Table PTT0U. Two group Chi-square test of equal proportions (odds ratio = 1) (unequal n’s)

Computed using the large sample normal approximation with adjustment for unequal n’s. Formula quoted widely, see for example, Fleiss JL, Tytun A, Ury SHK (1980) A simple approximation for calculating sample sizes for comparing independent proportions. Biometrics. 36:343-346. Figure PTT0U shows computations for one example for three values of r. Note that since the average of the two proportions differs for r and 1/r and the variance terms are πi (1-πi)/ni , the required total sample size will differ depending on whether the more extreme proportion is to have the smaller or the larger sample size. Solutions for r=1 checked against PTT0. Sample sizes giving a power of 80% for significance level .05 two- sided, proportion in group 1, .05, proportion in group 2 of .1,.4, .8, for r=1,2,3,4 used to compute power in DOS software Statistical Power Analysis: A Computer Program by Borenstein, M, Cohen J (1988) Lawrence Erlbaum Associates.

Figure PTT0U. In all three columns, nQuery Advisor® 7.0 solved for sample size, note that the variance terms differ between the two groups, so sample sizes differ depending on r.