Demonstrates how substantive researchers can use a Monte Carlo study to decide on sample size and determine power. Presents confirmatory factor analysis and growth models as examples, conducting these analyses with the Mplus program (B. Muthen and L. Muthen 1998). (SLD)

A Monte Carlo simulation examined the Type I error rates and power of four tests of the null hypothesis that a correlation matrix equals the identity matrix. The procedure of C. J. Brien and others (1984) was found to be the most powerful test maintaining stable empirical alpha values. (SLD)

The Type I error rates and statistical power of nine selected multiple comparison procedures were compared in a Monte Carlo study. The Peretz, Ryan, and Fisher-Hayter tests were the most powerful, and differences among these procedures were consistently small. Choosing among these procedures might be based on their calculational complexity. (SLD)

The normality of number distributions generated by various random-number generators were studied, focusing on when the random-number generator reached a normal distribution and at what sample size. Findings suggest the steps that should be followed when using a random-number generator in a Monte Carlo simulation. (SLD)

The problem of chance model modifications under varying levels of sample size, model size, and severity of misspecification in confirmatory factor analysis models was examined through Monte Carlo simulations. Findings suggest that practitioners should exercise caution when interpreting modified models unless sample size is quite large. (SLD)

Illustrates that sampling variance can be very large when a three-wave quasi simplex model is used to obtain reliability estimates. Also shows that, for the reliability parameter to be identified, the model assumes a Markov process. These problems are evaluated with both real and Monte Carlo data. (SLD)

Explains a situation in which the standard nonparametric one-sample runs test gives anomalous results and describes a procedure that allows the maximum run length to be determined empirically through a Monte Carlo permutation test. Illustrates the new procedure with examples from suicide research and psycholinguistics. (SLD)

Two bootstrap tests are proposed to test the independence hypothesis in a two-way cross table. Monte Carlo studies are used to compare the traditional asymptotic test with these bootstrap methods, and the bootstrap methods are found superior in two ways: control of Type I error and statistical power. (SLD)

Simulated data for factor analytic models is used in the evaluation of three methods for controlling Type I errors: (1) the standard approach that involves testing each parameter at the 0.05 level; (2) the Bonferroni approach; and (3) a simultaneous test procedure (STP). Advantages offered by the Bonferroni approach are discussed. (SLD)

Whether "more is ever too much" for the number of indicators per factor in confirmatory factor analysis was studied by varying sample size and indicators per factor in 35,000 Monte Carlo solutions. Results suggest that traditional rules calling for fewer indicators for smaller sample size may be inappropriate. (SLD)

Studied the relationship between internal test bias and regression slope differences. Monte Carlo simulation results indicate a strong relationship between internal test bias and slope differences, but this relationship does not imply that an absence of internal test bias leads to slope invariance or that slope differences imply internal test…

This article illustrates the use of the SAS system for Monte Carlo simulation work in structural equation modeling (SEM). Data generation procedures for both multivariate normal and nonnormal conditions are discussed, and relevant SAS codes for implementing these procedures are presented. A hypothetical example is presented in which Monte Carlo…

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness…

In this article we analyze the dynamics of endowment spending and real endowment values using rules that tie endowment spending to inflation. Numerical examples demonstrate that under a pure inflation rule, spending rates tend to drift away over time from the appropriate rate, leading to either rising or falling real endowment values. Under a…

The purpose of this study was to investigate and compare the performance of a stepwise variable selection algorithm to traditional exploratory factor analysis. The Monte Carlo study included six factors in the design; the number of common factors; the number of variables explained by the common factors; the magnitude of factor loadings; the number…