1. POLS 7000X STATISTICS IN POLITICAL SCIENCE CLASS 2 BROOKLYN COLLEGE – CUNY SHANG E. HA Leon-Guerrero and Frankfort-Nachmias, Essentials of Statistics for a Diverse Society, Chapter 2

2. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Chapter 2: The Organization and Graphic Presentation of Data  Frequency Distributions  Proportions and Percentages  Percentage Distributions  Statistics in Practice: Labor Force Participation Among Latinos  The Construction of Frequency Distributions  Cumulative Distributions  Rates  Reading the Research Literature: Statistical Tables  Graphic Presentation of Data  A Cautionary Note: Distortions in Graphs  Statistics in Practice: Diversity at a Glance

3. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Frequency Distributions  A table reporting the number of observations falling into each category of the variable. IdentityFrequency (f) Native American947,500 Native American of multiple ancestry269,700 Native American of Indian descent5,537,600 Total (N)6,754,800

4. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Example: Death Penalty Statutes  In 1993, 36 states and Washington, D.C. had statutes permitting capital punishment. Of these 36 states, 27 set a minimum age for execution. Assume you are a member of a legal reform group that is trying to get the states that do not have a minimum age for execution to change their laws. You want to prepare a report describing the minimum age for execution in the 27 states have an established minimum age for execution. (The data are on the following slide.)

5. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Death Penalty Statutes Source: Kathleen Maguire and Ann L. Pastore, eds., Sourcebook of Criminal Justice Statistics. 1994. U.S. Department of Justice, Bureau of Justice Statistics. Washington, D.C.: U.S. Government Printing Office, 1995, pp. 115-116.

6. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Creating a Frequency Distribution Minimum AgeFrequency 141 151 169 174 1812 Total (N)27

7. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Proportions and Percentages Proportion (P): a relative frequency obtained by dividing the frequency in each category by the total number of cases. Percentage (%): a relative frequency obtained by dividing the frequency in each category by the total number of cases and multiplying by 100. N: total number of cases Proportions and percentages are relative frequencies

8. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Proportions and Percentages Minimum AgeFrequencyProportionPercentage 1411/27=.0373.7% 151.0373.7% 169.33333.3% 174.14814.8% 1812.44444.4% Total (N)271.0100.0%

9. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Percentage Distributions  A table showing the percentage of observations falling into each category of the variable. Minimum AgeFrequencyPercentage 413.7 1513.7 16933.3 17414.8 181244.4 Total N27100.0

10. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Frequency Distributions for Nominal Variables GenderTalliesFrequencyPercentage MaleIIIIIIIIIIIIIII1537.5 FemaleIIIIIIIIIIIIIIIIIIIIIIIII2562.5 Total (N)40100.0 Note: The categories for nominal variables (e.g., gender: male, female) need not be listed in any particular order.

11. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Frequency Distributions for Ordinal Variables  Note: Because the categories or values of ordinal variables are rank-ordered, they must be listed in a way that reflects their rank-ordering from the lowest to the highest or from the highest to the lowest. Categories should be displayed in order. HappinessTalliesFreq. (f)Percentage Very HappyIIIIIIIII922.5 Pretty HappyIIIIIIIIIIIIIIIIIIIIIIIII2562.5 Not too HappyIIIIII615.0 Total (N)40100.0

12. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Employment Status Example

13. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Employment Status Example

14. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Frequency Distributions for Interval-Ratio Variables Number of Children Freq. (f)Percentage (%) 0512.5 11025.0 21025.0 3512.5 45 512.5 625.0 7 or more25.0 Total (N)40100.0

15. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Cumulative Distributions  Sometimes we are interested in locating the relative position of a given score in a distribution.  Cumulative frequency distribution: a distribution showing the frequency at or below each category (class interval or score) of the variable.  Cumulative percentage distribution: a distribution showing the percentage at or below each category (class interval or score) of the variable.

16. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Cumulative Frequency Distribution Minimum Age Freq. (f)PercentageCumulative Frequency 1413.71 1513.71 16933.32 17414.811 181244.427 Total (N)27100.1* *Doesn’t total to 100% due to rounding.

17. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Cumulative Percentage Distribution Minimum AgeFreq. (f)PercentageCumulative Percentage 113.7 1513.77.4 16933.340.7 17414.855.5 181244.499.9* Total (N)27100.1* *Does not total 100% due to rounding

18. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Rates A number obtained by dividing the number of actual occurrences in a given time period by the number of possible occurrences. What’s the problem with the “rate” computation below? Why is it not an accurate statistic? Marriage rate, 1990 =Number of marriages in 1990 Total population in 1990 Marriage rate, 1990 = 2,448,000 marriages 250,000,000 Americans Marriage rate, 1990=.0098

19. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Reading Statistical Tables Basic principles for understanding what the researcher is trying to tell you:  What is the source of the table?  How many variables are presented? What are their names?  What is represented by the numbers presented in the first column? In the second column?

20. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Graphic Presentation  The Pie Chart  The Bar Graph  The Histogram  The Line Graph  Times Series Charts  Distortions in Graphs It is important to choose the appropriate graphs to make statistical information coherent.

21. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Pie Chart: The Race and Ethnicity of the Elderly  Pie chart: a graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as segments of a circle whose pieces add up to 100 % of the total frequencies.

22. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Too many categories can be messy!

23. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications We can reduce some of the categories

24. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Bar Graph: The Living Arrangements and Labor Force Participation of the Elderly  Bar graph: a graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable. The categories are displayed as rectangles of equal width with their height proportional to the frequency or percentage of the category.

25. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Bar Graph: The Living Arrangements and Labor Force Participation of the Elderly

26. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Can Display More Info by Splitting Sex

27. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Histogram  Histogram: a graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. The categories are displayed as contiguous bars, with width proportional to the width of the category and height proportional to the frequency or percentage of that category.

28. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Histogram

29. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Line Graph  Line Graph: A graph showing the differences in frequencies or percentages among categories of an interval-ratio variable. Points representing the frequencies of each category are placed above the midpoint of the category and are joined by a straight line.

30. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications The Line Graph

31. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Time Series Charts  Time series chart: a graph displaying changes in a variables at different points in time. It shows time (measured in units such as years or months) on the horizontal axis and the frequencies (percentages or rates) of another variable on the vertical axis.

32. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Time Series Charts

33. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Time Series Charts

34. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Distortions in Graphs Graphs not only quickly inform us; they can quickly deceive us. Because we are often more interested in general impressions than in detailed analyses of the numbers, we are more vulnerable to being swayed by distorted graphs. What are graphical distortions? How can we recognize them?

35. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Shrinking and Stretching the Axes: Visual Confusion

36. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Statistics in Practice The following graphs are particularly suitable for making comparisons among groups: - Bar chart - Line graph - Time series chart

37. Leon-Guerrero/Frankfort-Nachmias: Essentials of Social Statistics for a Diverse Society © 2012 SAGE Publications Why use charts and graphs? –What do you lose? –ability to examine numeric detail offered by a table –potentially the ability to see additional relationships within the data –potentially time: often we get caught up in selecting colors and formatting charts when a simply formatted table is sufficient –What do you gain? –ability to direct readers’attention to one aspect of the evidence –ability to reach readers who might otherwise be intimidated by the same data in a tabular format –ability to focus on bigger picture rather than perhaps minor technical details