Sample size estimation for correlations with pre-specified confidence interval

Abstract

A common measure of association between two variables x and y is the bivariate Pearson correlation coefficient ρ(x,y) that characterizes the strength and direction of any linear relationship between x and y. This article describes how to determine the optimal sample size for bivariate correlations, reviews available methods, and discusses their different ranges of applicability. A convenient equation is derived to help plan sample size for correlations by confidence interval analysis. In addition, a useful table for planning correlation studies is provided that gives sample sizes needed to achieve 95% confidence intervals (CI) for correlation values ranging from 0.05 to 0.95 and for CI widths ranging from 0.1 to 0.9. Sample size requirements are considered for planning correlation studies.