I have three study arms on interventions A, B, and C, which are independent of each other. The primary outcome is categorical (positive or negative). The null hypothesis is A = B = C.
From prior studies, the likely proportion of subjects with positive outcomes in arms A, B, and C are 0.8, 0.7, and 0.6, respectively.
What is the sample size needed to prove that the null hypothesis is wrong, assuming a power of 0.8 and alpha of 0.05?
PS: I am able to calculate the sample size using GPower (chi-square tests) with effect size (w) and df (2). However, is there any way to calculate the sample size directly using the above proportions rather than the effect size (w)?