Estimates of various variance components, universe score variance, measurement error variances, and generalizability coefficients, like all statistics, are subject to sampling variability, particularly in small samples. Such variability is quantified traditionally through estimated standard errors and/or confidence intervals. The paper derived new…

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…

This simulation study examined the performance of the curve-of-factors model (COFM) when autocorrelation and growth processes were present in the first-level factor structure. In addition to the standard curve-of factors growth model, 2 new models were examined: one COFM that included a first-order autoregressive autocorrelation parameter, and a…

The purpose of this paper is to evaluate the use of MC2G program to teach certain topics in statistics education. MC2G is a program written in Pascal Delphi by Gordon Brooks of Ohio University based on Monte Carlo studies. MC2G provides students opportunity to practice important topics in an introductory statistics course, such as power, Type I…

This study investigates item parameter recovery, standard error estimates, and fit statistics yielded by the WINSTEPS program under the Rasch model and the rating scale model through Monte Carlo simulations. The independent variables were item response model, test length, and sample size. WINSTEPS yielded practically unbiased estimates for the…