Type II Error Problems in the Use of Moderated Multiple Regression for the Detection of Moderating Effects of Dichotomous Variables

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Abstract
Monte Carlo simulation procedures were used to assess the power of moderated multiple regression ( MMR) to detect the effects of a dichotomous moderator variable under conditions of: ( 1) between- group differences in within-group relationships between two variables ( i.e., |ρ XY(1) -ρ XY(2) |= .20, .40, .60) ; ( 2) different combined sample sizes for the two groups ( N1 + N2 = NT = 30, 60, 90, 180, 300); and ( 3) differing proportions of cases ( P-i) in the two groups ( i.e., P 1 = .10, .30, .50). Results showed that, consistent with our a priori predictions, the power of MMR increased as: ( 1) total sample size ( NT) increased; ( 2) the difference between within-group correlation coefficients increased; and ( 3) the difference between the proportion of cases in each group decreased. Moreover, the simulation showed that these three variables had interactive effects on power. The major implication of our findings is that in cases where tests of moderating effects are conducted with MMR and the proportion of cases in each group differs greatly, inferences of no moderating effect may be erroneous: Such inferences may be the result of low statistical power rather than the absence of a moderating effect.