There are good reasons for the growing popularity of Monte Carlo procedures; but with increasing use comes increasing misuse. A variety of exact and approximate alternatives should be considered before one chooses to approach a problem with Monte Carlo methods. Once it has been decided that simulation is desirable, consideration should be given to…

A computer program to perform a Monte Carlo simulation of counting experiments was written. The program was based on a mathematical derivation which started with counts in a time interval. The time interval was subdivided to form a binomial distribution with no two counts in the same subinterval. Then the number of subintervals was extended to…

A Monte Carlo simulation was used to compare the Mahalanobis "D" Squared and the Comrey "Dk" methods of detecting outliers in data sets. Under the conditions investigated, the "D" Squared technique was preferable as an outlier removal statistic. (SLD)

A Monte Carlo study, involving 6,000 "computer subjects" and three raters, explored the reliability of the inverse screen test for cluster analysis. Results indicate that the inverse screen may be a useful and reliable cluster analytic technique for determining the number of true groups. (TJH)

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…