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…

A formally simple expression for the maximal reliability of a linear composite is provided. Its theoretical implications and its relation to existing results for reliability are discussed. (Author/SLD)

Minimum trace factor analysis has been used to find the greatest lower bound to reliability. This technique, however, fails to be scale free. A solution to the scale problem is proposed through the maximization of the greatest lower bound as the function of weights. (Author/JKS)

An important relationship is given for two generalizations of coefficient alpha: (1) Rajaratnam, Cronbach, and Gleser's generalizability formula for stratified-parallel tests, and (2) Raju's coefficient beta. (Author/CTM)

Explores the asymptotic theory of a method of nonparametric item characteristic curve estimation based on kernel smoothing with the theory of obtaining the proper linear ordering of examinees with respect to their true latent abilities. Results support the usefulness of estimates of the type produced by the TESTGRAF program. (SLD)

The asymptotic standard deviation (SD) of the alpha coefficient with standardized variables is derived under normality. The research shows that the SD of the standardized alpha coefficient becomes smaller as the number of examinees and/or items increase. Furthermore, this research shows that the degree of the dependence of the SD on the number of…

An estimate and upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory of R. D. Bock and M. Aitken (1981). The practical uses of such estimates are discussed. (SLD)

For (0, 1) scored multiple-choice tests, a formula giving test reliability as a function of the number of item options is derived, assuming the "knowledge or random guessing model," the parallelism of the new and old tests (apart from the guessing probability), and the assumptions of classical test theory. It is shown that the formula is a more…

A multiple-answer multiple-choice test is one which offers several alternate choices for each stem and any number of those choices may be considered to be correct. In this article, a class of scoring procedures called the binary class is discussed. (Author/JKS)

Maximum likelihood and Bayesian procedures are presented for item selection and scoring of multidimensional adaptive tests. A demonstration with simulated response data illustrates that multidimensional adaptive testing can provide equal or higher reliabilities with fewer items than are required in one-dimensional adaptive testing. (SLD)