A popular method to assess measurement invariance of a particular item is based on likelihood ratio tests with all other items as anchor items. The results of this method are often only reported in terms of statistical significance, and researchers proposed different methods to empirically select anchor items. It is unclear, however, how many…

This article extends the work by Armstrong and Shi on CUmulative SUM (CUSUM) person-fit methodology. The authors present new theoretical considerations concerning the use of CUSUM person-fit statistics based on likelihood ratios for the purpose of detecting cheating and random guessing by individual test takers. According to the Neyman-Pearson…

Item scores that do not fit an assumed item response theory model may cause the latent trait value to be estimated inaccurately. Several person-fit statistics for detecting nonfitting score patterns for paper-and-pencil tests have been proposed. In the context of computerized adaptive tests (CAT), the use of person-fit analysis has hardly been…

Compared the nominal and empirical null distributions of the standardized log-likelihood statistic for polytomous items for paper-and-pencil (P&P) and computerized adaptive tests (CATs). Results show that the empirical distribution of the statistic differed from the assumed standard normal distribution for both P&P tests and CATs. Also…

Item scores that do not fit an assumed item response theory model may cause the latent trait value to be estimated inaccurately. For computerized adaptive tests (CAT) with dichotomous items, several person-fit statistics for detecting nonfitting item score patterns have been proposed. Both for paper-and-pencil (P&P) test and CATs, detection of…

Recent developments of person-fit analysis in computerized adaptive testing (CAT) are discussed. Methods from statistical process control are presented that have been proposed to classify an item score pattern as fitting or misfitting the underlying item response theory (IRT) model in a CAT. Most person-fit research in CAT is restricted to…

Two new methods have been proposed to determine unexpected sum scores on sub-tests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted p, was compared with a method where the probability for each score combination was calculated using a…