# Contingency Coefficient - The Contingency Coefficient C

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```					                  The Contingency Coefficient C

The Problem

A study was conducted to determine the correlation (association) between race
and type of sentence received by 960 misdemeanant offenders. The frequency
data was cast in a 3x3 table with three levels each for race and type of sentence.

The Variables

The data used in this exercise can be found in the Race & Type of Sentence
database, which includes the following variables:

Race was classified into 1 = white, 2 = black & 3 = other: race_3
Sentence was classified into 1=deferred adjudication, 2 = probation, &
3 = jail: sent_3
Race was also classified into 1=white & 2=nonwhite: race_2
Sentence as also classified into 1=deferred adjudication or probation, &
2 = jail: sent_2

The Analysis

Attached are the steps to compute a Phi coefficient.

After completing the SPSS analysis and studying the results, answer the
following questions.

1. What is the null hypothesis in this analysis?

2. What is the magnitude of contingency coefficient C?

3. In the case of this 3x3 crosstabulation table of nominal data, is the
question of the direction of the relationship relevant? If so why, if not why
not?
\
4. Is C significant or not and what level of significance?

5. Should the null hypothesis be accepted or rejected and on what statistic
do you base your decision?

6. How would you interpret C?

The Phi Coefficient: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University
2

7. The value of chi-square for this 3x3 table is 112.65. Using the appropriate
equation, demonstrate how the contingency coefficient C = 0.324 can be
derived from this value of chi-square.

The SPSS Procedures

Analyze
Descriptive Statistics
Crosstabs
Row(s): sent_3
Column(s): race_3
Statistics
Nominal
Contingency Coefficient
Continue
OK

Contingency Coefficient C: Charles M. Friel Ph.D., Criminal Justice Center, Sam Houston State University

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 views: 57 posted: 11/27/2010 language: English pages: 2