Helps
Communicating Relationships of Nominal Data Using Contingency Tables.
The Chi Square test is usually used for nominal data. But the relationship is usually conveyed more simply with a contingency table. Percentages make the point even clearer.
The following examples of contingency tables were presented in Applied Statistics for Public Administration, Revised Edition, by Kenneth Meier and Jeffery Brudney (1987), pp 253-5.
Contingency Table
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Independent Variable |
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|
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|
Category 1 |
Category 2 |
Total |
|
Dependent Variable |
Category 1 |
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|
Category 2 |
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|
|
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Total |
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An example with data.
Contingency Table: Raw Data
|
|
Race |
|
|
|
Civil Service Exam |
Black |
White |
Total |
|
No Pass |
70 |
70 |
140 |
|
Pass |
60 |
135 |
195 |
|
Total |
130 |
205 |
335 |
The table is clearer when the raw data is converted to a percentage.
Contingency Table: Percentage Data
|
|
Race |
|
|
Civil Service Exam |
Black |
White |
|
No Pass |
54% |
34% |
|
Pass |
46% |
66% |
|
Total |
100% (n = 130) |
100% (n = 205) |
Control Variable
Sometimes a third variable explains the difference in the dependent variable better than our original independent variable. Here is an example of how to present a control variable from Applied Statistics for Public Administration, Revised Edition, by Kenneth Meier and Jeffery Brudney (1987), pp 234-5.
Contingency Table
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Control Variable 1 |
|
Control Variable 0 |
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||||
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Independent Variable |
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|
Independent Variable |
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||
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|
|
Cat. 1 |
Cat. 2 |
Total |
|
Cat. 1 |
Cat. 2 |
Total |
|
Dep. Var. |
Cat. 1 |
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|
Cat. 1 |
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|
|
|
Cat. 2 |
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Cat. 2 |
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|
|
|
|
|
Total |
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|
|
Total |
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|
|
Contingency Table: Raw Data
|
College Graduates |
|
Not College Graduates |
|
||||
|
|
Race |
|
|
Race |
|
||
|
Exam |
Black |
White |
Total |
Exam |
Black |
White |
Total |
|
No Pass |
10 |
40 |
50 |
No Pass |
60 |
30 |
90 |
|
Pass |
30 |
120 |
150 |
Pass |
30 |
15 |
45 |
|
Total |
40 |
160 |
200 |
Total |
90 |
45 |
135 |
Contingency Table: Percentage Data
|
College Graduates |
|
Not College Graduates |
|
||||
|
|
Race |
|
|
Race |
|
||
|
Exam |
Black |
White |
|
Exam |
Black |
White |
|
|
No Pass |
25% |
25% |
|
No Pass |
67% |
67% |
|
|
Pass |
75% |
75% |
|
Pass |
33% |
33% |
|
|
Total |
100% (n = 40) |
100% (n = 160) |
|
Total |
100% (n = 90) |
100% (n = 45) |
|
As we can see, it is not enough
to just apply the statistical procedure. An analyst also has to identify
other variables that may be be affecting our dependent variable, and test them
when possible.