This paper focuses on mixtures of two binomials with one known success parameter. It is shown how moment estimators can be obtained for the remaining unknown parameters of such mixtures, and results are presented from a Monte Carlo study carried out to explore the statistical properties of these estimators. (PN)

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…

The Feldt-Gilmer congeneric reliability coefficients make it possible to estimate the reliability of a test composed of parts of unequal, unknown length. The approximate standard errors of the Feldt-Gilmer coefficients are derived via a method using the multivariate Taylor's expansion. Monte Carlo simulation is employed to corroborate the…

The standard error of measurement usefully provides confidence limits for scores in a given test, but is it possible to quantify the reliability of a test with just a single number that allows comparison of tests of different format? Reliability coefficients do not do this, being dependent on the spread of examinee attainment. Better in this…

Two approaches to criterion-referenced test construction are compared. Classical test theory is based on the practice of random sampling from a well-defined domain of test items; latent trait theory suggests that the difficulty of the items should be matched to the achievement level of the student. In addition to these two methods of test…

In most reliability studies, the precision of a reliability estimate varies inversely with the number of examinees (sample size). Thus, to achieve a given level of accuracy, some minimum sample size is required. An approximation for this minimum size may be made if some reasonable assumptions regarding the mean and standard deviation of the test…

This study compares the ability of the multiple indicators, multiple causes (MIMIC) confirmatory factor analysis model to correctly identify cases of differential item functioning (DIF) with more established methods. Although the MIMIC model might have application in identifying DIF for multiple grouping variables, there has been little…

Eight independent variables (differential item functioning [DIF] detection method, purification procedure, item response model, mean latent trait difference between groups, test length, DIF pattern, magnitude of DIF, and percentage of DIF items) were manipulated, and two dependent variables (Type I error and power) were assessed through…

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…

As item response theory (IRT) becomes popular in educational and psychological testing, there is a need of reporting IRT-based effect size measures. In this study, we show how the standardized mean difference can be generalized into such a measure. A disattenuation procedure based on the IRT test reliability is proposed to correct the attenuation…

When criterion-referenced tests are used to assign examinees to states reflecting their performance level on a test, the better known methods for determining test length, which consider relationships among domain scores and errors of measurement, have their limitations. The purpose of this paper is to present a computer system named TESTLEN, which…

Multiple matrix sampling of three subscales of the California Psychological Inventory was used to investigate the effects of four variables on error estimates of the mean (EEM) and variance (EEV). The four variables were examinee population size (600, 450, 300, 150, 100, and 75); number of subtests, (2, 3, 4, 5, 6, and 7), hence the number of…

Effects of dimensionality on ability estimation of an adaptive test were examined using generated data in Bayesian computerized adaptive testing (CAT) simulations. Generally, increasing interdimensional difficulty association produced a slight decrease in test length and an increase in accuracy of ability estimation as assessed by root mean square…

The sampling errors of maximum likelihood estimates of item-response theory parameters are studied in the case where both people and item parameters are estimated simultaneously. A check on the validity of the standard error formulas is carried out. The effect of varying sample size, test length, and the shape of the ability distribution is…