Most methods for fitting cognitive diagnosis models to educational test data and assigning examinees to proficiency classes require the Q-matrix that associates each item in a test with the cognitive skills (attributes) needed to answer it correctly. In most cases, the Q-matrix is not known but is constructed from the (fallible) judgments of…

DIMPACK Version 1.0 for assessing test dimensionality based on a nonparametric conditional covariance approach is reviewed. This software was originally distributed by Assessment Systems Corporation and now can be freely accessed online. The software consists of Windows-based interfaces of three components: DIMTEST, DETECT, and CCPROX/HAC, which…

Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another. One way to test items with ordinal response scales for DIF is likelihood ratio (LR) testing using item response theory (IRT), or IRT-LR-DIF. Despite the various advantages of…

DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, "D[subscript max]," denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite [theta][subscript TT]…

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…

The nonparametric Mokken model of test data was compared with parametric models using simulated data through latent class analysis. It is demonstrated that latent class analysis provides a consistent comparison of item response models. (SLD)

Through simulation, the power of the U3 statistic was compared with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases, a weighted version of the latter statistic performed as well as the U3 statistic. (SLD)

The Cartesian theory of dimensionality (defined in terms of geometric distances between points in the test space) and Leibnitzian theory (defined in terms of order-generative connected, transitive, and asymmetric relations) are contrasted in terms of the difference between a factor analysis and an order analysis of the same data. (Author/CTM)

Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

Questions are raised concerning differences between traditional metric multiple regression, which assumes all variables to be measured on interval scales, and nonmetric multiple regression. The ordinal model is generally superior in fitting derivation samples but the metric technique fits better than the nonmetric in cross-validation samples.…

A class of naive estimators of correlation was tested for robustness, accuracy, and efficiency against Pearson's r, Tukey's r, and Spearman's r. It was found that this class of estimators seems to be superior, being less affected by outliers, reasonably efficient, and frequently more easily calculated. (Author/CTM)

Differential item functioning (DIF) is an important consideration in assessing the validity of test scores (Camilli & Shepard, 1994). A variety of statistical procedures have been developed to assess DIF in tests of dichotomous (Hills, 1989; Millsap & Everson, 1993) and polytomous (Penfield & Lam, 2000; Potenza & Dorans, 1995) items. Some of these…

The Level-11 vocabulary subtest of the Iowa Tests of Basic Skills was analyzed using a two-stage latent trait approach and data set of 2,356 examinees, approximately 11 years of age. It is concluded that the nonparametric approach leads to efficient estimation of the latent trait. (SLD)