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# Statistical Concepts: Introduction

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This contains some important concepts in statistics and methods of research. It is a good material for beginners who plan to explore or write a thesis or dissertation.

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### Statistical Concepts: Introduction

1. 1. IN STATISTICS 06/28/14 eccphd@yahoo.com
2. 2. Think of these…Crime rate Unemployment figures 2010 BAR Passing rate Mortality rates Gasoline prices Proportion of voters favoring a candidate Enrolment trend Drop-out rate 06/28/14 eccphd@yahoo.com • Number of Accident per year • Annual growth rate • Monthly income • Annual budget • Shooting average • Registered vehicles annually • Ratio of male teachers to the female • Average life span
3. 3. Numerical descriptions…Numerical descriptions… Statistics 06/28/14 eccphd@yahoo.com ESTIMATES PREDICTIONSPREDICTIONS DECISIONS
4. 4.  Statistics is a branch of mathematics that deals with the methods of collection, presentation, analysis and interpretation of data. 06/28/14 eccphd@yahoo.com NATURE OF STATITICS
5. 5.  Descriptive Statistics  Inferential Statistics 06/28/14 eccphd@yahoo.com
6. 6. 06/28/14 eccphd@yahoo.com
7. 7.  It is concerned with the gathering, classification, and presentation of data and summarizing the values to describe the group characteristic.  06/28/14 eccphd@yahoo.com
8. 8.  It pertains to the methods dealing with making of inference, estimate or prediction about a large set of data (population) using the information gathered from a sample. 06/28/14 eccphd@yahoo.com
9. 9. • Population refers to groups or aggregate of people, animals, subjects, materials, events, or things of any form. • Samples are elements of the population selected through a process. They have of the same characteristics with the population. 06/28/14 eccphd@yahoo.com
10. 10. POPULATION SAMPLE 06/28/14 eccphd@yahoo.com
11. 11. POPULATION SAMPLE 06/28/14 eccphd@yahoo.com
12. 12. 06/28/14 eccphd@yahoo.com • Parameter – It is a descriptive measure of the population. Greek letters are used to represent parameters, e.g. population mean μ, population standard deviation σ, etc. • Statistic – It is a descriptive measure of the sample. Roman letters are used for statistic, e.g. sample mean x, sample standard deviation s, etc.
13. 13. 06/28/14 eccphd@yahoo.com •Raw Data •Grouped Data •Primary data •Secondary Data DataData are any bits or collection of information, ideas, figures or concepts.
14. 14. 06/28/14 eccphd@yahoo.com Try asking some Fourth Year students to give you his age, date of birth, ethnic group, religion, birth order, occupation of his father, occupation of her mother, educational background of his parents, place of birth, ambition, favorite subject, most liked Grade school teacher and hobbies – any information he will feed you are basically RAW DATA.
