This paper proposes an extension of linear equating that may be useful in one of two fairly common assessment scenarios. One is where different students have taken different combinations of test forms. This might occur, for example, where students have some free choice over the exam papers they take within a particular qualification. In this…

Item parameter estimation using an item response theory (IRT) model with fixed ability estimates is useful in equating with small samples on anchor items. The current study explores the impact of three ability estimation methods (weighted likelihood estimation [WLE], maximum a posteriori [MAP], and posterior ability distribution estimation [PST])…

Words read correctly per minute (WCPM) is the reporting score metric in oral reading fluency (ORF) assessments, which is popularly utilized as part of curriculum-based measurements to screen at-risk readers and to monitor progress of students who receive interventions. Just like other types of assessments with multiple forms, equating would be…

Equating is a statistical procedure used to adjust for the difference in form difficulty such that scores on those forms can be used and interpreted comparably. In practice, however, equating methods are often implemented without considering the extent to which two forms differ in difficulty. The study aims to examine the effect of the magnitude…

The part of responses that is absent in the nonequivalent groups with anchor test (NEAT) design can be managed to a planned missing scenario. In the context of small sample sizes, we present a machine learning (ML)-based imputation technique called chaining random forests (CRF) to perform equating tasks within the NEAT design. Specifically, seven…

Words read correctly per minute (WCPM) is the reporting score metric in oral reading fluency (ORF) assessments, which is popularly utilized as part of curriculum-based measurements to screen at-risk readers and to monitor progress of students who receive interventions. Just like other types of assessments with multiple forms, equating would be…

The current study proposed several variants of simple-structure multidimensional item response theory equating procedures. Four distinct sets of data were used to demonstrate feasibility of proposed equating methods for two different equating designs: a random groups design and a common-item nonequivalent groups design. Findings indicated some…

One result of recent changes in testing is that previously established linking frameworks may not adequately address challenges in current linking situations. Test linking through equating, concordance, vertical scaling or battery scaling may not represent linkings for the scores of tests developed to measure constructs differently for different…

While significant attention has been given to test equating to ensure score comparability, limited research has explored equating methods for rater-mediated assessments, where human raters inherently introduce error. If not properly addressed, these errors can undermine score interchangeability and test validity. This study proposes an equating…

In many large testing programs, equipercentile equating has been widely used under a random groups design to adjust test difficulty between forms. However, one thorny issue occurs with equipercentile equating when a particular score has no observed frequency. The purpose of this study is to suggest and evaluate six potential methods in…

This simulation study investigated to what extent departures from construct similarity as well as differences in the difficulty and targeting of scales impact the score transformation when scales are equated by means of concurrent calibration using the partial credit model with a common person design. Practical implications of the simulation…

In this study, it was aimed to examine the effect of missing data in different patterns and sizes on test equating methods under the NEAT design for different factors. For this purpose, as part of this study, factors such as sample size, average difficulty level difference between the test forms, difference between the ability distribution,…

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…

Test equating requires collecting data to link the scores from different forms of a test. Problems arise when equating samples are not equivalent and the test forms to be linked share no common items by which to measure or adjust for the group nonequivalence. Using data from five operational test forms, we created five pairs of research forms for…

This study aimed to evaluate the item model fit by equating the forms of the PISA 2018 mathematics subtest with concurrent common items equating in samples from Türkiye, the UK, and Italy. The answers given in mathematics subtest Forms 2, 8, and 12 were used in this context. Analyzes were performed using the Dichotomous Rasch Model in the WINSTEPS…