Sample size planning for multiple correlation: reply to Shieh (2013)

Bonett and Wright (2011) proposed a simple and accurate sample size planning formula for estimating a squared multiple correlation with desired relative precision. Shieh (2013) incorrectly evaluated the accuracy of the Bonett-Wright formula.

To address a criticism of Shieh that the Bonett-Wright formula was not examined under a wider range of conditions, the accuracy of the Bonett-Wright sample size formula is evaluated under the additional conditions proposed by Shieh. A simple 2-step sample size formula for desired absolute precision is proposed and its accuracy is evaluated under the conditions proposed by Shieh.

The analyses indicate that the Bonett-Wright sample size formula for relative prediction and the new 2-step sample size formula for absolute precision are remarkably accurate.

Simple sample size planning formulas for a squared multiple correlation are important tools in designing a multiple regression analysis where the primary goal is to obtain an acceptably accurate estimate of the squared multiple correlation. The computationally intensive and simulation-based methods proposed by Shieh are not necessary.