In practice, some test items may display misfit at the upper-asymptote of item characteristic curve due to distraction, anxiety, or carelessness by the test takers (i.e., the slipping effect). The conventional item response theory (IRT) models do not take the slipping effect into consideration, which may violate the model fit assumption in IRT.…

A didactic example is provided, using a Monte Carlo method, of how differential item functioning (DIF) can be eliminated (and thus better understood) when the complete latent space is used. The main source of DIF is that the matching single criterion used in some DIF procedures, Mantel Haenszel or Simultaneous Item Bias (SIBTEST), does not account…

A new approach to assessing unexpected differential item performance (item bias or item fairness) is introduced and applied to the item responses of different subpopulations of Scholastic Aptitude Test (SAT) takers. The essential features of the standardization approach are described. The primary goal of the standardization approach is to control…

A new index for assessing the dimensionality underlying a set of test items was investigated. The incremental fit index (IFI) is based on the sum of squares of the residual covariances. Purposes of the study were to: (1) examine the distribution of the IFI in the null situation, with truly unidimensional data; (2) examine the rejection rate of the…

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

The application of latent trait theory to classroom tests necessitates the use of small sample sizes for parameter estimation. Computer generated data were used to assess the accuracy of estimation of the slope and location parameters in the two parameter logistic model with fixed abilities and varying small sample sizes. The maximum likelihood…

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

Effects of the following methods for linking metrics on detection of differential item functioning (DIF) were compared: (1) test characteristic curve method (TCC); (2) weighted mean and sigma method; and (3) minimum chi-square method. With large samples, results were essentially the same. With small samples, TCC was most accurate. (SLD)

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…

A Monte Carlo study was conducted to estimate the small sample standard errors and statistical bias of psychometric statistics commonly used in the analysis of achievement tests. The statistics examined in this research were: (1) the index of item difficulty; (2) the index of item discrimination; (3) the corrected item-total point-biserial…

Empirical evidence is presented of the relative efficiency of two potential linkage plans to be used when equivalent test forms are being administered. Equating is a process by which scores on one form of a test are converted to scores on another form of the same test. A Monte Carlo study was conducted to examine equating stability and statistical…

A Monte Carlo study was conducted to compare the performance of three statistical indices of test item bias in small samples of examinees. The statistical indices compared were the Delta method, the Mantel-Haenszel (MH) method, and the Standardization method. Sample sizes of 50, 100, and 200 were examined. One thousand samples of each size were…

This study investigates two fixed parameter models for calibrating test items for an item bank under local school district control. Mathematics, reading, and language tests administered to students (Grades 7-9) provided the criterion information. Model I used calibrations from the Northwest Evaluation Association Item Bank to calibrate new items…

This paper demonstrates the relationship between the concept of unidimensionality and direction of an item in a multidimensional space. The basic premise is that if items that measure in the same direction are combined to form a test, that test will meet the item response theory requirements of unidimensionality. This will be true even if the…