RESEARCH METHODS HANDBOOK

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Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Coefficients for Measuring Association

The following are a few of the many measures of association used with chi-square and other contingency table analyses. When using the chi-square statistic, these coefficients can be helpful in interpreting the relationship between two variables once statistical significance has been established. The logic for using measures of association is as follows:

Even though a chi-square test may show statistical significance between two variables, the relationship between those variables may not be substantively important. These and many other measures of association are available to help evaluate the relative strength of a statistically significant relationship. In most cases, they are not used in interpreting the data unless the chi-square statistic first shows there is statistical significance (i.e., it doesn't make sense to say there is a strong relationship between two variables when your statistical test shows this relationship is not statistically significant).

Phi Only used on 2x2 contingency tables. Interpreted as a measure of the relative (strength) of an association between two variables ranging from 0 to 1.

Pearson's Contingency Coefficient (C) It is interpreted as a measure of the relative (strength) of an association between two variables. The coefficient will always be less than 1 and varies according to the number of rows and columns.

Cramer's V Coefficient (V) Useful for comparing multiple X² test statistics and is generalizable across contingency tables of varying sizes. It is not affected by sample size and therefore is very useful in situations where you suspect a statistically significant chi-square was the result of large sample size instead of any substantive relationship between the variables. It is interpreted as a measure of the relative (strength) of an association between two variables. The coefficient ranges from 0 to 1 (perfect association). In practice, you may find that a Cramer's V of .10 provides a good minimum threshold for suggesting there is a substantive relationship between two variables.

where q = smaller # of rows or columns