological sex (male or female) animal or non-animal married vs. single
15. 15. Nominal Scale  Sometimes numbers are used to designate category membership  Example: Country of Origin 1 = United States 3 = Canada 2 = Mexico 4 = Other  However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning
16. 16. Types of Measurement Scales Ordinal Scales - there are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude. For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth. 16
17. 17. Ordinal Scales  Does not assume that the intervals between numbers are equal Example: finishing place in a race (first place, second place) 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours 1st place 2nd place 3rd place 4th place 17
18. 18. Types of Measurement Scales (cont.) Interval Scales - it is possible to compare differences in magnitude, but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales -- used by most psychological tests. Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5 Example - Celsius temperature is an interval variable. It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius. Notice, however, that 0 degrees Celsius does not have a natural meaning. That is, 0 degrees Celsius does not mean the absence of heat! 18
19. 19. Types of Measurement Scales (cont.) Ratio Scales - captures the properties of the other types of scales, but also contains a true zero, which represents the absence of the quality being measured. For example - heart beats per minute has a very natural zero point. Zero means no heart beats. Weight (in grams) is also a ratio variable. Again, the zero value is meaningful, zero grams means the absence of weight. Example: the number of intimate relationships a person has had 0 quite literally means none a person who has had 4 relationships has had twice as many as someone who has had 219
20. 20. Types of Measurement Scales (cont.) • Each of these scales have different properties (i.e., difference, magnitude, equal intervals, or a true zero point) and allows for different interpretations. • The scales are listed in hierarchical order. Nominal scales have the fewest measurement properties and ratio having the most properties including the properties of all the scales beneath it on the hierarchy. • The goal is to be able to identify the type of measurement scale, and to understand proper use and interpretation of the scale.
21. 21. Types of scales  Nominal scales--qualitative, not quantitative distinction (no absolute zero, not equal intervals, not magnitude)  Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero)  Interval scales--scales that have magnitude and equal intervals but not absolute zero  Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios)
22. 22. Test Your Knowledge: A professor is interested in the relationship between the number of times students are absent from class and the letter grade that students receive on the final exam. He records the number of absences for each student, as well as the letter grade (A,B,C,D,F) each student earns on the final exam. In this example, what is the measurement scale for number of absences? a) Nominal b) Ordinal c) Interval d) Ratio
23. 23. In the previous example, what is the measurement scale of letter grade on the final exam? a) Nominal b) Ordinal c) Interval d) Ratio
24. 24. A researcher is interested in studying the effect of room temperature in degrees Fahrenheit on productivity of automobile assembly workers. She controls the temperature of the three manufacturing facilities, such that employees in one facility work in a room temperature of 60 degrees, employees in another facility work in a room temperature of 65 degrees, and the last group works in a room temperature of 70 degrees. The productivity of each group is indicated by the number of automobiles produced each day. In this example, what is the measurement scale of room temperature? a) Nominal b) Ordinal c) Interval d)Ratio
25. 25. In the previous example, what is the measurement scale of productivity? a) Nominal b) Ordinal c) Interval d) Ratio
26. 26. Select the highest appropriate level of measurement: Bicycle models: 1= Road 2 = Touring 3 = Mountain 4 = Hybrid 5 = Comfort 6 = Cruiser a) Nominal b) Ordinal c) Interval d) Ratio
27. 27. Select the highest appropriate level of measurement: Educational Level: 1 = Some High school 2 =High school Diploma 3 = Undergraduate Degree 4 = Masters Degree 5 = Doctorate Degree a) Nominal b) Ordinal c) Interval d) Ratio
28. 28. Select the highest appropriate level of measurement: Number of questions asked during a class lecture a) Nominal b) Ordinal c) Interval d) Ratio
29. 29. Select the highest level of measurement: Categories on a Likert-type scale measuring attitudes: 1 = Strongly Disagree 2 = Disagree 3 = Neutral 4 = Agree 5 = Strongly Agree a) Nominal b) Ordinal c) Interval d) Ratio
30. 30. Identify the level of measurement  Case 1: A study compared males and females on their verbal ability. More specifically, the study wanted to determine who is higher in verbal ability between the two groups. A test on verbal ability is given for the two groups and the mean scores were compared.  Case 2: The effect of Project-Based Learning (PBL) on the grades of students was studied among college students. It was hypothesized that students will achieve more in the PBL as compared to a group who received pure lecture. The grades of the students were compared at the end of the term.
31. 31. Identify the level of measurement  Case 3: Writing anxiety, writing metacognition, and topic knowledge was used to predict students writing proficiency. Students essays were scored which served as indicator for their writing proficiency. Scales were used to determine writing anxiety, writing metacognition, and topic knowledge.  Case 4: Neophyte and experienced principals, coordinators, and directors were compared on their degree of transformational leadership. A scale measuring transformational leadership was administered to the administrators across 200 school in NCR.
32. 32. Identify the level of measurement  Case 4: Filipino and Korean high school students were compared on their oral proficiency (TOEFL), vocabulary, and reading comprehension in English (English test).  Case 5: The effect of case study method on students critical thinking was studied. The Watson Glaser Critical Thinking Appraisal (WGCTA) was administered as a pretest then the case study method was implemented for the rest of the term. Towards the end of the term, the WGCTA was administered again.  Case 6: The frequencies of SV agreement errors in an essay were counted among high school students in the public and private. The comparison was also done among high and low ability students in these
33. 33. Statistics Used Parametric Non-Parametric •Enables researchers to make assumptions about the population •Large sample size is requires (N>30) •Used for interval and ratio scales •Difficult to make assumptions about the population •Large sample size is not a requirement •Used for nominal and ordinal scales
34. 34. Statistics Used Design Parametric Non-Parametric One sample -the mean of one sample is compared with a standard No. of comparisons: nominal DV: interval/ratio One sample, categories are nominal/ordinal One sample repeated measures (dependent groups) -One sample is studies but more measured twice (2 set of data) - e. g. pre and post test design No. of comparisons: nominal DV: interval/ratio No. of comparisons: nominal DV: nominal/ordinal Two independent groups -studying two distinct samples/groups Groups/IV: nominal DV: interval/ratio Groups/IV: nominal DV: nominal/ordinal Comparing multiple groups (independent or dependent groups) Groups/IV: nominal DV: interval/ratio Groups/IV: nominal DV: nominal Relating one variable to another
35. 35. Statistics Used Design Parametric Non-Parametric One sample -the mean of one sample is compared with a standard z-test t-test One-way chi-square Kolmogorov smirnov One sample repeated measures (dependent groups) -One sample is studies but more measured twice (2 set of data) - e. g. pre and post test design t-test for 2 dependent samples McNemar change test Wilcoxon signed ranks test Two independent groups -studying two distinct samples/groups t-test for 2 independent samples Two-way chi-square Mann Whitney U test Comparing multiple groups (independent or dependent groups) Analysis of Variance (ANOVA) 1 IV, 1 DV: one way ANOVA 2 IV, 1 DV: two way ANOVA 1 more IV, 2 or more DV: MANOVA Kruskal wallis test
36. 36. Case 1  It was hypothesized in a study that students ability in school is related to procrastination. College students were tested using the OTIS Lenon School Ablity Test (OLSAT) and the perfectionism scale by Frost was administered to the same group.  How many variables are studied?  What are the levels of measurement of the variables?  What is the purpose of the study?  What statistics will be used?
37. 37. Data OLSAT (X) Procrastination (Y) 100 99 95 98 90 94 85 87 82 84 80 81 75 78 70 73 65 68 50 60
38. 38. Regression Line between OLSAT and perfectionism S ca tte rp lo t: X vs. Y Y = 1 4 .3 7 9 + .8 5 6 3 3 * X C o rre la tio n : r = .9 8 9 6 6 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 X 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 Y 9 5 % co n fid e n ce
39. 39. Linear Regression  There is a straight line relationship between variables X and Y  When X increases, Y also increases-positive relationship  When X increases, Y decreases or vice versa – negative relationship
40. 40. Correlational Techniques  Pearson Product-Moment correlation – (r) used for interval/ratio sets of variables  Spearman Rank-order correlation – two sets of data are ordinal  Phi coefficient – each of the variables is a dichotomy
41. 41. OLSAT Perfectionism 100 35 95 40 90 45 85 50 75 55 70 60 65 64 60 70 55 76 50 80
42. 42. Relationship between Laziness and Perseverance S ca tte rp lo t: Y vs. X X = 1 3 9 .9 4 - 1 .1 3 8 * Y C o rre la tio n : r = -.9 9 5 9 3 0 4 0 5 0 6 0 7 0 8 0 9 0 Y 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 1 0 X 9 5 % co n fid e n ce
43. 43. Magnitude of the Relationship  Positive relationship – as one variable increases the other variable also increases  Ex. academic grades and intelligence  Negative relationship – as one variable increases, the other decreases or vice versa  Ex. procrastination and motivation  Absence of relationship between variables – denoted by .00 Show computation in statistica
44. 44. Strength of Relationship  A correlation coefficient is computed for a bivariate distribution using a statistical formula Correlation Coefficient Value Interpretation 0.80 – 1.00 Very strong relationship 0.6 – 0.79 Strong relationship 0.40 – 0.59 Substantial/marked relationship 0.2 – 0.39 Low relationship 0.00 – 0.19 Negligible relationship
45. 45. Variance  How much of Y’s is explained/accounted for by X  Proportion explained  Square of the correlation coefficient value
46. 46. Case 2: Spearman rho  Students ranked their degree of importance on poverty alleviation poverty and health policy. Poverty alleviation policy Health policy 14 13 11 12 10 9 10 8 14 10 13 14
47. 47. Case 3: Phi coefficient High Low Own choice 30 20 Others choice 10 40 Teaching Satisfaction Becoming a teacher
48. 48. Case 4: One sample t-test  7 Filipino college students have taken the Test for English as a Second Language (TESL). The researcher wanted to determine if their scores are far from the standard norm among speakers of ESL. The standard norm in the manual is 40.5 with a standard error of 4.54.42 45 46 45 43 46 47
49. 49. Case 5: one way chi-square Errors found F Expected frequency Poor sentence construction 26 21.11 Wrong choice of word 32 21.11 Faulty parallelism 12 21.11 Wrong case 14 21.11 Wrong punctuation 46 21.11 Fragment 8 21.11 Wrong article 16 21.11 Run-on sentence 27 21.11 Wrong verb 9 21.11 Total=190
50. 50. Case 6: Kolmogorov smirnov fo fe Asst. Instructor 25 15.6 Instructor 10 15.6 Ass. Prof 31 15.6 Prof 7 15.6 Full Prof 5 15.6 ft/∑ fo = 78
51. 51. Case 7: t-test for 2 dependent samples  A study investigated whether the effect of problem- based teaching in mathematics would develop students deep approach to learning. The students were first given a pre test using the learning process questionnaire (LPQ) that measures deep approach to learning. The students are exposed to different problems in mathematics before learning concepts and algorithms. After the instruction, the LPQ was again administered to the same 10 students.
