1. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 2/3/2014 Spring 2014 Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 2: Organizing the Data 1

2. 2.1 2 WRT the homework: You are allowed to literally “copy” and “paste” the problem from the book Announcement

3. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Create frequency distributions of nominal data Calculate proportions, percentages, ratios, and rates Create simple and grouped frequency distributions Create cross-tabulations Distinguish between various forms of graphic presentations CHAPTER OBJECTIVES 2.1 2.2 2.3 2.4 2.5

4. Create frequency distributions of nominal data Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.1

5. 5 Formulas and statistical techniques are used by researchers to: Organize raw data Test hypotheses Raw data is often difficult to synthesize Frequency tables make raw data easier to understand Introduction

6. 2.1 6 Frequency Distributions of Nominal Data Responses of Young Boys to Removal of Toy Response of Child f Cry 25 Express Anger 15 Withdraw 5 Ply with another toy 5 N=50 Characteristics of a frequency distribution of nominal data: Title Consists of two columns: Left column: characteristics (e.g., Response of Child) Right column: frequency (f)

7. 2.1 7 Comparisons clarify results, add information, and allow for comparisons Comparing Distributions Response to Removal of Toy by Gender of Child Gender of Child Response of ChildMaleFemale Cry2528 Express Anger153 Withdraw54 Play with another toy 5 15 Total50

8. Calculate proportions, percentages, ratios, and rates Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.2

9. 9 Allows for a comparison of groups of different sizes Proportion – number of cases compared to the total size of distribution Percentage – the frequency of occurrence of a category per 100 cases Proportions and Percentages

10. 10 Examples Responses of Young Boys to Removal of Toy Response of Child f Cry 25 Express Anger 15 Withdraw 5 Ply with another toy 5 N=50 Proportion of children that cried Percentage of children that cried

11. 2.2 11 Ratio – compares the frequency of one category to another Rate – compares between actual and potential cases Ratio and Rates

12. 12 Examples Responses of Young Boys to Removal of Toy Response of Child f Cry 25 Express Anger 15 Withdraw 5 Ply with another toy 5 N=50 Ratio of children that cried for every child that withdraw Rate of children that cried

13. Create simple and grouped frequency distributions Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.3

14. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.3 Table 2.4

15. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.3 Table 2.5 Not in Order!

16. 2.3 16 Used to clarify the presentation of interval-level scores spread over a wide range Class Intervals Smaller categories or groups containing more than one score Class interval size determined by the number of score values it contains Grouped Frequency Distribution of Interval Data

17. 2.3 17 Class Limits The point halfway between adjacent intervals Upper and lower limits –Distance from upper and lower limit determines the size of class interval The Midpoint The middlemost score value in a class interval –The sum of the lowest and highest value in a class interval divided by two Class Limits and the Midpoint Careful, many time they are not as evident as they seem

18. 18 More about the length of class intervals f 50-544 55-595 60-645 65-6912 70-7417 75-7912 80-847 85-894 90-942 95-953 71 TABLE 2.7 Grouped Frequency Distribution of Final-Examination Grades for 71 Students Usually the second category would be considered to be from 54.5 to 59.5 But notice that in a survey about age the respondents would consider to be from 55.0 to 55 + (364/365) In other words “…comes down to personal preference, feasibility and logical sense, not what is strictly right or wrong” (page 52) Midpoint = (55 +59)/2 = 114/2 =57

19. 2.3 19 Cumulative Frequencies Total number of cases having a given score or a score that is lower –Shown as cf –Obtained by the sum of frequencies in that category plus all lower categories’ frequencies Cumulative Percentage Percentage of cases having a given score or a score that is lower Cumulative Distributions

20. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.3 Table 2.7 f%cfc% 50-5445.634 55-5957.04912.68 60-6457.041419.72 65-691216.902636.62 70-741723.944360.56 75-791216.905577.46 80-8479.866287.32 85-8945.636692.96 90-9422.826895.77 95-9534.2371100.00 71100.00 TABLE 2.7 Grouped Frequency Distribution of Final-Examination Grades for 71 Students

21. 2.3 21 The percentage of cases falling at or below a given score Deciles – points that divide a distribution into 10 equally sized portions Quartiles – points that divide a distribution into quarters Median – the point that divides a distribution in two, half above it and half below it Let’s talk about it after the Frequency Polygons and Line Charts Percentiles

22. Create cross-tabulations Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.4

23. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.4 Table 2.17 Notice that sometimes is useful to divide the data using more than one variable, e.g. by Relationship and by Victim Sex

24. 2.4 24 Percents within Cross-Tabulations The choice comes down to which is more relevant to the purpose of the analysis If the independent variable is on the rows, use row percents If the independent variable is on the columns, use column percents If the independent variable is unclear, use whichever percent is most meaningful

25. 25

26. 26 Solution a)Does you class determine if you buy a new car? Or Does buying a new car determines your class? b)Pct. New Car = 100(17/ 73) = 23.28% c)Pct. Upper class with new car = 100(23/33) = 69.69% d)Pct. Middle class with new car = 100(6/27) = 22.22% e)Pct. Lower class with new car = 100(1/13) = 7.69% f)Effect of social class in buying a car? No New CarNew CarTotal row Upper Class231033 Middle Class21627 Lower Class12113 Total Column561773

27. 27

28. 28 Solution Score ValuefClass IntervalfMidpointPercentagecfCum. Pct. 394 15-19 12(15+19)/2 =17100(12/74)=16.2112100(12/74)=16.21 384 20-24 23(20+24)/2=22100(23/74)=31.0812+23=35100(35/74)=47.29 352 25-29 22(25+29)/2=27100(22/74)=29.7235+22=57100(57/74)=77.02 323 30-34 7(30+34)/2=32100(7/74)=9.4557+7=64100(64/74)=86.48 314 35-39 10(35+39)/2=37100(10/74)=13.5164+10=74100 279 74 99.97=100 approx. 267 256 2113 2010 175 157 74

29. Distinguish between various forms of graphic presentations Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.5

30. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.4 Pie Charts

31. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.6 Bar Graph & Histograms

32. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.9 Frequency polygons (frequency indicated at midpoint of each class)

33. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Midpointf%cfc% 50-5452.545.634 55-5957.557.04912.68 60-6462.557.041419.72 65-6967.51216.92636.62 70-7472.51723.944360.56 75-7977.51216.95577.46 80-8482.579.866287.32 85-8987.545.636692.96 90-9492.522.826895.77 95-9597.534.2371100 71100 From Table 2.7 50 percentile =70 approx The smaller the class interval the better

34. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.11 Taller than who? Flatter than who?

35. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.12

36. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.14 Line Chart (discrete values)

37. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved 2.5 Figure 2.15 Maps

38. 38 Let’s work in MS Excel

39. © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Frequency distributions can be created to help researchers visualize distributions Proportions, percentages, ratios, and rates can be calculated as a way to describe data Simple frequency distributions can be created using data at any level of measurement, while interval level data is needed to create a grouped frequency data Cross-tabulations can be created to illustrate the relationship between two variables CHAPTER SUMMARY 2.1 2.2 2.3 2.4 Several forms of graphs can be used to demonstrate patterns and relationships between variables 2.5

40. 2.3 40 Problems: 14 and 31 I know that they are not exactly the same as those solved in class No Excel this time, but maybe next Homework