The standardized group mean difference, Cohen's "d", is among the most commonly used and intuitively appealing effect sizes for group comparisons. However, reporting this point estimate alone does not reflect the extent to which sampling error may have led to an obtained value. A confidence interval expresses the uncertainty that exists between…

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact…

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

The ability of the Minnesota Multiphasic Personality Inventory-Adolescent (MMPI-A; J. N. Butcher et al., 1992) validity scales to detect random, partially random, and nonrandom MMPI-A protocols was investigated. Investigations included the Variable Response Inconsistency scale (VRIN), F, several potentially useful new F and VRIN subscales, and…

A hierarchical latent regression model is suggested to estimate nested and nonnested relationships in complex samples such as found in the National Assessment of Educational Progress (NAEP). The proposed model aims at improving both parameters and variance estimates via a two-level hierarchical linear model. This model falls naturally within the…

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

Validity generalization meta-analysis (VG) examines the extent to which the validity of an instrument can be transported across settings. VG offers correction and summarization procedures designed in part to remove the effects of statistical artifacts on estimates of association between criterion and predictor. By employing a random effects model,…

Type I error rates of the likelihood ratio test for the detection of differential item functioning (DIF) were investigated using Monte Carlo simulations. The graded response model with five ordered categories was used to generate data sets of a 30-item test for samples of 300 and 1,000 simulated examinees. All DIF comparisons were simulated by…

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…

The Type I error and power properties of the 2x2x2 analysis of variance (ANOVA) and tests developed by McSweeney (1967), Bradley (1979), Harwell-Serlin (1989; Harwell, 1991), and Blair-Sawilowsky (1990) were compared using Monte Carlo methods. The ANOVA was superior under the Gaussian and uniform distributions. The Blair-Sawilowsky test was…

Induced probabilities have been largely ignored by educational researchers. Simply stated, if a new or random variable is defined in terms of a first random variable, then induced probability is the probability or density of the new random variable that can be found by summation or integration over the appropriate domains of the original random…

P. O. Johnson and J. Neyman (1936) proposed a general linear hypothesis testing procedure for testing the null hypothesis of no treatment difference in the presence of some covariates. This is generally known as the Johnson-Neyman (JN) technique. The need for the hypothesis testing step (often omitted) as originally presented and the…

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

Psychology studies often have low statistical power. Sample size tables, as given by J. Cohen (1988), may be used to increase power, but they are based on Monte Carlo studies of relatively "tame" mathematical distributions, as compared to psychology data sets. In this study, Monte Carlo methods were used to investigate Type I and Type II…

Monte Carlo studies of statistical tests are prominently featured in the methodological research literature. Unfortunately, the information from these studies does not appear to have significantly influenced methodological practice in educational and psychological research. One reason is that Monte Carlo studies lack an overarching theory to guide…