Parameter linking in item response theory is generally necessary to adjust for differences between the true values for the same item and ability parameters due to the use of different identifiability restrictions in different calibrations. The research reported in this article explores a precision-weighted (PW) approach to the problem of…

The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee's ability and optimally…

Linking functions adjust for differences between identifiability restrictions used in different instances of the estimation of item response model parameters. These adjustments are necessary when results from those instances are to be compared. As linking functions are derived from estimated item response model parameters, parameter estimation…

The traditional way of equating the scores on a new test form X to those on an old form Y is equipercentile equating for a population of examinees. Because the population is likely to change between the two administrations, a popular approach is to equate for a "synthetic population." The authors of the articles in this issue of the…

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of test takers on one version of the test to make…

A statistical test for detecting answer copying on multiple-choice tests based on Cohen's kappa is proposed. The test is free of any assumptions on the response processes of the examinees suspected of copying and having served as the source, except for the usual assumption that these processes are probabilistic. Because the asymptotic null and…

In adaptive testing, item selection is sequentially optimized during the test. Since the optimization takes place over a pool of items calibrated with estimation error, capitalization on these errors is likely to occur. How serious the consequences of this phenomenon are depends not only on the distribution of the estimation errors in the pool or…

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and in the population of examinees. This definition underlies, for example, the well-known approximation to the standard error of equating by Lord (1982).…

It has often been argued that all techniques of standard setting are arbitrary and likely to yield different results for different techniques or persons. This paper deals with a related but hitherto ignored aspect of standard setting, namely, the possibility that Angoff or Nedelsky judges misspecify the probabilities of the borderline student's…

Occasionally, situations arise where mixtures of two binomials with one known success parameter are met. An example in educational testing is the mastery or random guessing model in which an examinee is supposed either to master the items or not to master them and to guess blindly. This paper gives moment estimators for such mixtures and presents…

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

R. J. Owen (1975) proposed an approximate empirical Bayes procedure for item selection in adaptive testing. The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach, but…

For six tests, coefficient delta as an index for internal optimality is computed. Internal optimality is defined as the magnitude of risk of the decision procedure with respect to the true score. Results are compared with an alternative index (coefficient kappa) for assessing the consistency of decisions. (Author/JKS)

A latent trait method is presented to investigate the possibility that Angoff or Nedelsky judges specify inconsistent probabilities in standard setting techniques for objectives-based instructional programs. It is suggested that judges frequently specify a low probability of success for an easy item but a large probability for a hard item. The…