We explain how to simulate both univariate and bivariate raw data sets having specified values for common summary statistics. The first example illustrates how to "construct" a data set having prescribed values for the mean and the standard deviation--for a one-sample t test with a specified outcome. The second shows how to create a bivariate data…

In educational effectiveness research, multilevel data analyses are often used because research units (most frequently, pupils or teachers) are studied that are nested in groups (schools and classes). This hierarchical data structure complicates designing the study because the structure has to be taken into account when approximating the accuracy…

In multigroup covariance structure analysis with structured means, the traditional latent selection model is formulated as a special case of phenotypic selection. Illustrations with real and simulated data demonstrate how one can test specific hypotheses concerning selection on latent variables. (SLD)

The work of R. MacCallum et al. (1992) was extended by examining chance modifications through a Monte Carlo simulation. The stability of post hoc model modifications was examined under varying sample size, model complexity, and severity of misspecification using 2- and 4-factor oblique confirmatory factor analysis (CFA) models with four and eight…

In the present study Monte Carlo methods were employed to evaluate the degree to which canonical function and structure coefficients may be differentially sensitive to sampling error. Sampling error influences were investigated across variations in variable and sample (n) sizes, and across variations in average within-set correlation sizes and in…

Simulation studies were used to explore the relationship between Type I error rates (statistical conclusion validity) and multiple testing in data sets exhibiting varying degrees of independence. Implications for reporting and interpreting educational data are discussed, and methods of determining or reducing Type I error incidence are presented.…

Comparisons of the Wilcoxon test, Friedman test, and repeated-measures analysis of variance (ANOVA) on ranks in a computer simulation show that the Friedman test performs like the sign test whereas the ANOVA performs like the Wilcoxon test. Classification of these tests in introductory statistics textbooks should be revised. (SLD)

The effect of reducing the number of score groups in the matching criterion of the Mantel-Haenszel procedure when screening for differential item functioning was investigated with a simulated data set. Results suggest that more than modest reductions cannot be recommended when ability distributions of reference and focal groups differ. (SLD)

Computer simulations indicate that the correlation between baseline and change, by itself, does not invalidate the use of gain scores to measure change, but when the negative correlation is accompanied by decrease in variance from pretest to posttest, covariance is a superior measure of change. (SLD)

The derivation of the variance of similarity judgments is made from the 3-D process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter that represents the degree of a form of interdimensional cross-sampling. (SLD)

This study presents an overview of Monte Carlo studies in discriminant analysis. Some common questions about the use of Monte Carlo techniques are answered through a brief literature review of articles on discriminant analysis in which Monte Carlo methods are used. The articles cover many research points, such as comparing error rate estimates,…

Using simulated and real data, this study compares the performance of three methodologies for assessing unidimensionality: (1) DIMTEST; (2) the approach of Holland and Rosenbaum; and (3) nonlinear factor analysis. All three models correctly confirm unidimensionality, but they differ in their ability to detect the lack of unidimensionality.…

C. L. Olson (1976, 1979) suggests the Pillai-Bartlett trace (V) as an omnibus multivariate analysis of variance (MANOVA) test statistic for its superior robustness to heterogeneous variances. J. Stevens (1979, 1980) contends that the robustness of V, Wilk's lambda (W) and the Hotelling-Lawley trace (T) are similar, and that their power functions…

An equating design in which two groups of examinees from slightly different populations are administered a different test form with a subset of common items is widely used. This paper presents standard errors and a simulation that verifies the equation for large samples for an equipercentile equating procedure for this design. (Author/BS)

A modification of a test of the equality of nonindependent alpha reliability coefficients is proposed. It avoids the limitation that the product of the number of test parts times the number of subjects be quite large. Monte Carlo studies indicate that this test can be used in comparing interrater reliabilities. (SLD)