15. 15. Grouped Data – those data placed in tabular form characterized by category or class intervals with the corresponding frequency Ethnic Groups Frequency Ilongo 24 Ilocano 56 Cebuano 78 Tagalog 52 Bicolano 9 Maguindanaon 23 Maranao 21 Total 263 06/28/14 eccphd@yahoo.com
16. 16. English Grades Frequency 75 – 79 4 80 – 84 16 85 – 89 27 90 – 94 5 95 - 99 2 Total 54 Age Bracket Frequency 10 – 19 40 20 – 29 26 30 – 39 17 40 – 49 52 50 - 59 20 Total 155 Grouped Data class intervals 06/28/14 eccphd@yahoo.com
17. 17. Primary Data – data are measured and gathered by the researcher who published it You submit a statistical data to your Professor regarding the educational profile of the teachers in your school which you yourself had gathered through interview. Educ'l Attainment Percentage BSED 13% BEED 26% AB w/ Educ Units 10% BEED w/ MA units 45% Master's Degree Holder 3% MA w/ doctoral units 3% Total 100% Table 1. Educational Profile of Teachers in Balintong Elementary School, SY 2012-2013 06/28/14 eccphd@yahoo.com
18. 18. Secondary Data – data being republished by another researcher for agency PNARUs Officers and EPs Percentage NARF 5,622 53% 4TH NCRes Bn 268 3% 30TH NARG 1,107 10% 502ND NRS 199 2% 503RD NRS 125 1% 705TH NRS 1,667 16% 706TH NRS 1,561 15% Total 10,549 100% Table 4. Personnel Capability of the Philippine Navy Affiliated Reserve Units (PNARUs) Source: NAVRESCOM, 2010 This data is lifted from an original source by Col Robles (2011) and aptly included in his study on PNARUs. 06/28/14 eccphd@yahoo.com
19. 19. Monthly Income Percent below 7,500.00 47.60 7,501.00 - 10,000.00 18.80 10,001.00 - 12,500.00 14.70 12,501.00 - 15,000.00 5.80 above 15,000.00 13.10 Total 100.00 Table 6. Monthly Income of the Parents of the Senior High School Students in Arakan Valley, Division of Cotabato, SY 2010-2011 Source: Alpajando, 2011 Secondary DataSecondary Data If this data would be used in another study, then it turns into a secondary data. 06/28/14 eccphd@yahoo.com
20. 20. • It is a characteristic or attribute of the experimental unit (persons, units or objects) which assumes different values or labels. • The process of assigning value or label of a particular experimental unit is called measurement. 06/28/14 eccphd@yahoo.com
21. 21. 06/28/14 eccphd@yahoo.com  Qualitative Variables  Quantitative Variables
22. 22. Quantitative Variables – When measured from the experimental units, they yield numerical responses. Examples height, age, income, family size Age - 15, 18, 29, 45, 54, 60 Family size – 2, 4, 5, 8 Height – 150 cms, 164 cms 06/28/14 eccphd@yahoo.com
23. 23. 06/28/14 eccphd@yahoo.com • Discrete Variables • Continuous Variables
24. 24. Discrete variablesDiscrete variables assume a finite or countable infinite values such as 0, 1, 2, 3, etc. Ex: number of studentsnumber of students population of teacherspopulation of teachers score in a testscore in a test female Senatorsfemale Senators 06/28/14 eccphd@yahoo.com
25. 25. Continuous variables cannot take finite values. These values are related with points on an interval of the real line. Ex: Height - 23.3 cm, 23.456 m, 123.8 ft Mass – 28.56 kgs, 8.36 lbs 06/28/14 eccphd@yahoo.com
26. 26. 06/28/14 eccphd@yahoo.com • Nominal • Ordinal • Interval • Ratio
27. 27. Nominal Level is the crudest form of measurement. The numbers or symbols are used for the purpose of categorizing forms into groups. The categories are mutually exclusive, that is, being in one category automatically excludes another. Ex: Gender (F – Female; M – Male) Faculty (1 – Tenured; 0 – Non-tenured) Response (1- Yes, 0 - No) 06/28/14 eccphd@yahoo.com
28. 28. Student Attitude 1 – Strongly Disagree 2 – Slightly Disagree 3 – Disagree 4 – Moderately Agree 5 – Strongly Agree Ordinal Level is a sort of improvement of nominal level because data are ranked from the “bottom to the top” or from the “low to high” manner.  Statements such as “greater than” or “lesser than” may be used in this level. Administrative Performance • Excellent -1 • Very Satisfactory - 2 • Good - 3 • Fair - 4 • Poor - 5 Examples: 06/28/14 eccphd@yahoo.com
