Appropriate Moderated Regression and Inappropriate Research Strategy: A Demonstration of Information Loss Due to Scale Coarseness

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Abstract
Paunonen and Jackson (1988) demonstrated that stepwise moderated regression provides a test of interaction effects that protects the nominal Type I error rate. However, the stepwise procedure has also been characterized as failing to detect interaction effects in empirical studies. This issue has led to questions regarding the method’s statistical power (Bobko, 1986; Zedeck, 1971) in applied research. It is demonstrated that, because of a research strategy frequently used in empirical investigations, the probability of Type II error in detecting a true interaction effect is unknown. Specifically, the number of scale steps used in measuring the dependent variable is shown to result in a form of systematic error that can spuriously increase or decrease the expected effect size of the interaction. The problem is also discussed in the context of testing more complex models. Recommendations for eliminating this problem in future research designs are provided. Index terms: information loss, interaction effects, Likert scales, moderated regression, response transformation

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