Tests of independence in 2 by 2 contingency tables
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The purpose of this study is to investigate not only the performance of five statistical tests of independence but also the relationships among power, sample size, effect size, marginal distribution, and type I error rates. The five statistics are: Pearson's chi-square test, the likelihood ratio chi-square test, Mantel-Haenszel chi-square, Fisher's exact test, and the continuity adjusted chi-square. The empirical Type I error rates and statistical power of the five statistical tests were estimated for 2 x 2 tables under various conditions. Five sample sizes: 8, 16, 32, 100, 300; three marginal distributions: equal (50:50), moderately skewed (60:40), and extremely skewed (90:10); and three effect sizes, small (.1), medium (.3), and large (.5) were examined for the empirical Type I error rates and the statistical power. For each condition studied, 10,000 samples were generated. Results were analyzed using logistic regression analysis.