Sample Size Determination in a Chi-Squared Test Given Information From an Earlier Study

Abstract

When an effect size estimate from an earlier study is available, it is common practice to calculate a sample size for a future study by postulating that the true effect size equals the point estimate from the previous study. Such an approach is methodologically flawed because it ignores the presence of uncertainty in the point estimate. In view of the fact that the sample size needed for a specified power does not vary linearly with effect size, the traditional approach typically leads to less power than is desired for the specified effect. A rigorous method of utilizing information from a previous study when determining the sample size for a chi-squared test is outlined. The approach is able to guarantee that the average power of all experiments in a discipline attains the desired level.