The Appelbaum and Cramer comparison of models strategy for analysis of data from nonorthogonal designs is compared with the Overall and Spiegel Method 1 general linear model analysis. Data were generated by Monte Carlo methods to include known true analysis of variance (ANOVA) main and interaction effects. In the presence of a true but nonsignificant interaction, estimates of main effect parameters derived from the Method 1 general linear model analysis were significantly closer to the true values. Greater accuracy in estimation of main effects in the presence of a significant interaction was also observed. The power of tests of significance did not appear to differ. The danger of letting observed data determine the ANOVA model and the hypotheses to be tested is emphasized.

This article evaluates power and Type I error probabilities for a modified Fisher exact test for homogeneity of response probabilities in 2 × 2 tables. The original Fisher exact test and the Pearson chi-square are employed as standards for comparison. The continuity-corrected Fisher statistic is shown to be considerably more powerful than the uncorrected Fisher exact test, while it is less often nonconservatively biased than the Pearson chi-square.

Estimates of sample size requirements for 2 × 2 tables, derived from three approximate formulae, were evaluated by comparison wlth exact calculations. Although different, the estimates derived from all three formulae were judged adequate for most practical purposes, with the most accurate results being obtained from Cohen's formula. The strategy for exact determination of the minimum N required to provide specified power for tests of significance of differences in proportions in two treatment groups is described.

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