ITEM RESPONSE THEORY MODELS AND SPURIOUS INTERACTION EFFECTS IN FACTORIAL ANOVA DESIGNS

In many psychological experiments, interaction effects in factorial an alysis of variance (ANOVA) designs are often estimated using total sco res derived from classical test theory. However, interaction effects c an be reduced or eliminated by nonlinear monotonic transformations of a dependent variable. Although cross-over interactions cannot be elimi nated by transformations, the meaningfulness of other interactions hin ges on achieving a measurement scale level for which nonlinear transfo rmations are inappropriate (i.e., at least interval scale level). Clas sical total test scores do not provide interval level measurement acco rding to contemporary item response theory (IRT). Nevertheless, rarely are IRT models applied to achieve more optimal measurement properties and hence more meaningful interaction effects. This paper provides se veral conditions under which interaction effects that are estimated fr om classical total scores, rather than IRT trait scores, can be mislea ding. Using derived asymptotic expectations from an IRT model, interac tion effects of zero on the IRT trait scale were often not estimated a s zero from the total score scale. Further, when nonzero interactions were specified on the IRT trait scale, the estimated interaction effec ts were biased inward when estimated from the total score scale. Test difficulty level determined both the direction and the magnitude of th e biased interaction effects.