Population invariance is a desirable property of test equating which might not hold when significant changes occur in the test population, such as those brought about by the COVID-19 pandemic. This research aims to investigate whether equating functions are reasonably invariant when the test population is impacted by the pandemic. Based on…

Recent research has suggested that re-setting the standard for each administration of a small sample examination, in addition to the high cost, does not adequately maintain similar performance expectations year after year. Small-sample equating methods have shown promise with samples between 20 and 30. For groups that have fewer than 20 students,…

The aim of this study was to compare, by simulation, the accuracy of mapping a cut-score from one test to another by expert judgement (using the Angoff method) versus the accuracy with a small-sample equating method (chained linear equating). As expected, the standard-setting method resulted in more accurate equating when we assumed a higher level…

Examinees who attempt the same test multiple times are often referred to as "repeaters." Previous studies suggested that repeaters should be excluded from the total sample before equating because repeater groups are distinguishable from non-repeater groups. In addition, repeaters might memorize anchor items, causing item drift under a…

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

In this study, we apply jackknifing to anchor items to evaluate the impact of anchor selection on equating stability. In an ideal world, the choice of anchor items should have little impact on equating results. When this ideal does not correspond to reality, selection of anchor items can strongly influence equating results. This influence does not…

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally…

This paper investigates four methods of linear equating under the common item nonequivalent groups design. Three of the methods are well known: Tucker, Angoff-Levine, and Congeneric-Levine. A fourth method is presented as a variant of the Congeneric-Levine method. Using simulation data generated from the three-parameter logistic IRT model we…

This article proposes that sampling design effects have potentially huge unrecognized impacts on the results reported by large-scale district and state assessments in the United States. When design effects are unrecognized and unaccounted for they lead to underestimating the sampling error in item and test statistics. Underestimating the sampling…

A series of resampling studies investigated the accuracy of equating by four different methods in a random groups equating design with samples of 400, 200, 100, and 50 test takers taking each form. Six pairs of forms were constructed. Each pair was constructed by assigning items from an existing test taken by 9,000 or more test takers. The…

Small sample equating remains a largely unexplored area of research. This study attempts to fill in some of the research gaps via a large-scale, IRT-based simulation study that evaluates the performance of seven small-sample equating methods under various test characteristic and sampling conditions. The equating methods considered are typically…

This study examined the effect of including or excluding repeaters on the equating process and results. New forms of two tests were equated to their respective old forms using either all examinees or only the first timer examinees in the new form sample. Results showed that for both tests used in this study, including or excluding repeaters in the…

A series of resampling studies was conducted to compare the accuracy of equating in a common item design using four different methods: chained equipercentile equating of smoothed distributions, chained linear equating, chained mean equating, and the circle-arc method. Four operational test forms, each containing more than 100 items, were used for…

Scores on the multiple-choice sections of alternate forms are equated through anchor-test equating for the Advanced Placement Program (AP) examinations. There is no linkage of free-response sections since different free-response items are given yearly. However, the free-response and multiple-choice sections are combined to produce a composite.…

The adequacy of equipercentile, linear, one-parameter (Rasch), and three-parameter logistic item-response theory procedures for equating 12 forms of five tests of general educational development were compared. Results indicated the equating method adequacy depends on a variety of factors such as test characteristics, equating design, and sample…