A Simple Approximation for Calculating Sample Sizes for Comparing Independent Proportions

A simple approximation is provided to the formula for the sample sizes needed to detect a difference between two binomial probabilities with specified significance level and power. The formula for equal sample sizes was derived by Casagrande, Pike and Smith (1978, Biometrics 34 , 483-486) and can be easily generalized to the case of unequal sample sizes. It is shown that over fairly wide ranges of parameter values and ratios of sample sizes, the percentage error which results from using the approximation is no greater than 1%. The approximation is especially useful for the inverse problem of estimating power when the sample sizes are given.