One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…

Conditions under which interaction effects estimated from classical total scores, rather than item response theory trait scores, can be misleading are discussed with reference to analysis of variance (ANOVA). When no interaction effects exist on the true latent variable, spurious interaction effects can be observed from the total score scale. (SLD)