In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such…

Multidimensional computer adaptive testing (MCAT) can provide higher precision and reliability or reduce test length when compared with unidimensional CAT or with the paper-and-pencil test. This study compared five item selection procedures in the MCAT framework for both domain scores and overall scores through simulation by varying the structure…

This article is concerned with estimation of components of maximum generalizability in multifacet experimental designs involving multiple dependent measures. An example of a two-facet partially nested design is provided. (Author/RC)

Coefficient Alpha can be used to estimate the reliability of a test when the test is split into several parts. It is known that alpha can severly underestimate test reliability when the parts have an unequal number of items. A generalization of alpha is proposed to correct this defect. (Author/JKS)

Several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. The convergence properties of these methods are examined. A uniqueness proof for the desired solution is offered. (Author/JKS)

We make theoretical comparisons among five coefficients--Cronbach's [alpha], Revelle's [beta], McDonald's [omega][sub h], and two alternative conceptualizations of reliability. Though many end users and psychometricians alike may not distinguish among these five coefficients, we demonstrate formally their nonequivalence. Specifically, whereas…

Two designs for comparing a judge's ratings with a known standard are compared: (1) Subjects are categorized into classes, with no knowledge of the size of either group; and (2) the judge is told the actual number allowed in each class. The probability distribution of the total number of correct choices is developed for each case, and their power…

A simple stochastic model is formulated in order to determine the optimal time between the first test and the second test when the test-retest method of assessing reliability is used. A forgetting process and a change in true score process are postulated. Some numerical examples and suggestions are presented. (Author/JKS)

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. In such a case, neither Cronbach's coefficient alpha nor Kristof's three-part approach are satisfactory. A technique is developed for estimating reliability in such situations. (Author/BJG)

Parameter estimation for Keats generalization of the Rasch model that takes account of guessing behavior is investigated. It is shown that no minimal sufficient statistics for the ability parameters independent of the difficulty parameters exist. (Author/JKS)

Use of the same term "split-half" for division of an n-item test into two subtests containing equal (Cronbach), and possibly unequal (Guttman), numbers of items sometimes leads to a misunderstanding about the relation between Guttman's maximum split-half bound and Cronbach's coefficient alpha. This distinction is clarified. (Author/JKS)

To assess the reliability of congeneric tests, specifically designed reliability measures have been proposed. This paper emphasizes that such measures rely on a unidimensionality hypothesis, which can neither be confirmed nor rejected when there are only three test parts, and will invariably be rejected when there are more than three test parts.…

Use of Tukey's Jackknife in establishing a confidence interval around the population coefficient alpha is explored and the robustness of Feldt's procedure along with ten variants of the Jackknife when the data do not conform to the necessary normality requirements are evaluated. Only two of the variants compared to Feldt's approach. (RC)