HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

1. Fox/Levin/Forde, Elementary Statistics in Social Research, 12e • Chapter 2: Organizing the Data HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D. 2/3/2014 Spring 2014

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

3. CHAPTER OBJECTIVES 2.1 • Create frequency distributions of nominal data 2.2 • Calculate proportions, percentages, ratios, and rates 2.3 • Create simple and grouped frequency distributions 2.4 • Create cross-tabulations 2.5 • Distinguish between various forms of graphic presentations

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

5. 2.1 Introduction 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

6. 2.1 Frequency Distributions of Nominal Data • 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 Comparing Distributions Comparisons clarify results, add information, and allow for comparisons

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

9. 2.2 Proportions and Percentages Allows for a comparison of groups of different sizes Proportion – number of casescompared to the total size of distribution Percentage – the frequency of occurrence of a category per 100 cases

10. Examples Proportion of children that cried Percentage of children that cried

11. 2.2 Ratio and Rates Ratio – compares the frequencyof one category to another Rate – compares betweenactual and potential cases

12. Examples Ratio of children that cried for every child that withdraw Rate of children that cried

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

14. 2.3 Table 2.4

15. 2.3 Not in Order! Table 2.5

16. 2.3 Grouped Frequency Distribution of Interval Data 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

17. 2.3 Class Limits and the Midpoint 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 Careful, many time they are not as evident as they seem

18. More about the length of class intervals Grouped Frequency TABLE 2.7 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 Cumulative Distributions 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

20. 2.3 Grouped Frequency TABLE 2.7 Distribution of Final-Examination Grades for 71 Students Table 2.7

21. 2.3 Percentiles 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

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

23. 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 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

26. Solution • Does you class determine if you buy a new car? Or Does buying a new car determines your class? • Pct. New Car = 100(17/ 73) = 23.28% • Pct. Upper class with new car = 100(23/33) = 69.69% • Pct. Middle class with new car = 100(6/27) = 22.22% • Pct. Lower class with new car = 100(1/13) = 7.69% • Effect of social class in buying a car?

28. Solution

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

30. 2.5 Figure 2.4 Pie Charts

31. 2.5 Figure 2.6 Bar Graph & Histograms

32. 2.5 Figure 2.9 Frequency polygons (frequency indicated at midpoint of each class)

33. From Table 2.7 The smaller the class interval the better 50 percentile =70 approx

34. 2.5 Figure 2.11 Taller than who? Flatter than who?

35. 2.5 Figure 2.12

36. 2.5 Figure 2.14 Line Chart (discrete values)

37. 2.5 Figure 2.15 Maps

38. Let’s work in MS Excel

39. CHAPTER SUMMARY • Frequency distributions can be created to help researchers visualize distributions 2.1 • Proportions, percentages, ratios, and rates can be calculated as a way to describe data 2.2 • 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 2.3 • Cross-tabulations can be created to illustrate the relationship between two variables 2.4 • Several forms of graphs can be used to demonstrate patterns and relationships between variables 2.5

40. 2.3 Homework 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