29. 29. Interval Level possesses both the properties of the nominal and ordinal levels. The distances between any two numbers on the scale are known and it does not have a stable standing point (or an absolute zero). Ex: temperature 06/28/14 eccphd@yahoo.com
30. 30. Ratio Level possesses all the properties of nominal, ordinal and interval levels.  In addition, it has an absolute zero point and data can be classified and placed in a proper order to compare their magnitudes. ZeroZero stands for of something or absence absolutely nothing. Ex: grades income tuition fees 06/28/14 eccphd@yahoo.com
31. 31. 06/28/14 eccphd@yahoo.com Sampling techniques are used to economize (on the part of the researcher) the following:  Time  Effort  Money
32. 32. POPULATION SAMPLE 06/28/14 eccphd@yahoo.com
33. 33. Sampling techniquesSampling techniques are classified into:are classified into: • probability sampling • non-probability sampling 06/28/14 eccphd@yahoo.com
34. 34. PROBABILITY SAMPLING  It is a method of selecting a sample (n) from a universe (N) such that each member of the population has an equal chance of being included in the sample and all possible combinations of size (n) have an equal chance of being chosen as the sample. 06/28/14 eccphd@yahoo.com
35. 35. NON-PROBABILTY SAMPLING It is a method wherein the manner of selecting a sample (n) from a universe (N) depends on some inclusioninclusion rulerule as specified by the researcher. 06/28/14 eccphd@yahoo.com
36. 36. 06/28/14 eccphd@yahoo.com • Simple Random (Lottery) Sampling • Systematic Sampling • Stratified Sampling • Cluster or Area Sampling • Multi-stage Sampling
37. 37. 06/28/14 eccphd@yahoo.com
38. 38. 06/28/14 eccphd@yahoo.com Ex: N = 100, n = 25 N/n = 100/25 = 4 • This means every 4th element in a series should be taken as a sample. This method still uses the concept of random sampling and involves the selection of the nth element of a series representing the population.
39. 39. 06/28/14 eccphd@yahoo.com 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100
40. 40. 06/28/14 eccphd@yahoo.com  This is a random sampling technique in which the population is divided into non-overlapping subpopulations called strata.
41. 41. Respondents n Administrators 10 Teachers 50 Students 100 Parents 50 STRATIFIED SAMPLES Gender n Female 170 Male 250 Schools n Public 20 Private non-sectarian 10 Private sectarian 10 06/28/14 eccphd@yahoo.com
42. 42. 06/28/14 eccphd@yahoo.com  barangays in a municipality  municipalities in a province This is a random sampling technique in which the populationis divided into non- overlapping clusters or area.
43. 43. 06/28/14 eccphd@yahoo.com Ex: Region – 1st level Province – 2nd Level City – 3rd Level Barangay – 4th A technique that considers different stages orphases in sampling.
44. 44. 06/28/14 eccphd@yahoo.com MULTI-STAGE SAMPLING
45. 45. 06/28/14 eccphd@yahoo.com
46. 46. 06/28/14 eccphd@yahoo.com • Purposive SamplingPurposive Sampling  It is based on a criteria orIt is based on a criteria or qualifications given by thequalifications given by the researcher. Those who willresearcher. Those who will satisfy the criteria are included.satisfy the criteria are included.
47. 47. • Quota Sampling  It is quick and cheap since the interviewer is given a definite instruction and quota about the section of the population he is to work on.  The final choice of the actual person is left to his preference. NON-PROBABILITY SAMPLING TECHNIQUES 06/28/14 eccphd@yahoo.com
48. 48. 06/28/14 eccphd@yahoo.com • Convenience SamplingConvenience Sampling  It uses some instruments or equipment that provide convenience like the telephone or hand set to pick his samples units.  That means, people with no telephones can not be given a chance at all.
49. 49. 06/28/14 eccphd@yahoo.com  How many samples do weHow many samples do we need to use sufficiently inneed to use sufficiently in our study?our study? Is this number enough forIs this number enough for the study?the study? Will it give a valid resultWill it give a valid result for the study?for the study?
