It is desirable for an educational assessment to be constructed of items that can differentiate different performance levels of test takers, and thus it is important to estimate accurately the item discrimination parameters in either classical test theory or item response theory. It is particularly challenging to do so when the sample sizes are…

We make a distinction between the operational practice of using an observed score to assess differential item functioning (DIF) and the concept of departure from measurement invariance (DMI) that conditions on a latent variable. DMI and DIF indices of effect sizes, based on the Mantel-Haenszel test of common odds ratio, converge under restricted…

Different variants of the selected-response (SR) item type have been developed for various reasons (i.e., simulating realistic situations, examining critical-thinking and/or problem-solving skills). Generally, the variants of SR item format are more complex than the traditional multiple-choice (MC) items, which may be more challenging to test…

We derive formulas for the differential item functioning (DIF) measures that two routinely used DIF statistics are designed to estimate. The DIF measures that match on observed scores are compared to DIF measures based on an unobserved ability (theta or true score) for items that are described by either the one-parameter logistic (1PL) or…

In this report, we demonstrate use of differential response time (DRT) methodology, an extension of differential item functioning methodology, for examining differences in how students from different backgrounds engage with assessment tasks. We analyze response time data from a digitally delivered mathematics assessment to examine timing…

The Mantel-Haenszel delta difference (MH D-DIF) and the standardized proportion difference (STD P-DIF) are two observed-score methods that have been used to assess differential item functioning (DIF) at Educational Testing Service since the early 1990s. Latentvariable approaches to assessing measurement invariance at the item level have been…

With advances in technology, researchers and test developers are developing new item types to measure complex skills like problem solving and critical thinking. Analyzing such items is often challenging because of their complicated response patterns, and thus it is important to develop psychometric methods for practitioners and researchers to…

Two families of analysis methods can be used for differential item functioning (DIF) analysis. One family is DIF analysis based on observed scores, such as the Mantel-Haenszel (MH) and the standardized proportion-correct metric for DIF procedures; the other is analysis based on latent ability, in which the statistic is a measure of departure from…

The early detection of item drift is an important issue for frequently administered testing programs because items are reused over time. Unfortunately, operational data tend to be very sparse and do not lend themselves to frequent monitoring analyses, particularly for on-demand testing. Building on existing residual analyses, the authors propose…

Data collected from online learning and tutoring systems for individual students showed strong autocorrelation or dependence because of content connection, knowledge-based dependency, or persistence of learning behavior. When the response data show little dependence or negative autocorrelations for individual students, it is suspected that…

In this report, systematic applications of statistical and psychometric methods are used to develop and evaluate scoring rules in terms of test reliability. Data collected from a situational judgment test are used to facilitate the comparison. For a well-developed item with appropriate keys (i.e., the correct answers), agreement among various…

Unmotivated test takers using rapid guessing in item responses can affect validity studies and teacher and institution performance evaluation negatively, making it critical to identify these test takers. The authors propose a new nonparametric method for finding response-time thresholds for flagging item responses that result from rapid-guessing…