Table PTT0. Two group Chi-square test of equal proportions (odds ratio = 1) (equal n’s)

Computed using the large sample normal approximation shown in the nQuery Advisor® manual appendix. 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 PTT0 shows computations for two examples. Solutions for n for significance level .01,.1, one and two-sided, proportion in group 1 of .05, proportion in group 2 of .1,.5, .8, power of 50%, 80%, 99% checked for exact agreement against Table 3.1 in Machin D, Campbell MJ (1987) Statistical Tables for the Design of Clinical Trials, Blackwell Scientific Publications Oxford. Additional values tested: significance level .001, .20 one and two-sided for proportion in group 1 of .05, .5, .95 by proportions in group 2 of .1,.6,.9 for power of 50% and 99% to sample size and sample size of 20, 500 to power checked for general consistency with DOS software Stat-Power version 2.0 by Bavry JL (1991) Scientific Software, Inc which uses a different calculation routine.

Figure PTT0. In the first and third columns, nQuery Advisor® 7.0 solved for n, in the second and fourth columns, nQuery Advisor® 7.0 solved for power.