This article uses simulation to compare two test equating methods under the common-item nonequivalent groups design: the frequency estimation method and the chained equipercentile method. An item response theory model is used to define the true equating criterion, simulate group differences, and generate response data. Three linear equating…

Restricted the range of nonnormal distributions by eliminating scores above a designated cutoff value or eliminating scores above or below the mean by a certain distance. Results of a simulation study show that range restriction sometimes increased the correlation between variables having outlier prone distributions. Discusses practical…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

Studied whether the theoretical sampling distribution of the U3 person-fit statistic is in agreement with the simulated sampling distribution under different item response theory models and varying item and test characteristics. Simulation results suggest that the use of standard normal deviates for the standardized version of the U3 statistic may…

A person-fit method that allows researchers to identify nonfitting response vectors is the l(z) statistic. Simulation results show that l(z) may not perform as expected when estimated person parameters are used rather than true person parameters. Other considerations in using true and estimated person parameters are discussed. (SLD)

Theoretical null distributions of several fit statistic have been derived for paper-and-pencil tests. Examined whether these distributions also hold for computerized adaptive tests through simulation. Rates for two statistics studied were found to be similar in most cases. (SLD)

Evaluated the distribution of person fit within the computerized-adaptive testing (CAT) environment through simulation. Found that, within the CAT environment, these indexes tend not to follow a standard normal distribution. Person fit indexes had means and standard deviations that were quite different from the expected. (SLD)

Comparing variability of test scores across alternate forms, test conditions, or subpopulations is a fundamental problem in psychometrics. A confidence interval for a ratio of standard deviations is proposed that performs as well as the classic method with normal distributions and performs dramatically better with nonnormal distributions. A simple…

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)