Setting Sample Size to Ensure Narrow Confidence Intervals for Precise Estimation of Population Values

Background: Sample sizes set on the basis of desired power and expected effect size are often too small to yield a confidence interval narrow enough to provide a precise estimate of a population value. Approach: Formulae are presented to achieve a confidence interval of desired width for four common statistical tests: finding the population value of a correlation coefficient (Pearson r), the mean difference between two populations (independent- and dependent-samples t tests), and the difference between proportions for two populations (chi-square for contingency tables). Discussion: Use of the formulae is discussed in the context of the two goals of research: (a) determining whether an effect exists and (b) determining how large the effect is. In addition, calculating the sample size needed to find a confidence interval that captures the smallest benefit of clinical importance is addressed.