Sample size for testing and estimating the difference between two paired and unpaired proportions: a 'two-step' procedure combining power and the probability of obtaining a precise estimate.

Clinical trials and scientific research studies are currently planned calculating sample sizes to fulfill power requirements, but the simultaneous need to obtain a satisfactorily precise effect estimate is not widely recognized. I have devised a 'two-step' iterative procedure for comparing two binomial parameters for two paired and unpaired proportions (the most frequent situations in scientific research), which takes into account power and the probability of obtaining a predetermined precision of the effect estimate. The first step provides the sample size for the power of the statistical test, the expected width of its corresponding confidence interval, and the probability of obtaining, under the alternative hypothesis, confidence intervals whose width is less than that expected. The second step iteratively increases this sample size until the probability of obtaining such confidence intervals exceeds a required threshold.