Chapter 2 Organizing the Data

1. Chapter 2Organizing the Data

2. Frequency Distributions of Nominal Data • Formulas and statistical techniques used by social researchers to: • Organize raw data • Test hypotheses • Raw data is often difficult to synthesize • Most common types of distributions are: • Frequency • Percentage • Combination

3. Nominal Data and Distributions • Frequency distribution of nominal data consists of two columns: • Left column has characteristics (e.g., Response of Child) • Right column has frequency (f)

4. Comparing Distributions • Comparisons clarify and add information

5. Proportions and Percentages • Proportions - Compares the number of cases in a given category with the total size of the distribution • Most prefer percentages to show relative size. • Percentage – The frequency per 100 cases Formula for proportion Formula for percentage

6. Illustration: Gender of Students Majoring in CJ(f)

7. Illustration: Gender of Students Majoring in CJ (f and %)

8. Rates • Rates usually preferred by social researchers • Rate – comparison between actual and potential cases • Base terms in rates may vary

9. Rate of Change • Compare the same population at two points in time • Rate of Change = time 2f – time1f time 1f (100)* 1Source: National Crime Victimization Survey

10. Ordinal/Interval Data and Distributions

12. Grouped Frequency Distributions of Interval Data

13. Flexible Class Intervals N = 77688

14. Cumulative Distributions • Cumulative frequencies involve the total number of cases having a given score or a score that is lower • Cumulative frequency shown as cf • cf obtained by the sum of frequencies in that category plus all lower category frequencies • Cumulative percentage – percentage of cases having any score or a lower score

15. Grouped Frequency Distributions of Interval Data

16. Grouped Frequency Distributions of Interval Data

17. Cross-tab

18. What Type to Choose? • There are three sets of percentages • Total • Row • Column • All are correct, mathematically speaking • Total percentages may be misleading • Row and column percentages come down to which is more relevant to the purpose of the analysis

19. Formula for total percents Formula for column percents Formula for row percents Cross-tab Formulas

20. Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Row%)

21. Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Row%)

22. Cross Tabulations –Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Column%)

23. Cross Tabulations –Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Column%)

24. Graphic Presentations • Graphs are useful tools to emphasize certain aspects of data. • Many prefer graphs to tables. • Types of graphs include: • Pie charts, bar graphs, frequency polygons, line charts, and maps

26. Exploded Pie Chart

27. Bar Graph

28. Histogram of Distribution of Children in Little Rock Community Survey

29. Frequency Polygon Example

30. Number of Adolescents (< 18 y/o) Using for the First Time by Month

32. Shape of a Distribution • Kurtosis • Leptokurtic • Platykurtic • Mesokurtic • Skewness • Negative • Positive • Normal Curve

33. Kurtosis Leptokurtic Platykurtic Mesokurtic Some Variation in Kurtosis among Symmetrical Distributions

34. Skewness Negatively skewed Positively skewed Symmetrical (Normal) Three Distributions Representing Direction of Skewness

35. Summary • Organizing raw data is critical • Data can be summarized using frequency distributions. • Comparisons of groups possible through proportions, percentages and rates. • Cross-tabs allow dimensional (and more) analysis • Graphic presentations: • help to emphasize findings • make data more accessible to consumers of research • help researchers identify trends