The impact of ignoring random features of predictor and moderator variables on sample size for precise interval estimation of interaction effects

Abstract

The influence of the joint distribution of predictor and moderator variables on the identification of interactions has been well described, but the impact on sample size determinations has received rather limited attention within the framework of moderated multiple regression (MMR). This article investigates the deficiency in sample size determinations for precise interval estimation of interaction effects that can result from ignoring the stochastic nature of continuous predictor and moderator variables in MMR. The primary finding of our examinations is that failure to accommodate the distributional properties of regressors can lead to underestimation of the necessary sample size and distortion of the desired interval precision. In order to take account of the randomness of regressor variables, two general and effective procedures for computing sample size estimates are presented. Moreover, corresponding programs are provided to facilitate use of the suggested approaches. This exposition helps to correct drawbacks in the existing techniques and to advance the practice of reporting confidence intervals in MMR analyses.Keywords Moderation . Precision . Sample size Moderated multiple regression (MMR) has been extensively employed to study the interaction effects between predictor and moderator variables in management, psychology, education, and related disciplines. It follows from the comprehensive reviews of Stone-Romero, Alliger, and Aguinis (1994), Aguinis (1995), Aguinis and Stone-Romero (1997), Aguinis, Beaty, Boik, and Pierce (2005), and relatedwork that most of the methodological research in MMR has been concerned with the statistical power of hypothesis testing for detecting moderating effects. Although null hypothesis significance testing is useful in various applications, the dichotomous accept-reject decision ignores other useful information in its analysis. As an alternative, the notion of interval estimation has been stressed in studies such as Hahn and Meeker (1991), Steiger andFouladi (1997), andSmithson (2003). Accordingly, the inferential procedures of interval estimators are strongly recommended by Wilkinson and the American Psychological Association Task Force on Statistical Inference (1999), as well as the Publication Manualof the American Psychological Association (American Psychological Association, 2001). Since confidence intervals constructed with the desired reliability are more informative about the location of a targeted parameter, they should be the best reporting strategy in practical study. However, the methodological artifacts and statistical implications associated with interval estimation of moderating effects have received little attention within the framework of MMR.The interactional formulation of MMR can be viewed as a special case of the statistical linear models, and so the inferential procedures of hypothesis testing and interval estimation of moderation can be conducted with standard methods and software packages for linear regression analysis. In this article, we ...