Tests of Independence in Contingency Tables with Small Samples: A Comparison of Statistical Power

The chi-square test of independence is a frequently used nonparametric test. Although the Type I error estimates for small-sample chi-square statistics applied to 2 x 2 tables have been relatively thoroughly studied, the Type II error rate (or power) has not been as extensively investigated. Additionally, most of the previous research has been limited to 2 x 2 tables and has not been extended to tables of larger dimensions. The objectives of the present research were (a) to investigate the small-sample power of several statistical tests in 2 x 2 and 3 x 3 contingency tables, and (b) to examine the Type I error rates for these tests under studied conditions. Various marginal distributions, sample sizes, and effect sizes were examined.