Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon…

We revisit the empirically observed positive correlation between DIF and difficulty studied by Freedle and commonly seen in tests of verbal proficiency when comparing populations of different mean latent proficiency levels. It is shown that a positive correlation between DIF and difficulty estimates is actually an expected result (absent any true…

The efficiency of cognitive component skills is typically assessed with speeded performance tests. Interpreting only effective ability or effective speed as efficiency may be challenging because of the within-person dependency between both variables (speed-ability tradeoff, SAT). The present study measures efficiency as effective ability…

Multiple-choice (MC) items are widely used in educational tests. Distractor analysis, an important procedure for checking the utility of response options within an MC item, can be readily implemented in the framework of item response theory (IRT). Although random guessing is a popular behavior of test-takers when answering MC items, none of the…

For any testing programs that administer multiple forms across multiple years, maintaining score comparability via equating is essential. With continuous testing and high-stakes results, especially with less secure online administrations, testing programs must consider the potential for cheating on their exams. This study used empirical and…

A key consideration when giving any computerized adaptive test (CAT) is how much adaptation is present when the test is used in practice. This study introduces a new framework to measure the amount of adaptation of Rasch-based CATs based on looking at the differences between the selected item locations (Rasch item difficulty parameters) of the…

A conceptualization of multiple-choice exams in terms of signal detection theory (SDT) leads to simple measures of item difficulty and item discrimination that are closely related to, but also distinct from, those used in classical item analysis (CIA). The theory defines a "true split," depending on whether or not examinees know an item,…

Calibration of an item bank for computer adaptive testing requires substantial resources. In this study, we investigated whether the efficiency of calibration under the Rasch model could be enhanced by improving the match between item difficulty and student ability. We introduced targeted multistage calibration designs, a design type that…

In a signal detection theory (SDT) approach to multiple choice exams, examinees are viewed as choosing, for each item, the alternative that is perceived as being the most plausible, with perceived plausibility depending in part on whether or not an item is known. The SDT model is a process model and provides measures of item difficulty, item…

An Angoff standard setting study generally yields judgments on a number of items by a number of judges (who may or may not be nested in panels). Variability associated with judges (and possibly panels) contributes error to the resulting cut score. The variability associated with items plays a more complicated role. To the extent that the mean item…

Studies have shown that item difficulty can vary significantly based on the context of an item within a test form. In particular, item position may be associated with practice and fatigue effects that influence item parameter estimation. The purpose of this research was to examine the relevance of item position specifically for assessments used in…

Even though guessing biases difficulty estimates as a function of item difficulty in the dichotomous Rasch model, assessment programs with tests which include multiple-choice items often construct scales using this model. Research has shown that when all items are multiple-choice, this bias can largely be eliminated. However, many assessments have…

Bayesian methods incorporate model parameter information prior to data collection. Eliciting information from content experts is an option, but has seen little implementation in Bayesian item response theory (IRT) modeling. This study aims to use ethical reasoning content experts to elicit prior information and incorporate this information into…

The equating performance of two internal anchor test structures--miditests and minitests--is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods…

This inquiry is an investigation of item response theory (IRT) proficiency estimators' accuracy under multistage testing (MST). We chose a two-stage MST design that includes four modules (one at Stage 1, three at Stage 2) and three difficulty paths (low, middle, high). We assembled various two-stage MST panels (i.e., forms) by manipulating two…