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In many psychological experiments, interactioneffects in factorial analysis of variance (ANOVA)designs are often estimated using total scores derivedfrom classical test theory. However, interaction effectscan be reduced or eliminated by nonlinear monotonictransformations of a dependent variable. Althoughcross-over interactions cannot be eliminated by transformations,the meaningfulness of other interactionshinges on achieving a measurement scale level forwhich nonlinear transformations are inappropriate (i.e.,at least interval scale level). Classical total test scoresdo not provide interval level measurement according 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 several conditionsunder which interaction effects that are estimatedfrom classical total scores, rather than IRT trait scores,can be misleading. Using derived asymptotic expectationsfrom an IRT model, interaction effects of zero onthe IRT trait scale were often not estimated as zerofrom the total score scale. Further, when nonzero interactionswere specified on the IRT trait scale, the estimatedinteraction effects were biased inward whenestimated from the total score scale. Test difficultylevel determined both the direction and the magnitudeof the biased interaction effects. Index terms: factorialdesigns, interaction effects, interval measurement,item response theory, level of measurement, measurementscales, statistical inference

Item Response Theory Models and Spurious Interaction Effects in Factorial ANOVA Designs