52. 52. Case 7: t-test for 2 dependent samples LPQ pre test LPQ post test 24 2 28 30 32 37 18 22 24 29 36 40 40 38 37 41 24 29 20 28
53. 53. Case 8: Wilcoxon signed ranks test  One group of pre-school students were asked to rank a picture by giving the age of a very simple person in a picture without make-up. On a second occasion, the same person in the first picture was again shown but with elaborate clothes and with make-up. Is there a difference in the 2 sets of rankings?
54. 54. Case 8: Wilcoxon signed ranks test Student No. 1st Pic 2nd Pic 1 12 12 2 14 16 3 15 14 4 12 11 5 16 14 6 15 18 7 13 16 8 10 11
55. 55. Case 9: McNemar Change test  An experiment was conducted to determine whether hypnosis can be a clinical intervention to increase students test performance. A test was given and students who passed and failed were identified. The students have undergone hypnosis and after session they were again given an identical test. The students who passed and failed were again identified. Before hypnosis Pass Fail After hypnosis Fail 7 10 Pass 15 20
56. 56. Case 10: t-test for 2 independent samples  The effect of picture-taste association on memory recall was investigated among 30 volunteer college students. The 15 participants in the experiment group looked at 20 pictures matched with the food that they have to taste. The other 15 participants in the control group just looked at the pictures. After the procedure, both groups were tested in their memory where they have to enumerate in order the labels of the pictures they saw.
57. 57. Case 10: t-test for 2 independent samples Experimental group Control group 9 4 14 9 11 3 9 6 12 4 13 2 14 5 9 5 11 4 13 5 11 6 13 6 12 4 14 7 15 8 ∑x1 = 180 ∑x2= 78 1 = 12 2 = 5.2
58. 58. Case 11: Mann-Whitney U test  In the study, 8 single individuals and 7 married individuals were asked to rank their life satisfaction using a ranking scale. Test whether they differ in their rankings. Single Married 40 10 37 75 35 40 37 32 51 25 38 62 42 5 49
59. 59. Case 12: Chi-square  A survey was conducted among 29 prisoners in manila city jail. They were asked crimes that they committed and their educational attainment through a checklist. The following data was tabulated Crimes Committed Educational Attainment Elementary HS College Total Murder 3 7 1 11 Homicide 2 3 6 11 Robbery 1 2 5 8 Total 6 12 12 30
60. 60. Case 13: One-Way ANOVA  In an experiment, the effect of nonbehavioral intervention techniques was investigated on the computational ability of fourth year high school students. The non-behavioral intervention techniques has three levels: bibliotherapy, small group interaction, and games. These techniques were used as a teaching strategy in a lesson in a math class for three sections. Each of the strategy was used for each section. One section did not receive any strategy which served as the control group. After undergoing the strategy, the students were tested where they answered a series of computation items.
61. 61. Case 13: One-Way ANOVA Control bibliotherap y Small group Games 8 14 19 15 9 13 18 15 6 12 19 14 7 15 19 15 2 15 17 13 4 14 18 14 4 13 18 13
62. 62. Self-efficacy Achievement Effect of Achievement and Type of school on self-efficacy Low Achievers High Achievers Type of school Public school Private School Case 14: Two way ANOVA
63. 63. Case 14: Two way ANOVA low achiever high achiever Public 10 15 9 16 5 17 6 15 5 16 Private 15 19 14 20 14 19 13 18 15 18
64. 64. Case 15: MANOVA  Public and Private schools were compared on their self-monitoring and goal-setting Self-monitoring goal-setting Public 10 9 10 8 9 7 7 7 8 5 7 5 6 4 Private 18 17 19 19 18 19 17 18 17 18 18 17 18 18
65. 65. Case 16: Multiple regression  Goal-setting, self-evaluation, seeking assistance, and environmental structuring were used to predict learning responsibility.
66. 66. Workshop  Work with a team  Make an outline of a study that will make use of quantitative analysis  State the purpose of the study (research question)  Possible hypothesis (if there is)  Framework that supports the study  Research Design  Participants  Instruments  Procedure  Data Analysis