Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions,…

A Monte Carlo study was conducted to assess the effects of some potential confounding factors on structural equation modeling (SEM) fit indices and parameter estimates for both true and misspecified models. The factors investigated were data nonnormality, SEM estimation method, and sample size. Based on the fully crossed and balanced 3x3x4x2…

This study considers the problem of performing all pairwise comparisons of column means for a two-by-four additive nonorthogonal factorial analysis of variance (ANOVA) model where cell variances are heterogeneous. Extensions of the following procedures are considered: (1) Games-Howell (1976) procedure; (2) the C. W. Dunnett (1980) T3 and C…

The L statistic of E. B. Page (1963) tests the agreement of a single group of judges with an a priori ordering of alternative treatments. This paper extends the two group test of D. W. Leitner and C. M. Dayton (1976), an extension of the L test, to analyze difference in consensus between two unequally sized groups of judges. Exact critical values…

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…

The power of the procedure of W. Stout to detect deviations from essential unidimensionality in two-dimensional data was investigated for minor, moderate, and large deviations from unidimensionality using criteria for deviations from unidimensionality based on prior research. Test lengths of 20 and 40 items and sample sizes of 700 and 1,500 were…

A study on sampling errors of variance components was conducted within the framework of generalizability theory by P. L. Smith (1978). The study used an intuitive approach for solving the problem of how to allocate the number of conditions to different facets in order to produce the most stable estimate of the universe score variance. Optimization…

The Pearson product-moment correlation, r, is commonly applied in educational research. Almost all researchers realize that r ranges between -1.00 and +1.00, and that negative coefficients indicate that the bivariate relationship is inverse. Researchers also recognize that the Pearson r only evaluates linear relationship, and is not sensitive to…

A didactic example is provided, using a Monte Carlo method, of how differential item functioning (DIF) can be eliminated (and thus better understood) when the complete latent space is used. The main source of DIF is that the matching single criterion used in some DIF procedures, Mantel Haenszel or Simultaneous Item Bias (SIBTEST), does not account…

The psychometric objections to using essays and other subjective tests for measurement can be overcome by a many-facet Rasch model. This model enables judge-awarded grades to be transformed from their arbitrary, local, non-linear rating scale form into linear measures with explicit generalizable meaning of specifiable reliability (standard error)…

The way that graphs can be used to make calculations that are commonly used by institutional researchers is described using specific examples, and the technique of constructing computational graphs (and nomographs) is outlined. It is shown that once a calculation involving several variables has been represented by a computation diagram or a…

A new procedure is proposed for developing, evaluating, and implementing routing procedures for use with individualized instruction programs. An item response theory model for describing the relationship between performance on sequentially arranged units of instruction, and procedures for using the model to evaluate sequential relationships and…

A set of criteria for determining faculty workloads in light of changing roles and responsibilities is presented along with a formula that institutions can use to assess faculty workloads. After introductory material, the first section defines a workload formula as a method of determining the responsibilities a faculty member must carry out in a…

Some cognitive psychologists, who have tried to approach psychometric theories, say that the psychometric approach does not provide them with theories and methods with which they can deal with differential strategies. In this paper, a general latent trait model for differential strategies in cognitive processes is proposed which includes three…

Four problems in which elementary mathematics can be used in constructing models are described. (SD)