A Generalized Solution for Approximating the Power to Detect Effects of Categorical Moderator Variables Using Multiple Regression

Abstract

Investigators in numerous organization studies disciplines are concerned about the low statistical power of moderated multiple regression (MMR) to detect effects of categorical moderator variables. The authors provide a theoretical approximation to the power of MMR. The theoretical result confirms, synthesizes, and extends previous Monte Carlo research on factors that affect the power of MMR tests of categorical moderator variables and the low power of MMR in typical research situations. The authors develop and describe a computer program, which is available on the Internet, that allows researchers to approximate the power of MMR to detect the effects of categorical moderator variables given user-input information (e.g., sample size, reliability of measurement). The approximation also allows investigators to determine the effects of violating certain assumptions required for MMR. Given the typically low power of MMR, researchers are encouraged to use the computer program to approximate power while planning their research design and methodology.

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“…The moderated multiple regression approach we used is the optimal method for examining interaction effects between a categorical predictor variable (in the current study, sex) and a continuous moderating variable (age). The power of such analyses is affected by several factors including variability of the predictor variables; measurement error; total sample size; and unequal group size (Aguinis et al 2001). In the current study measurement error was minimal, due to the use of demographic predictor variables and psychometrically sound symptom measures.…”

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“…The reason is that MMR suffers from low statistical power (Aguinis, Boik, & Pierce, 2001;Aguinis, Culpepper, & Pierce, in press). Low statistical power means that, when they exist, the probability that population effects will be detected in the sample is low.…”

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“…Thus, the power of our results was close or above the .80 value recommended (Cohen, 1992), and clearly exceed values found in previous research. For example, Aguinis, Boik, and Pierce (2001) found that the power to detect interaction effects in a typical study is .20 to .34. On the other hand, the effect sizes found in the current study were small.…”