The purpose of this paper is to calculate the upper limit of the correlation between normal and dichotomous variables. An empirically obtained correlation should be evaluated in view of this limit, instead of the usual limit of Pearson correlation. (Author)

The structure of information matrices in latent-variable models is explicated, and the degree to which missing information can be recovered by exploring collateral variables for respondents is characterized. Results are illustrated in the context of item-response-theory models, and practical implications are discussed. (SLD)

Eight models that can be used to analyze data from a pretest-posttest design are discussed. Artificial data are used to demonstrate that comparisons among some of the models generate results identical to those obtained by using repeated analysis of variance measures. Such results are shown to be potentially misleading. (Author/TJH)

The average response method (ARM) of scaling nonbinary data was developed to scale data from the assessments of writing conducted by the National Assessment of Educational Progress (NAEP). The method is described and illustrated with data from the 1983-84 NAEP. (SLD)

Confidence envelopes for one-parameter, two-parameter, and three-parameter logistic item response models are illustrated. M-line plots showing the genesis of the envelope and the density of lines in the confidence region are described and illustrated. (Author/SLD)

Two methods of handling unequal variances in the two-way fixed effects analysis of variance (ANOVA) model are described. One is based on an improved Wilcox (1988) method for the one-way model, and the other is an extension of G. S. James' (1951) second order method. (TJH)

Interpretations of relative variable importance in multivariate analysis of variance are discussed, with attention to (1) latent construct definition; (2) linear discriminant function scores; and (3) grouping variable effects. Two numerical ranking methods are proposed and compared by the bootstrap approach using two real data sets. (SLD)

Reasons/methods for standardizing discriminant function coefficients are reviewed, and use of the pooled within-groups variance estimate is examined. Use of total or pooled within-groups estimates can be justified only on purely mathematical grounds. Total variance estimates offer a more consistent and parsimonious approach than do pooled…

Estimation theory in educational statistics and the application of hierarchical linear models are reviewed. Observations within each group vary as a function of microparameters. Microparameters vary across the population of groups as a function of macroparameters. Bayes and empirical Bayes viewpoints review examples with two levels of hierarchy.…

The purpose of the present paper is to derive linear equating methods for the common item nonequivalent populations design from explicitly stated congeneric type test score models. The equating methods developed are compared with previously developed methods and applied to five professionally constructed examinations administered to approximately…

An approach is presented to simultaneously optimize decision rules for combinations of elementary decisions through a framework derived from Bayesian decision theory. The developed linear utility model for selection-mastery decisions was applied to a sample of 43 first year medical students to illustrate the procedure. (SLD)

An Edgeworth approximation for accurate significance probabilities for the Wilcoxon two-sample test is substantially simplified. A method is developed that allows quick calculations of very accurate probabilities. Exact formulas are given for most of the remaining cases, and tables are presented comparing the new simplification to likely…

The formula developed by R. Levine (1955) for equating unequally reliable tests is described. The formula can be interpreted as a method of moments estimate of an equating function that results in first order equity of the equated test score under a classical congeneric model. (TJH)

The construction of parallel tests from item-response-theory-based item banks is discussed. Two methods for sequentially selecting parallel tests and two methods for simultaneously constructing tests using 0-1 linear programing are compared. Advantages and disadvantages of these techniques are reviewed. (SLD)

Methods for approximating confidence intervals for the population standardized mean difference (delta) were evaluated analytically in small samples. An empirically determined simple linear adjustment to the sample delta demonstrated the most consistent precision when used to construct confidence intervals for the delta parameter. (SLD)