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,…

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations found that standard errors derived without the normality assumption were more accurate than those derived with the normality assumption in a large sample with moderately skewed score distributions. (SLD)

D. W. Zimmerman argues that the interpretation by J. D. Gibbons and S. Chakraborti of recent simulation results and their recommendations are misleading and suggests use of an alternate test when homogeneity of variance and normality are violated. Gibbons and Chakraborti review their differences with Zimmerman's position. (SLD)

This study examined the sampling distribution of the analysis of variance F ratio in the two sample cases when it followed a preliminary test for variance equality. When the population variances were equal, the sampling distribution approximated the theoretical F distribution quite well, but not when population variances differed. (JAZ)

Investigates the BILOG computer program's ability to recover known item parameters for different numbers of items, examinees, and variances of the prior distributions of discrimination parameters for the two-parameter logistic item-response theory model. For samples of at least 250 examinees and 15 items, simulation results support using BILOG.…

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…

A Monte Carlo study was done to determine the adequate sample size for quasi-experimental regression studies, which compare regression lines for two groups and estimate their point of intersection. Populations of 1,000 subjects in each of two groups were constructed (using random normal deviates) to yield equivalent regression lines of opposite…

Modifications are proposed to the recently developed method of comparing one-step M-estimators of location corresponding to two independent groups that provides good control over the probability of Type I error even for unequal sample size, unequal variances, and different shaped distributions. Simulation results reveal cautions required. (SLD)

The feasibility of quick norms derived by the procedure described by B. D. Wright and M. H. Stone (1979) was investigated. Norming differences between traditionally calculated means and Rasch "quick" means were examined for simulated data sets of varying sample size, test length, and type of distribution. A 5 by 5 by 2 design with a…

This study investigated the robustness of the James second-order test (James 1951; Wilcox, 1989) and the univariate F test under a two-factor fixed-effect analysis of variance (ANOVA) model in which cell variances were heterogeneous and/or distributions were nonnormal. With computer-simulated data, Type I error rates and statistical power for the…

This paper investigates three methods for comparing medians rather than means in studying two independent treatment groups. The method that gave the best results is based on a normal approximation of the distribution of the sample median where the variance is estimated using results reported by Maritz and Jarrett. (Author/JAZ)

A normally distributed data set of 1,000 values--ranging from 50 to 150, with a mean of 50 and a standard deviation of 20--was created in order to evaluate the bootstrap method of repeated random sampling. Nine bootstrap samples of N=10 and nine more bootstrap samples of N=25 were randomly selected. One thousand random samples were selected from…

The purpose of this study was to compare two non-parametric procedures, the Mantel-Haenszel (MH) procedure and the simultaneous item bias (SIB) procedure, with respect to their Type I error rates and power, and to investigate the conditions under which asymptotic distributional properties of the SIB and MH were obtained. Data were simulated to…

Effects of test length, sample size, and assumed ability distribution were investigated in a multiple replication Monte Carlo study under the 1-parameter (1P) and 2-parameter (2P) logistic graded model with five score levels. Accuracy and variability of item parameter and ability estimates were examined. Monte Carlo methods were used to evaluate…

The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects…