A recursive equation is proposed for computing higher order derivatives of elementary symmetric functions in the Rasch model. A simulation study indicates a small loss in accuracy for the proposed formula compared to Gustafsson's sum algorithm (1980) for computing higher order derivatives when tests contain 60 items or less. (SLD)

In this paper, we apply sequential one-sided confidence interval estimation procedures with beta-protection to adaptive mastery testing. The procedures of fixed-width and fixed proportional accuracy confidence interval estimation can be viewed as extensions of one-sided confidence interval procedures. It can be shown that the adaptive mastery…

Type I error rates and rejection rates for three-dimensionality assessment procedures were studied with data sets simulated to reflect short tests and small samples. Results show that the G-squared difference test (D. Bock, R. Gibbons, and E. Muraki, 1988) suffered from a severely inflated Type I error rate at all conditions simulated. (SLD)

N. S. Raju, W. J. van der Linden, and P. F. Fleer (in press) have proposed an item response theory-based, parametric procedure for the detection of differential item functioning (DIF)/differential test functioning (DTF) known as differential functioning of item and test (DFIT). DFIT can be used with dichotomous, polytomous, or multidimensional…

An index is proposed to detect cheating on multiple-choice examinations, and its use is evaluated through simulations. The proposed index is based on the compound binomial distribution. In total, 360 simulated data sets reflecting 12 different cheating (copying) situations were obtained and used for the study of the sensitivity of the index in…

Studied five factors that can affect the equating of scores from two tests onto a common score scale through the simulation and equating of 4,860 item data sets. Findings indicate three statistically significant two-way interactions for common item length and test length, item difficulty standard deviation and item distribution type, and item…

Examined the effects of test length and sample size on the alternate forms reliability and equating of simulated mathematics tests composed of constructed response items scaled using the two-parameter partial credit model. Results suggest that, to obtain acceptable reliabilities and accurate equated scores, tests should have at least 8 6-point…

Traditionally, the fixed-length linear paper-and-pencil (P&P) mode of administration has been the standard method of test delivery. With the advancement of technology, however, the popularity of administering tests using adaptive methods like computerized adaptive testing (CAT) and multistage testing (MST) has grown in the field of measurement…

Compared differential item functioning detection rates for logistic regression and analysis of variance for dichotomously scored items using simulated data and varying test length, sample size, discrimination rate, and underlying ability. Explains why the logistic regression method is recommended for most applications. (SLD)

The effect of person misfit to an item response theory model on a mastery/nonmastery decision was investigated. Furthermore, it was investigated whether the classification precision can be improved by identifying misfitting respondents using person-fit statistics. A simulation study was conducted to investigate the probability of a correct…

The usefulness of a goodness-of-fit index proposed by R. P. McDonald (1989) was investigated with regard to assessing the dimensionality of item response matrices. The m subscript k index, which is based on an estimate of the noncentrality parameter of the noncentral chi-square distribution, possesses several advantages over traditional tests of…

The purpose of this study was to examine empirical Type I error rates and rejection rates for three dimensionality assessment procedures with data sets simulated to reflect short tests and small samples. The TESTFACT G superscript 2 difference test suffered from an inflated Type I error rate with unidimensional data sets, while the approximate chi…

Monte Carlo research with TAILOR, a program using implied orders as a basis for tailored testing, is reported. TAILOR typically required about half the available items to estimate, for each simulated examinee, the responses on the remainder. (Author/CTM)

The power of the nonparametric person-fit statistic, U3, is investigated through simulations as a function of item characteristics, test characteristics, person characteristics, and the group to which examinees belong. Results suggest conditions under which relatively short tests can be used for person-fit analysis. (SLD)

Adaptive tests offer the advantages of reduced test length and increased accuracy in ability estimation. However, adaptive tests require large pools of precalibrated items. This study looks at the development of an item pool for 1 type of adaptive administration: the computer-adaptive sequential test. An important issue is the sample size required…