The most critical feature of a common-item nonequivalent groups equating design is that the average score difference between the new and old groups can be accurately decomposed into a group ability difference and a form difficulty difference. Two widely used observed-score linear equating methods, the Tucker and the Levine observed-score methods, have different statistical assumptions when decomposing the score difference. Variation in the decomposition of group ability and form difficulty differences can affect the equating results.This study confirmed previous findings in the literature that when form and group differences are small, both equating methods produce similar results. When the group ability difference is large, however, the Levine observed-score method produces more accurate equating results than the Tucker method. The results indicated that the Levine observed-score method not only decomposes form and group differences more accurately, but also yields smaller unweighted absolute equating differences and average weighted root mean square differences.This study showed that the Levine observed-score method is also robust to the form difference.ii Evaluating the Effects of Differences in Group Abilities on the Tucker and the LevineObserved-Score Methods for Common-Item Nonequivalent Groups Equating

An assessment of graphic literacy was developed by articulating and subsequently validating a skills‐based cognitive model intended to substantiate the plausibility of score interpretations. Model validation involved use of multiple sources of evidence derived from large‐scale field testing and cognitive labs studies. Data from large‐scale field testing were evaluated using traditional psychometric methods. The psychometric analyses were augmented using eye tracking technology to perform gaze pattern and pupillometry analyses to gain better understanding of problem‐solving strategies and cognitive load. Findings from the data sources were integrated to provide strong evidence supporting the model and score interpretations. Implications for using gaze pattern and pupillometry analyses to enhance learning and assessment are discussed.

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