Using simulated data, the MULTILOG and PARSCALE software packages were compared for their recovery of item and trait parameters under the graded response and generalized partial credit item response theory models. The shape of the latent population distribution (normal, skewed, or uniform) and the sample size (250 or 500) were varied. Parameter…

Previous studies that investigated the effect of unequal ability distributions on the Type I error (TIE) of the Mantel-Haenszel chi-square test for detecting differential item functioning (DIF) simulated ability distributions that differed only in means. This simulation study suggests that the magnitude of TIE inflation is increased, and the type…

This paper evaluated multidimensional linking procedures with which multidimensional test data from two separate calibrations were put on a common scale. Data were simulated with known ability distributions varying on two factors which made linking necessary: mean vector differences and variance-covariance (v-c) matrix differences. After the…

To satisfy the security requirements of computerized adaptive tests (CATs), efforts have been made to control the exposure rates of optimal items directly by incorporating statistical methods into the item selection procedure. Since differences are likely to occur between the exposure control parameter derivation stage and the operational CAT…

The assumption of normality underlies much of the standard statistical methodology. Knowing how to determine whether a sample of measurements is from a normally distributed population is crucial both in the development of statistical theory and in practice. W. Ware and J. Ferron have developed a new test statistic, modeled after the K-squared test…

In this paper, six statistical tests of stochastic equality are compared with respect to Type I error and power through a Monte Carlo simulation. In the simulation, the skewness and kurtosis levels and the extent of variance heterogeneity of the two parent distributions were varied across a wide range. The sample sizes applied were either small or…

This simple method for simulating the Central Limit Theorem with students in a beginning nonmajor statistics class requires students to use dice to simulate drawing samples from a discrete uniform distribution. On a chalkboard, the distribution of sample means is superimposed on a graph of the discrete uniform distribution to provide visual…

The utility of the three-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. Simulation studies demonstrate that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly…

The extent to which properties of the ability scale and the form of the latent trait distribution influence the estimated item parameters of item response theory (IRT) was investigated using real and simulated data. Simulated data included 5,000 ability values randomly drawn from the standard normal distribution. Real data included the results for…

The main goal of this study was to assess how sensitive unidimensional parameter estimates derived from BILOG were when the unidimensionality assumption was violated and the underlying ability distribution was not multivariate normal. A multidimensional three-parameter logistic distribution that was a straightforward generalization of the…

The functioning of two population-based Mantel-Haenszel (MH) common-odds ratios was compared. One ratio is conditioned on the observed test score, while the other is conditioned on a latent trait or true ability score. When the comparison group distributions are incongruent or nonoverlapping to some degree, the observed score represents different…

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

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,…

This study compared the model of J. E. Grizzle, C. F. Starmer, and G. G. Koch (GSK, 1969) and log-linear model-based approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-effect size, and column-effect size. Test statistics for column (main) and interaction effects were…

Simulated data are used to assess the appropriateness of using separate calibration and between-fit approaches to detecting item bias in the Rasch rating scale model. Results indicate that Type I error rates for the null distribution hold even when there are different ability levels for reference and focal groups. (SLD)