Determining sample size for accurate estimation of the squared multiple correlation coefficient

While several resources are available to help researchers determine the min imum sample size needed to achieve target power for a wide variety of hypot hesis 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 s hould not be used for estimation because providing evidence that a paramete r is not equal to some specific value is a fundamentally different task tha n 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 estimatio n. As interest in reporting estimates of effect sizes increases, sample siz e guidelines are needed for accurate estimation of these parameters. The pr esent article focuses on the squared multiple correlation coefficient and p resents regression equations that permit determination of sample size for e stimating 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.