1. Chapter 2 Organizing the Data

2. Introduction Learn how to show variable relationship through diagrams
Thematically cover graphs and maps
Understand the importance of using appropriate data in representing variables
Become comfortable in applying graphical representation within various types of analyses (e.g., bivariate and multivariate)

3. 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

4. Conventions for Building Tables
Title of distribution explains contents
Variable(s) in table
Shows data distribution
Use column headings
Relevant columns are totaled
Footnotes added if needed

5. 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)
Responses of Young Boys to Removal of Toy
Response of Child f
Cry 25
Express Anger 15
Withdraw 5
Ply with another toy
N=50

6. Comparing Distributions
Comparisons clarify and add information
Response to Removal of Toy by Gender of Child
Gender of Child
Response of Child
Male
Female
Cry 25 14
Express Anger 15 1
Withdraw 5 2
Play with another toy 8
Total 50

7. 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

8. Illustration: Gender of Students Majoring in CJ(f)
Criminal Justice Majors
Gender
College A
College B
Male
879
119
Female
473 64
Total
1,352
183

9. Illustration: Gender of Students Majoring in CJ (f and %)
Criminal Justice Majors
College A
College B
Gender f %
Male
879 65
119
Female
473 35 64
Total
1,352
100
183

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

11. Some Common Rate Calculations
Suppose 500 births occur among 4,000 women of childbearing age. This would be a rate of 125 live births for every 1,000 women of childbearing age.
Suppose 562 suicides occur in a state with 4.6 million residents. The suicide rate would be 12.2 suicides per 100,000 residents.

12. Rate of Change Compare the same population at two points in time
time 2f – time1f
time 1f
Year
Theft Rate1
% Change
2005
120.3
2006
127.4
5.9%
2007
116.8
-8.3%
2008
107.4
-8.0%
2009
98.7
-8.1%
2010
94.6
-4.2%
(100)*
A negative sign signifies a reduction
A positive sign signifies an increase
1Source: National Crime Victimization Survey

13. Ordinal/Interval Data and Distributions
Attitudes Toward Televised Trials F
Slightly Favorable 9
Somewhat Unfavorable 7
Strongly Favorable 10
Slightly Unfavorable 6
Strongly Unfavorable 12
Somewhat Favorable 21
Total 65
Incorrect
Attitudes Toward Televised Trials F
Strongly Favorable 10
Somewhat Favorable 21
Slightly Favorable 9
Slightly Unfavorable 6
Somewhat Unfavorable 7
Strongly Unfavorable 12
Total 65
Correct
Must go from highest (at the top) to lowest (at the bottom).

14. Frequency Distribution of Final-Examination Grades for 71 Students 99 85 2 71 4 57 98 1 84 70 9 56 97 83 69 3 55 96 82 68 5 54 95 81 67 53 94 80 66 52 93 79 8 65 51 92 78 64 50 91 77 63
N = 71 90 76 62 89 75 61 88 74 60 87 73 59 86 72 58
Hard to see any patterns.

15. Grouped Frequency Distributions of Interval Data
Grouped frequency distribution used to clarify presentation of data.
Categories or groups referred to a class intervals
Class interval size determined by the number of values

16. Grouped Frequency Distributions of Interval Data
Grouped Frequency Distribution of Final-Examination Grades for 71 Students
Class Interval f %
95-99 3
4.23
90-94 2
2.82
85-89 4
5.63
80-84 7
9.86
75-79 12
16.90
70-74 17
23.94
65-69
60-64 5
7.04
55-59
50-54 71
100
Results are more easily shown/displayed

17. Constructing Class Intervals
Categories must be mutually exclusive and exhaustive
Designed to reveal or emphasize patterns
Possible to have too few or too many groups – blurs the data
Class intervals have a midpoint
Dealing with decimal data
M exclusive – Every case can only be placed in one, and only one, category M exhaustive – All cases are able to be put into a category

18. Flexible Class Intervals
Income Category F %
$100,000 and above
16,886
21.9
$75,000-$99,999
10,471
13.5
$50,000-$74,000
15,754
20.3
$40,000-$49,999
7488
9.7
$30,000-$39,999
7996
10.3
$20,000-$29,999
8169
10.6
$15,000-$19,999
3709
4.8
$10,000-$14,999
2890
3.7
$5000-$9999
2024
2.6
Under $5000
2031
N = 77688

19. 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
Only find CF/C% IF data is at least ordinal. Cannot do it for nominal data.

