The percentage of students retaking college admissions tests is rising (Harmston & Crouse, 2016). Researchers and college admissions offices currently use a variety of methods for summarizing these multiple scores. Testing companies, interested in validity evidence like correlations with college first-year grade-point averages (FYGPA), often…

This paper investigates four methods of linear equating under the common item nonequivalent groups design. Three of the methods are well known: Tucker, Angoff-Levine, and Congeneric-Levine. A fourth method is presented as a variant of the Congeneric-Levine method. Using simulation data generated from the three-parameter logistic IRT model we…

Professional standards for educational testing recommend that both the overall standard error of measurement and the conditional standard error of measurement (CSEM) be computed on the score scale used to report scores to examinees. Several methods have been developed to compute scale score CSEMs. This paper compares three methods, based on…

Education officials and journalists frequently track changes over time in the average ACT® College Readiness Assessment Composite scores and ACT College Readiness Benchmark attainment rates of individual high schools. Using standard statistical methods, I examined how often changes in these statistics are unambiguously positive or negative, rather…

The most critical feature of a common-item nonequivalent groups equating design is that the average score difference between the new and old groups can be accurately decomposed into a group ability difference and a form difficulty difference. Two widely used observed-score linear equating methods, the Tucker and the Levine observed-score methods,…