Determining Sample Size for Accurate Estimation of the Squared Multiple Correlation Coefficient

Abstract

While several resources are available to help researchers determine the minimum sample size needed to achieve target power for a wide variety of hypothesis tests, such resources are generally not available for determining the sample size when accurate parameter estimation is of interest. Sample size tables and procedures used to determine sample size for hypothesis tests should not be used for estimation because providing evidence that a parameter is not equal to some specific value is a fundamentally different task than accurately estimating the parameter. In particular, the necessary sample size required for hypothesis testing declines as the difference between the parameter and the specified value increases, but this difference does not have the same relationship to the sample size needed for accurate estimation. As interest in reporting estimates of effect sizes increases, sample size guidelines are needed for accurate estimation of these parameters. The present article focuses on the squared multiple correlation coefficient and presents regression equations that permit determination of sample size for estimating this parameter for up to 20 predictor variables. A comparison of the sample sizes reported here with those needed to test the hypothesis of no relationship between the predictor and criterion variables demonstrates the need for researchers to consider the purpose of their research and what is to be reported when determining the sample size for the study.