Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated.…

This paper deals with test fairness regarding a test consisting of two parts: (1) a "common" section, taken by all students; and (2) a "variable" section, in which some students may answer a different set of questions from other students. For example, a test taken by several thousand students each year contains a common multiple-choice portion and…

A primary goal of this study was to determine the extent to which item difficulty was related to item position and, if a significant relationship was found, to suggest adjustments to predicted item difficulty that reflect differences in item position. Item response data from the Medical College Admission Test (MCAT) were analyzed. A data set was…

This study compares the contribution to measurement accuracy of the verbal score of each of four verbal item types included in the Graduate Record Examinations (GRE) General Test. Comparisons are based on item response theory, a methodology that allows the researcher to look at the accuracy of individual points on the score scale. This methodology…

This paper examines how various equating methods are affected by: (1) sampling error; (2) sample characteristics; and (3) characteristics of anchor test items. It reviews empirical studies that investigated the invariance of equating transformations, and it discusses empirical and simulation studies that focus on how the properties of anchor tests…