POWER OF TESTING PROPORTIONS IN SMALL 2-SAMPLE STUDIES WHEN SAMPLE SIZES ARE EQUAL

In planning experiments having two groups of equal but small size, investigators face the uncertainty of power calculations that rely on asymptotic methods. This paper presents a method for determining power for two-sided tests. I compare two randomization tests, Fisher's exact test (FET), and the mid-P (MID), with the uncorrected chi-square test (CHI). Results show power as a function of relative risk for these methods, and assesses their relative power and type I error rates. MID is shown to have intermediate power between CHI, which is the most powerful, and FET, the least powerful. Situations are shown in which CHI and MID occasionally exceed the nominal level of alpha.