In recent guidelines for fair educational testing it is advised to check the validity of individual test scores through the use of person-fit statistics. For practitioners it is unclear on the basis of the existing literature which statistic to use. An overview of relatively simple existing nonparametric approaches to identify atypical response…

This study investigated how population parameters representing heterogeneity of variance, skewness, kurtosis, bimodality, and outlier-proneness, drawn from normal and eleven non-normal distributions, also characterized the ranks corresponding to independent samples of scores. When the parameters of population distributions from which samples were…

Causal inference in observational studies typically requires making comparisons between groups that are dissimilar. For instance, researchers investigating the role of a prolonged duration of breastfeeding on child outcomes may be forced to make comparisons between women with substantially different characteristics on average. In the extreme there…

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

Person-fit methods are used to uncover atypical test performance as reflected in the pattern of scores on individual items in a test. Unlike parametric person-fit statistics, nonparametric person-fit statistics do not require fitting a parametric test theory model. This study investigates the effectiveness of generalizations of nonparametric…

DETECT is a nonparametric, conditional covariance-based procedure to identify dimensional structure and the degree of multidimensionality of test data. The ability composite or conditional score used to estimate conditional covariance plays a significant role in the performance of DETECT. The number correct score of all items in the test (T) and…

Combined several developments in statistics and item response theory to develop a procedure for analysis of dichotomously scored test data. This version of nonparametric item response analysis, as illustrated through simulation and with data from other studies, marginalizes the role of the ability parameter theta. (SLD)

Studied the use of the person response function (PRF) for identifying nonfitting item score patterns. Proposed a person-fit method reformulated in a nonparametric item response theory (IRT) context. Conducted a simulation study to compare the use of the PRF with a person-fit statistic, resulting in the conclusion that the PRF can be used as a…

The power of the nonparametric person-fit statistic, U3, is investigated through simulations as a function of item characteristics, test characteristics, person characteristics, and the group to which examinees belong. Results suggest conditions under which relatively short tests can be used for person-fit analysis. (SLD)

Several existing group-based statistics to detect improbable item score patterns are discussed, along with the cut scores proposed in the literature to classify an item score pattern as aberrant. A simulation study and an empirical study are used to compare the statistics and their use and to investigate the practical use of cut scores. (SLD)

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…