50. 50. 06/28/14 eccphd@yahoo.com This equation is commonly used by statisticians to determine the samples when the population is equal ormore than 500. N n = ----------------- (1 + e2 N) wherewhere n = the desired number ofn = the desired number of samplessamples N = total populationN = total population e = sampling errore = sampling error e = 0.05, 0.02 or 0.01 (arbitrary)e = 0.05, 0.02 or 0.01 (arbitrary)
51. 51. Case 1: A study is to be conducted in a big School Division of 25,000 students. Determine the appropriate sample using a 5% sampling error. Solution: n = [N/1 + e2 N] = {25,000/[1 + (0.05)(.05)(25,000)]} = 393.7 or ≈ 394 students 06/28/14 eccphd@yahoo.com
52. 52. 06/28/14 eccphd@yahoo.com  Descriptive Research –Descriptive Research – 10% of the population (20% for smaller N)10% of the population (20% for smaller N)  Correlational Research -Correlational Research - 30 subjects30 subjects Ex-post Facto Research -Ex-post Facto Research - 15 per group15 per group  Experimental Research -Experimental Research - 15 subjects per group15 subjects per group
53. 53. Where Zα/2 is the confidence level value  At 99% confidence level, Zα/2 = 2.58  At 95% confidence level, Zα/2 = 1.96  At 90% confidence level, Zα/2 = 1.65 06/28/14 eccphd@yahoo.com , N = population n = desired sample size p = largest possible proportion (0.50) e = sampling error e = 0.01 for 99% confidence level e = 0.05 for 95% confidence level e = 0.10 for 90% confidence level
54. 54. 06/28/14 eccphd@yahoo.com 1000 (1.96) 2 [0.50 (1 – 0.50)] n = --------------------------------------------------- 1000 (.05)2 + (1.96)2 [0.05(1 – 0.05)] = 277.54 or278
55. 55. where Zα/2 is the confidence level value  At 99% confidence level, Zα/2 = 2.58  At 95% confidence level, Zα/2 = 1.96  At 90% confidence level, Zα/2 = 1.65 E = allowable error (±E) in the estimate of the true value of μ n = desired sample size 06/28/14 eccphd@yahoo.com SAMPLE SIZE FROM THE ESTIMATION OFSAMPLE SIZE FROM THE ESTIMATION OF μμ THIS CAN BE USED WHEN THE POPULATION IS NOT KNOWN.
56. 56. 06/28/14 eccphd@yahoo.com (1.96) (.05) 2 n = --------------------- .01 = 96.04 or 96
57. 57. 06/28/14 eccphd@yahoo.com NN11 nnii = -------- x n; for i = 1, 2, 3,..= -------- x n; for i = 1, 2, 3,.. NN where n = the total size of the stratified random sample N = total population N1 = number of the 1st stratum elements N2 = number of the 2nd stratum elements N3 = number of the 3rd stratum elements
58. 58. PROPORTIONAL ALLOCATION n1 = [119/1000](286) = 34 (seniors) n2 = [210/1000](286) = 60 (juniors) And so with n3, n4, and n5. Strata Population (N) Seniors 119 Juniors 210 Sophomores 325 Freshmen 346 Total 1000 n = 286 (desired samples) 06/28/14 eccphd@yahoo.com
59. 59. Strata Population (N) Sample (n) Seniors 119 34 Juniors 210 60 Sophomores 325 93 Freshmen 346 99 Total 1000 286 PROPORTIONAL ALLOCATION 06/28/14 eccphd@yahoo.com
60. 60. 06/28/14 eccphd@yahoo.com The choice of the appropriate methods to be used in gathering of data depends mainly on some factors. These include:  the nature of the problem  the population under investigation  the time the material factors
61. 61. 06/28/14 eccphd@yahoo.com  Direct or Interview Method  Indirect or Questionnaire Method  Registration Method Other MethodsOther Methods  ObservationObservation  Phone interviewPhone interview  ExperimentsExperiments
62. 62. 06/28/14 eccphd@yahoo.com Direct or Interview Method
63. 63. 06/28/14 eccphd@yahoo.com It is one of the easiest methods of data gathering. It takes time to prepare because questionnaires need to be attractive. The content of a typical questionnaire, directions included, must be precise, clear and self- explanatory.
