Violations of assumptions, inflated Type I error rates, and robustness are important concepts for students to learn in an introductory statistics course. However, these abstract ideas can be difficult for students to understand. Monte Carlo simulation methods can provide a concrete way for students to learn abstract statistical concepts. This…

The Welch-James (WJ) and the Huynh Improved General Approximation (IGA) tests for interaction were examined with respect to Type I error in a between- by within-subjects repeated measures design when data were non-normal, non-spherical and heterogeneous, particularly when group sizes were unequal. The tests were computed with aligned ranks and…

Student ratings of teaching effectiveness are widely used to make judgments of faculty teaching performance. Research, however, has found that such ratings may not be accurate indicators of teaching performance because they are contaminated by course easiness. Using student ratings of 9855 professors employed at 79 different colleges and…

In well-defined domains such as Physics, Mathematics, and Chemistry, solutions to a posed problem can objectively be classified as correct or incorrect. In ill-defined domains such as medicine, the classification of solutions to a patient problem as correct or incorrect is much more complex. Typical tutoring systems accept only a small set of…

Item response models can be applied in many test equating situations by making strong statistical assumptions. Thus, studying the robustness of the models to violations of the assumptions and investigating model-data fit are essential in all item response theory (IRT) equating applications (M. Kolen and R. Brennan, 1995). Previous studies dealing…

The iterative expanding reweighted least squares (IERLS), a weighted-least-squares robust regression procedure, is developed and compared with Huber's M estimator (P. Huber, 1973), the Least Absolute Deviations, the Least Median of Squares, and the Ordinary Least Squares. Data with various outliers contamination were simulated and analyzed. The…

A variety of approaches have been suggested by which to assess the equality of population mean vectors under conditions of population covariance matrix homogeneity and heterogeneity. The nonrobustness of commonly used multivariate tests of means to population covariance matrix heterogeneity has been long documented. However, most studies have…

The performance of analysis of covariance (ANCOVA) and six selected competitors was examined under varying experimental conditions through Monte Carlo simulations. The six alternatives were: (1) Quade's procedure (D. Quade, 1967); (2) Puri and Sen's solution (M. Puri and P. Sen, 1969); (3) Burnett and Barr's rank difference scores (T. Burnett and…

Studied the efficiency and robustness of alternative estimators of regression coefficients for three-level data. A simulation study shows that, as expected, the hierarchical model analyses produced more efficient point estimates than did analyses that ignored the covariance structure in the data, even when the normality assumption was violated.…

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. Majorization is used at several stages in the minimization procedure to obtain a monotonically convergent algorithm. A simulation study and empirical data illustrate the procedure. (SLD)

Hierarchical models are extremely promising tools for data analysis, but it is important not to lessen hard thinking about data and iterative model checking when fitting hierarchical models. More and better software, methods to assure proper calibration, and materials in support of hierarchical model use are all needed. (SLD)

Monte Carlo studies were conducted to compare four multivariate analysis of variance (MANOVA) simultaneous test procedures (STPs) in terms of power and Type I error under various conditions including violations of MANOVA assumptions. Results do not support the hypothesis that the moderately restricted STP is a good compromise between…

Type I error rates for the Johansen test were estimated using simulated data for a variety of conditions. Results indicate that Type I error rates for the Johansen test depend heavily on the number of groups and the ratio of the smallest sample size to the number of dependent variables. Sample size guidelines are presented. (SLD)

The authors argue that a robust version of Cohen's effect size constructed by replacing population means with 20% trimmed means and the population standard deviation with the square root of a 20% Winsorized variance is a better measure of population separation than is Cohen's effect size. The authors investigated coverage probability for…

The aim of this study was to evaluate the effect of aging on the storage of visual and spatial working memory according to Logie's model of working memory (1995). In a first experiment young, elderly, and very old subjects carried out two tasks usually used to measure visual span (Visual Patterns Test) and spatial span (Corsi Block Tapping test).…