Three mode comparability studies were conducted on the following Saturday national ACT test dates: October 26, 2019, December 14, 2019, and February 8, 2020. The primary goal of these studies was to evaluate whether ACT scores exhibited mode effects between paper and online testing that would necessitate statistical adjustments to the online…

Views on testing--its purpose and uses and how its data are analyzed--are related to one's perspective on test takers. Test takers can be viewed as learners, examinees, or contestants. I briefly discuss the perspective of test takers as learners. I maintain that much of psychometrics views test takers as examinees. I discuss test takers as a…

Various applications of item response theory often require linking to achieve a common scale for item parameter estimates obtained from different groups. This article used a simulation to examine the relative performance of four different item response theory (IRT) linking procedures in a random groups equating design: concurrent calibration with…

One of the important underlying assumptions of all item response theory (IRT) models is that of local independence. This assumption requires that the response to an item on a test not be influenced by the response to any other items. This assumption is often taken for granted, with little or no scrutiny of the response process required to answer…

ACT college test publisher provided scores. On average, non-homeschoolers performed better than homeschoolers, by about two items, out of sixty items, on the ACT mathematics test that was analyzed. This result may be due to the different teaching/learning media used in teaching each of the two groups, to different teacher/student interaction, or…

The purpose of this study was to investigate the effect of using multidimensional items in a computer adaptive test (CAT) setting which assumes a unidimensional item response theory (IRT) framework. Previous research has suggested that the composite of multidimensional abilities being estimated by a unidimensional IRT model is not constant…

The effects of anchor test characteristics in the accuracy and precision of test equating in the "common items, nonequivalent groups design" were studied. The study also considered the effects of nonparallel based and new forms on the equating solution, and it investigated the effects of differential weighting on the success of equating…

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

This report builds on and extends existent research on population invariance to new tests and issues. The authors lay the foundation for a deeper understanding of the use of population invariance measures in a wide variety of practical contexts. The invariance of linear, equipercentile and IRT equating methods are examined using data from five…

Tables of specifications are used to guide test developers in sampling items and maintaining consistency from form to form. This paper is a generalizability study of the American College Testing Program (ACT) Achievement Program Mathematics Test (AAP), with the content areas of the table of specifications representing multiple dependent variables.…

The work presented in this paper defined conceptually the concepts of multidimensional discrimination and information, derived mathematical expressions for the concepts for a particular multidimensional item response theory (IRT) model, and applied the concepts to actual test data. Multidimensional discrimination was defined as a function of the…

This paper demonstrates the relationship between the concept of unidimensionality and direction of an item in a multidimensional space. The basic premise is that if items that measure in the same direction are combined to form a test, that test will meet the item response theory requirements of unidimensionality. This will be true even if the…