64. 64. 06/28/14 eccphd@yahoo.com Examples:Examples:  MarriageMarriage registrationregistration  birth certificatesbirth certificates  vehicle registrationsvehicle registrations  firearms licenses ,firearms licenses , Registration Method
65. 65. 06/28/14 eccphd@yahoo.com Observation • It is utilized to gatherIt is utilized to gather data regardingdata regarding attitudes, behavior,attitudes, behavior, values, and culturalvalues, and cultural patterns of the samplespatterns of the samples under investigation.under investigation.
66. 66. Phone Interview It is employed if the questions to be asked are brief and few. 06/28/14 eccphd@yahoo.com
67. 67. Experiments 06/28/14 eccphd@yahoo.com  It is applied to collect or gather data if the investigator wants to control the factors affecting the variable being studied.
68. 68. 06/28/14 eccphd@yahoo.com Data needs to beData needs to be organized to showorganized to show important propertiesimportant properties that may help in thethat may help in the analysis andanalysis and interpretation.interpretation.
69. 69. 06/28/14 eccphd@yahoo.com  Textual  Tabular • Graphical
70. 70. 06/28/14 eccphd@yahoo.com • In this form, the presentation is in narrative or paragraph mode. •The data are within the text of the paragraph. • In most cases, it cannot not get the immediate interest of the reader but it can present a more comprehensive picture of the data because of its written explanation.
71. 71. 06/28/14 eccphd@yahoo.com • The data shows the grades of a student in the FirstThe data shows the grades of a student in the First Quarter. As indicated, he got an excellent grade inQuarter. As indicated, he got an excellent grade in Values Education (96). On the other hand, heValues Education (96). On the other hand, he achieved the same level of performance in bothachieved the same level of performance in both Filipino and English (90). As shown also, he gained fairFilipino and English (90). As shown also, he gained fair performance in Science and Social Studies where heperformance in Science and Social Studies where he got 89 and 86, respectively. With a grade of 80, it onlygot 89 and 86, respectively. With a grade of 80, it only suggests that he finds Math a difficult subject.suggests that he finds Math a difficult subject.
72. 72. 06/28/14 eccphd@yahoo.com • In this form, the presentation makes use of rows and columnsrows and columns like a frequency table or distribution. • The data are presented in a systematic and orderly manner which catches one’s attention and may facilitate the comprehension and analysis of the data presented.
73. 73. Subject Areas First Quarter Grades Math 80 English 90 Science 89 Social Studies 86 Filipino 90 Values Education 94 06/28/14 eccphd@yahoo.com Average 88.17 ILLUSTRATIVE EXAMPLEILLUSTRATIVE EXAMPLE
74. 74. TABULAR PRESENTATION Gender Frequency Percent Male 20 40% Female 30 60% Total 50 100% 06/28/14 eccphd@yahoo.com
75. 75. 06/28/14 eccphd@yahoo.com • In this form, the numerical data in a frequency distribution can be made more interesting and easier to understand when presented in pictures or geometrical representations.
76. 76. 06/28/14 eccphd@yahoo.com
77. 77. 06/28/14 eccphd@yahoo.com
78. 78. 06/28/14 eccphd@yahoo.com
79. 79. GRAPHICAL PRESENTATION (Pie Graph) 06/28/14 eccphd@yahoo.com
80. 80. GRAPHICAL PRESENTATION (Cylindrical Graph) 06/28/14 eccphd@yahoo.com
81. 81. 06/28/14 eccphd@yahoo.com
82. 82. Figure 1. The Ethnic Profile of PhD Students in SKSUFigure 1. The Ethnic Profile of PhD Students in SKSU Graduate Studies Program iGraduate Studies Program i 06/28/14
83. 83. Ethnic Groups Frequency Ilongo 20 Bicolano 5 Tagalog 2 Ilocano 3 Total 30 Table 1. The Ethnic Profile of PhD Students at SKSU Graduate Extension Program in Iloilo City Category or labelCategory or label 06/28/14 eccphd@yahoo.com
84. 84. 06/28/14 eccphd@yahoo.com