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…

The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of…

This module describes and extends X-to-Y regression measures that have been proposed for use in the assessment of X-to-Y scaling and equating results. Measures are developed that are similar to those based on prediction error in regression analyses but that are directly suited to interests in scaling and equating evaluations. The regression and…

The purpose of this study was to investigate the potential impact of misrouting under a 2-stage multistage test (MST) design, which includes 1 routing and 3 second-stage modules. Simulations were used to create a situation in which a large group of examinees took each of the 3 possible MST paths (high, middle, and low). We compared differences in…

In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

This study investigated differences between two approaches to chained equipercentile (CE) equating (one- and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other…

Nonequivalent groups with anchor test (NEAT) equating functions that use a single anchor can have accuracy problems when the groups are extremely different and/or when the anchor weakly correlates with the tests being equated. Proposals have been made to address these issues by incorporating more than one anchor into NEAT equating functions. These…

This study compared the accuracies of nine previously proposed statistical significance tests for selecting identity, linear, and equipercentile equating functions in an equivalent groups equating design. The strategies included likelihood ratio tests for the loglinear models of tests' frequency distributions, regression tests, Kolmogorov-Smirnov…

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…