The property of item parameter invariance in item response theory (IRT) plays a pivotal role in the applications of IRT such as test equating. The scope of parameter invariance when using estimates from finite biased samples in the applications of IRT does not appear to be clearly documented in the IRT literature. This article provides information…

An automated item selection procedure in Mokken scale analysis partitions a set of items into one or more Mokken scales, if the data allow. Two algorithms are available that pursue the same goal of selecting Mokken scales of maximum length: Mokken's original automated item selection procedure (AISP) and a genetic algorithm (GA). Minimum…

Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm…

A new model for confidence judgments in recognition memory is presented. In the model, the match between a single test item and memory produces a distribution of evidence, with better matches corresponding to distributions with higher means. On this match dimension, confidence criteria are placed, and the areas between the criteria under the…

Technical considerations associated with item selection and reliability assessment are considered in relation to criterion-referenced tests constructed to provide group information. The purpose is to emphasize test building and the evaluation of test scores in program evaluation studies. It is stressed that an evaluator employ a performance or…

Coefficient "H" is used as an index of scalability in nonparametric item response theory (NIRT). It indicates the degree to which a set of items rank orders examinees. Theoretical sampling distributions, however, have only been derived asymptotically and only under restrictive conditions. Bootstrap methods offer an alternative possibility to…

Many academic tests (e.g. short-answer and multiple-choice) sample required knowledge with questions scoring 0 or 1 (dichotomous scoring). Few textbooks give useful guidance on the length of test needed to do this reliably. Posey's binomial error model of 1932 provides the best starting point, but allows neither for heterogeneity of question…

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori…

The third section of this two-volume report examines the utility of the model developed in section I for application in a classroom testing situation. The model was applied in arithmetic classes through a weekly testing program. The teacher specified the generic task being taught, tests were constructed using a table of random numbers to select…

This Monte Carlo study examined the effect of complex sampling of items on the measurement of differential item functioning (DIF) using the Mantel-Haenszel procedure. Data were generated using a three-parameter logistic item response theory model according to the balanced incomplete block (BIB) design used in the National Assessment of Educational…

The hypothesis that faulty classical psychometric and sampling procedures in test construction could generate systematic bias against ethnic groups with smaller representation in the test construction sample was studied empirically. Two test construction models were developed: one with differential representation of ethnic groups (White, African…