This article proposes a method for testing equality of variances which exploits Pitman's idea and the computational power of simulations. Several advantages to this method are illustrated. A Monte Carlo study for several combinations of sample sizes and number of variables is presented. (Author/LMO)

Two measures of association between sets of variables have been proposed for set correlation: the proportion of generalized variance, and the proportion of additionive variance. Because these measures are strongly positively biased, approximate expected values and estimators of these measures are derived and checked. (Author/BW)

A computer program which allows the solution of a Monte Carlo simulation (probabilistic sensitivity analysis) has been developed for the Vic-20 microcomputer. Theory of Monte Carlo simulation, program capabilities and operation, and sample calculations are discussed. Student comments on the program are included. (JN)

A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel…

In some areas of measurement item parameters should not be modeled as fixed but as random. Examples of such areas are: item sampling, computerized item generation, measurement with substantial estimation error in the item parameter estimates, and grouping of items under a common stimulus or in a common context. A hierarchical version of the…

While it is imperative that attempts be made to assess the predictive accuracy of any prediction model, traditional measures of predictive accuracy have been criticized as suffering from "the base rate problem." The base rate refers to the relative frequency of occurrence of the event being studied in the population of interest, and the…

Monte Carlo simulation compared chi-square statistics, parameter estimates, and root mean square error of approximation values using normal and elliptical estimation methods. Three research conditions were imposed on the simulated data: sample size, population contamination percent, and kurtosis. A Bentler-Weeks structural model established the…

A procedure was developed to analyze data with missing observations by extracting data from a sparsely filled data matrix into analyzable smaller subsets of data. This subdividing method, based on the conceptual framework of meta-analysis, was accomplished by creating data sets that exhibit structural designs and then pooling variance components…

The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal…

This paper suggests that statistical significance testing and effect size are two sides of the same coin; they complement each other, but do not substitute for one another. Good research practice requires that both should be taken into consideration to make sound quantitative decisions. A Monte Carlo simulation experiment was conducted, and a…

A discussion of the importance and procedures for including probability in the elementary through secondary mathematics curriculum is presented. Many examples and problems are presented which the author feels students can understand and will be motivated to do. Random digits, Monte Carlo methods, combinatorial theory, and Markov chains are…

The paper describes the small sample stability of least square estimates of variance components within the context of generalizability theory. Monte Carlo methods are used to generate data conforming to some selected multifacet generalizability designs to illustrate the sampling behavior of variance component estimates. (Author/CTM)

Presents a Monte Carlo simulation on probability using a telephone directory as a pseudorandom-number generator. Claims that Monte Carlo simulations offer a way to teach probability concretely and with understanding and that students enjoy the probability experiments. (ASK)

A Monte Carlo study evaluated the effectiveness of different factor analysis extraction and rotation methods for identifying the known population multiple-indicator measurement model. Results demonstrate that exploratory factor analysis can contribute to a useful heuristic strategy for model specification prior to cross-validation with…

Used Monte Carlo simulation to determine the psychometric conditions under which differences between raw scores and Rasch transformations of those raw scores are detectable through two-way analysis of variance. Findings demonstrate the inherent inadequacy of untransformed raw scores for two-way analysis of variance. (SLD)