When students receive the same score on a test, does that mean they know the same amount about the topic? The answer to this question is more complex than it may first appear. This paper compares classical and modern test theories in terms of how they estimate student ability. Crucial distinctions between the aims of Rasch Measurement and IRT are…

A conceptualization of multiple-choice exams in terms of signal detection theory (SDT) leads to simple measures of item difficulty and item discrimination that are closely related to, but also distinct from, those used in classical item analysis (CIA). The theory defines a "true split," depending on whether or not examinees know an item,…

This simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…