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…

Three different bootstrap methods for estimating confidence intervals (CIs) for coefficient alpha were investigated. In addition, the bootstrap methods were compared with the most promising coefficient alpha CI estimation methods reported in the literature. The CI methods were assessed through a Monte Carlo simulation utilizing conditions…

Ramsay-curve item response theory (RC-IRT) is a nonparametric procedure that estimates the latent trait using splines, and no distributional assumption about the latent trait is required. For item parameters of the two-parameter logistic (2-PL), three-parameter logistic (3-PL), and polytomous IRT models, RC-IRT can provide more accurate estimates…

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)

A new item-fit index is proposed that is both a descriptive measure of deviance of single items and an index for statistical inference. This index is based on assumptions of the dichotomous and polytomous Rasch models for items with ordered categories. A simulation study is described. (SLD)

Inferential conditions in the statistical detection of measurement bias are discussed in the contexts of differential item functioning and predictive bias in educational and employment settings. It is concluded that bias measures that rely strictly on observed measures are not generally diagnostic of measurement bias or lack of bias. (SLD)