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Organizing Data: Understanding Frequency Distributions of Nominal Data in Social Research

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This chapter explores the organization of raw data using frequency distributions, emphasizing nominal data in social research. It covers various statistical techniques for testing hypotheses and synthesizing data. Key topics include calculating proportions and percentages, analyzing grouped frequency distributions, and using cross-tabulations for detailed comparisons. Additionally, it highlights the importance of graphic presentations in data analysis, showcasing different types of graphs like pie charts and bar graphs, and discusses concepts of kurtosis and skewness that affect data interpretation.

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Organizing Data: Understanding Frequency Distributions of Nominal Data in Social Research

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  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

  11. Grouped Frequency Distributions of Interval Data

  12. Flexible Class Intervals N = 77688

  13. 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

  14. Grouped Frequency Distributions of Interval Data

  15. Grouped Frequency Distributions of Interval Data

  16. Cross-tab

  17. 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

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

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

  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 Column%)

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

  23. 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

  24. Exploded Pie Chart

  25. Bar Graph

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

  27. Frequency Polygon Example

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

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

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

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

  32. 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

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