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…

The present study investigates the influence of multidimensionality on linking and equating in a unidimensional IRT. Two hypothetical multidimensional scenarios are explored under a nonequivalent group common-item equating design. The first scenario examines test forms designed to measure multiple constructs, while the second scenario examines a…

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…

This dissertation was designed to foster a deeper understanding of population invariance in the context of composite-score equating and provide practitioners with guidelines for addressing score equity concerns at the composite score level. The purpose of this dissertation was threefold. The first was to compare different composite equating…

In this digital ITEMS module, Dr. Stella Kim provides an overview of multidimensional item response theory (MIRT) equating. Traditional unidimensional item response theory (IRT) equating methods impose the sometimes untenable restriction on data that only a single ability is assessed. This module discusses potential sources of multidimensionality…

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…

Oral reading fluency (ORF) assessments are commonly used to screen at-risk readers and to evaluate the effectiveness of interventions as curriculum-based measurements. As with other assessments, equating ORF scores becomes necessary when we want to compare ORF scores from different test forms. Recently, Kara et al. (2023) proposed a model-based…

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…

The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions…

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…