20. Grouped Frequency Distributions of Interval Data
Grouped Frequency Distribution of Final-Examination Grades for 71 Students
Class Interval f %
95-99 3
4.23
90-94 2
2.82
85-89 4
5.63
80-84 7
9.86
75-79 12
16.90
70-74 17
23.94
65-69
60-64 5
7.04
55-59
50-54 71
100
Results are more easily shown/displayed

21. Grouped Frequency Distributions of Interval Data
Grouped Frequency Distribution of Final-Examination Grades for 71 Students
Class Interval f Cf % C%
95-99 3 71
4.23
100
90-94 2 68
2.82
95.76
85-89 4 66
5.63
92.94
80-84 7 62
9.86
87.31
75-79 12 55
16.90
77.45
70-74 17 43
23.94
60.55
65-69 26
36.31
60-64 5 14
7.04
19.71
55-59 9
12.67
50-54
Results are more easily shown/displayed

22. Cross-Tabulations Frequency distributions are limited
Sometimes we want to know how is one variable (usually the dependent variable) distributed across another (usually the independent variable)
Cross-tabulations meet this need as they allow us to consider two or more dimensions of data.

23. Cross-tab Cross-Tabulation of Seat Belt Use by Gender
Frequency Distribution of Seat Belt Use
Use of Seat Belts f %
All the time
499
50.1
Most of the time
176
17.7
Some of the time
124
12.4
Seldom 83
8.3
Never
115
11.5
Total
997
100
Cross-Tabulation of Seat Belt Use
by Gender
Gender of Respondents
Use of Seat Belts
Male
Female
Total
All the time
144
355
499
Most of the time 66
110
176
Some of the time 58
124
Seldom 39 44 83
Never 60 55
115
367
630
997

24. 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

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

26. Victim-Offender Relationship
Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Row%)
Victim-Offender Relationship
Gender
Intimate
Intimate %
Family
Family %
Other
Other %
Total
Total %
Male
617
1,310
11,235
13,161
Female
1,470
639
1,421
3,531
2,087
1,949
12,656
16,692

27. Victim-Offender Relationship
Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Row%)
Victim-Offender Relationship
Gender
Intimate
Intimate %
Family
Family %
Other
Other %
Total
Total %
Male
617
4.7%
1,310
10.0%
11,235
85.4%
13,161
100%
Female
1,470
41.6%
639
18.1%
1,421
40.2%
3,531
2,087
12.5%
1,949
11.7%
12,656
75.8%
16,692

28. Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Column%)
Victim-Offender Relationship
Male
Female
Total
Intimate
617
1,470
2,087
Family
1,310
639
1,949
Acquaintance
7,237
998
8,235
Stranger
3,998
423
4,421
13,161
3,531
16,692

29. Cross Tabulations – Victim-Offender Relationship by Gender of Victim for Homicides in US for 2005 (With Column%)
Victim-Offender Relationship
Male
Female
Total
Intimate
617
1,470
2,087
4.7%
41.6%
12.5%
Family
1,310
639
1,949
10.0%
18.1%
11.7%
Acquaintance
7,237
998
8,235
55.0%
28.3%
49.3%
Stranger
3,998
423
4,421
30.4%
12.0%
26.5%
13,161
3,531
16,692
100%

30. 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

31. Pie Charts Pie chart – a circular chart whose pieces add up to 100%.
Especially good for nominal data.
Possible to highlight or “explode” certain pieces for emphasis

33. Exploded Pie Chart

34. Bar Graphs and Histograms
Represent frequency distribution plot of:
Categories/variables on one axis
Responses as bars on another axis
Bar length represents category frequency
Bar graphs used primarily for discrete variables
Histograms used to show continuity along a scale

35. Bar Graph

36. Histogram of Distribution of Children in Little Rock Community Survey
Y axis represents the percentage of number of respondents X axis represnts number of children of respondents ie, 35% of respondents have 0 or 1 children, 15% have 2 or 3 children, etc

37. Frequency Polygons
Best suited to emphasize continuity rather than differences
Frequency distribution of a single variable
Used for:
Continuous data
Interval data
Ratio data
Continuous data = count data, # of arrests. Typically, has no limit

38. Frequency Polygon Example
Commonly done with homicide rates, etc

39. Line Charts Generally show change (trends) temporally
Show trends in:
One variable
Plotting two or more variables
Similar to polygons, but not enclosed on the right margin

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

41. Maps Growing in popularity due to geo-coding and geo-mapping
Unparalleled method for exploring geographical patterns in data
For instance, a map of the U.S.
Helps show which area has more or less points

42. Example of mapping within criminal justice research

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

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

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

46. 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