Optimal unconditional tables for comparing two independent proportions

Comparing two independent binomial proportions is quite a common problem in statistical practice. The unconditional method for doing so is more powerful than the conditional method (Fisher's exact test), but the computational difficulties of the former are much greater, and beyond the reach of most researchers. The solution adopted so far has been the publication of tables for critical regions, but the only ones that exist (MCDONALD et al., 1977; SUISSA and SHUSTER, 1985; and HABER, 1986) have certain limitations which prevent their general use (they are only valid for one-tailed tests; they allow very limited values of sample size and α error, and they are not constructed using the most powerful version of the test). In this paper the authors present tables which do not contain these limitations and which are valid for α errors of 1%, 5% and 10% and for sample size of n 1 ≤ n 2 ≤ 25 (beyond this figure, approximations may be used). They also illustrate the way to apply these tables (albeit in a conservative fashion) to the case of multinomial 2 x 2 trials.