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What is Cramer's V and when should it be used? Cramer's V is a correlation coefficient that indicates the relationship among two categorical variables. It is similar to Pearson's correlation coefficient for two quantitative variables. Like Pearson's coefficient, Cramer's V ranges from -1 to 1, with 0 indicating no relationship and -1 or 1 indicating a perfect relationship. Also like Pearson's coefficient, the square of Cramer's V indicates the proportion of the total possible association (i.e., the maximum possible value of the chi-square statistic) that is present in the data. Despite these similarities, Cramer's V is more difficult to interpret that Pearson's correlation coefficient for several reasons. First, the maximum possible association (chi-square) is related to the sample size and the number of levels of each categorical variable. Thus, just changing the definitions of the levels of a categorical variable can change Cramer's V. Also, small values of Cramer's V often correspond to quite large proportional differences between groups, so the proximity of V to 0 can be misleading. These problems suggest that it is more reasonable to compare proportions than it is to focus solely on Cramer's V. If V is used as a measure of a relationship, it should be a secondary index that is interpreted in conjunction with a discussion of proportional differences. What is the purpose of the chi-square test? The chi-square test is an inferential test of a null hypothesis about any statistic that has a chi-square distribution when the null hypothesis is true. The most common use of the test is as a test of an omnibus hypothesis about two categorical variables (i.e., H0: V = 0) or an omnibus hypothesis that the proportion of responses in each response category is the same for K different groups. Although these hypotheses are used with two different sampling models (the model of independence and the model of homogeneity, respectively), the manner in which the test is conducted is identical for tests of both hypotheses. These are omnibus hypotheses, therefore the test should be employed in exploratory research studies when the intent is to search for a possible association or group differences. When is it useful to construct a confidence interval for a difference in proportions? Confidence intervals for differences in proportions provide specific information about group differences. Specific information is useful when (a) an omnibus test in an exploratory analysis suggests that there are differences among two or more of the groups in at least one response category or (b) specific hypotheses are of interest because of theoretical predictions. In the first instance post hoc confidence intervals can be constructed, and in the latter case, a priori intervals will most likely be more powerful (i.e., narrower). The exception to this is when there are many a priori intervals so that the post hoc intervals would actually be narrower. URL http://edpsych.ed.sc.edu/seaman/edrm711/questions/categorical.htm |
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This web was developed by Michael A. Seaman.
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