Within polytomous items, differential item functioning (DIF) can take on various forms due to the number of response categories. The lack of invariance at this level is referred to as differential step functioning (DSF). The most common DSF methods in the literature are the adjacent category log odds ratio (AC-LOR) estimator and cumulative…

The Rasch model, a member of a larger group of models within item response theory, is widely used in empirical studies. Detection of uniform differential item functioning (DIF) within the Rasch model typically employs null hypothesis testing with a concomitant consideration of effect size (e.g., signed area [SA]). Parametric equivalence between…

A primary concern with testing differential item functioning (DIF) using a traditional point-null hypothesis is that a statistically significant result does not imply that the magnitude of DIF is of practical interest. Similarly, for a given sample size, a non-significant result does not allow the researcher to conclude the item is free of DIF. To…

Researchers sometimes need a statistical test of the hypothesis that two values of Cronbach's alpha reliability coefficient are equal. The situation may involve scores from two different measures administered to independent random samples or from the same measure administered to random samples from two different populations. Feldt derived a test…