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…

The characteristic curve methods have been applied to estimate the equating coefficients in test equating under the graded response model (GRM). However, the approaches for obtaining the standard errors for the estimates of these coefficients have not been developed and examined. In this study, the delta method was applied to derive the…

Building on prior research on the relationships between key concepts in item response theory and classical test theory, this note contributes to highlighting their important and useful links. A readily and widely applicable latent variable modeling procedure is discussed that can be used for point and interval estimation of the individual person…

In the current study, two pools of 250 essays, all written as a response to the same prompt, were rated by two groups of raters (14 or 15 raters per group), thereby providing an approximation to the essay's true score. An automated essay scoring (AES) system was trained on the datasets and then scored the essays using a cross-validation scheme. By…

Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…

The simultaneous item bias test (SIBTEST) method regression procedure and the differential item functioning (DIF)-free-then-DIF strategy are applied to the logistic regression (LR) method simultaneously in this study. These procedures are used to adjust the effects of matching true score on observed score and to better control the Type I error…

The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design.…

Several factors could cause variability in item response theory (IRT) linking and equating procedures, such as the variability across examinee samples and/or test items, seasonality, regional differences, native language diversity, gender, and other demographic variables. Hence, the following question arises: Is it possible to select optimal…

A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method--which uses the normal approximation to the binomial distribution--have actual coverage probabilities that are closest to their nominal level. It has also recently…

This report introduces a short, hands-on activity that addresses a key challenge in teaching quantitative methods to students who lack confidence or experience with statistical analysis. Used near the beginning of the course, this activity helps students develop an intuitive insight regarding a number of abstract concepts which are key to…

Grouped jackknifing may be used to evaluate the stability of equating procedures with respect to sampling error and with respect to changes in anchor selection. Properties of grouped jackknifing are reviewed for simple-random and stratified sampling, and its use is described for comparisons of anchor sets. Application is made to examples of item…

In the nonequivalent groups with anchor test (NEAT) design, there are several ways to use the information provided by the anchor in the equating process. One of the NEAT-design equating methods is the linear observed-score Levine method (Kolen & Brennan, 2004). It is based on a classical test theory model of the true scores on the test forms…

This study evaluated the impact of unequal reliability on test equating methods in the nonequivalent groups with anchor test (NEAT) design. Classical true score-based models were compared in terms of their assumptions about how reliability impacts test scores. These models were related to treatment of population ability differences by different…

An equation comparable to Spearman's correction for attenuation, which does not depend upon the assumption that error scores are uncorrelated with true scores and with other sets of scores, is derived. (Editor)

Although partial correlation is a correlation of residuals, the correlation of the true-score components of these residuals is not equivalent to the partial correlation of the true scores themselves. The source of this discrepancy is explained and its implications are briefly discussed. (Author)