In separate studies, observers viewed upright biological motion, inverted biological motion, or arbitrary motion created from systematically randomizing the positions of point-light dots. Results showed that observers (a) could learn to detect the presence of arbitrary motion, (b) could not learn to discriminate the coherence of arbitrary motion,…

In the common two-step structural equation modeling process, modifications are routinely made to the measurement portion of the model prior to assessing structural relations. The effect of such measurement model modifications on the structural parameter estimates, however, is not well known and is the subject of the current investigation. For a…

The standard univariate and multivariate methods are conventionally used to analyze continuous data from groups by trials repeated measures designs, in spite of being extremely sensitive to departures from the multisample sphericity assumption when group sizes are unequal. However, in the last 10 years several authors have offered alternative…

We develop a simple model of teacher behavior that offers a solution to the ''class size puzzle'' and is useful for analyzing the potential effects of the No Child Left Behind Act. When teachers must allocate limited classroom time between multiple instructional methods, rational teachers may respond to reductions in class size by reallocating…

The accuracy of estimation procedures in item response theory was studied using Monte Carlo methods and varying sample size, number of subjects, and distribution of ability parameters for: (1) joint maximum likelihood as implemented in the computer program LOGIST; (2) marginal maximum likelihood; and (3) marginal Bayesian procedures as implemented…

A Monte Carlo approach is proposed, using the Statistical Analysis System (SAS) programming language, for estimating reliability coefficients in generalizability theory studies. Test scores are generated by a probabilistic model that considers the probability for a person with a given ability score to answer an item with a given difficulty…

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 paper compares various methods of smoothed equipercentile equating and linear equating in the random groups equating design. Three presmoothing methods (based on the beta binomial model, four-parameter beta binomial model and a log-linear model) are compared to postsmoothing using cubic splines, linear equating and unsmoothed equipercentile…

The accuracy of the Markov chain Monte Carlo procedure, Gibbs sampling, was considered for estimation of item and ability parameters of the one-parameter logistic model. Four data sets were analyzed to evaluate the Gibbs sampling procedure. Data sets were also analyzed using methods of conditional maximum likelihood, marginal maximum likelihood,…

This study integrates into one comprehensive Monte Carlo simulation a vast array of previously defined and substantively interrelated research studies of the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) statistical procedures. Three sets of balanced ANOVA and ANCOVA designs (group sizes of 15, 30, and 45) and one…

This Monte Carlo study examines whether, given various numbers of variables, treatments, and sample sizes, in a one-way multivariate analysis of variance, Type I error rates of the test approximations provided by the BMDP program, the Statistical Analysis System (SAS), and the Statistical Package for the Social Sciences (SPSS) for Roy's largest…

The mixed model analysis of variance assumes a mathematical property known as sphericity. Several preliminary tests have been proposed to detect departures from the sphericity assumption. The logic of the preliminary testing procedure is to conduct the mixed model analysis of variance if the preliminary test suggests that the sphericity assumption…

The theoretical differences between the traditional definition of dimensionality and the more recently defined notion of essential dimensionality are presented. Monte Carlo simulations are used to demonstrate the utility of W. F. Stout's procedure to assess the essential unidimensionality of the latent space underlying a set of terms. The…

A Monte Carlo study was conducted to estimate the efficiency of and the relationship between five equations and the use of cross validation as methods for estimating shrinkage in multiple correlations. Two of the methods were intended to estimate shrinkage to population values and the other methods were intended to estimate shrinkage from sample…

The applicability of a mathematical theorem designed to trace causality of a three-variable path that consists of an initial cause variable, an intermediate variable, and a final-effect variable with control over other system variables is evaluated. The formula was used with a horizontal rather than a normal distribution, as had been done in an…