Sample size determination is an important issue in planning research. In the context of one-way fixed-effect analysis of variance, the conventional sample size formula cannot be applied for the heterogeneous variance cases. This study discusses the sample size requirement for the Welch test in the one-way fixed-effect analysis of variance with…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

Grading on the curve is a common practice in higher education. While there are many critics of the practice it still finds wide spread acceptance particularly in science classes. Advocates believe that in large classes student ability is likely to be normally distributed. If test scores are also normally distributed instructors and students tend…

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

This study was designed to derive the distribution of a test statistic based on normal probability plots. The first purpose was to provide an empirical derivation of the critical values for the Line Test (LT) with an extensive computer simulation. The goal was to develop a test that is sensitive to a wide range of alternative distributions,…

A convention commonly used to describe interaction effects within moderated regression frameworks was examined through logical exposition and a Monte Carlo approach to simulate various moderator conditions. Results, which indicate that the convention may lead to incorrect inferences, are discussed in terms of interpreting moderator effects. (SLD)

A simulation study compares nonhierarchical clustering capabilities of a class of neural networks using Kohonen learning with a K-means clustering procedure. The focus is on the ability of the procedures to recover correctly the known cluster structure in the data. Advantages and disadvantages of the procedures are reviewed. (SLD)

The probabilities of attaining varying magnitudes of standardized effect sizes by chance and when protected by a 0.05 level statistical test were studied. Monte Carlo procedures were used to generate standardized effect sizes in a one-way analysis of variance situation with 2 through 5, 6, 8, and 10 groups with selected sample sizes from 5 to 500.…

Monte Carlo simulations were used to examine three cases using analyses of variance (ANOVAs) sequentially. Simulation results show that Type I error rates increase when using ANOVAs in this sequential fashion, and the detrimental effect is greatest in situations in which researchers would most likely use ANOVAs sequentially. (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.…

A complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)

Results of a Monte Carlo study with 4 populations (3,072 conditions) indicate that when distributions depart markedly from normality, nonparametric analysis and parametric analysis of transformed data show superior power to parametric analysis of raw data. Under conditions studied, parametric analysis of transformed data is more powerful than…

Whether it is possible to develop a classification function that identifies the underlying range restriction from sample information alone was investigated in a simulation. Results indicate that such a function is possible. The procedure was found to be relatively accurate, robust, and powerful. (SLD)