The authors introduced nominal weights mean equating, a simplified version of Tucker equating, as an alternative for dealing with very small samples. The authors then conducted three simulation studies to compare nominal weights mean equating to six other equating methods under the nonequivalent groups anchor test design with sample sizes of 20,…

Because of concerns about test security, different test forms are typically used across different testing occasions. As a result, equating is necessary in order to get scores from the different test forms that can be used interchangeably. In order to assure the quality of equating, multiple equating methods are often examined. Various equity…

Koretz, in his article published in this issue, provides compelling arguments that the high stakes currently associated with accountability testing lead to behavioral changes in students, teachers, and other stakeholders that often have negative consequences, such as inflated scores. Koretz goes on to argue that these negative consequences require…

In operational equating situations, frequency estimation equipercentile equating is considered only when the old and new groups have similar abilities. The frequency estimation assumptions are investigated in this study under various situations from both the levels of theoretical interest and practical use. It shows that frequency estimation…

Calibration and equating is the quintessential necessity for most large-scale educational assessments. However, there are instances when no consideration is given to the equating process in terms of context and substantive realization, and the methods used in its execution. In the view of the authors, equating is not merely an exhibit of the…

In common-item equating the anchor block is generally built to represent a miniature form of the total test in terms of content and statistical specifications. The statistical properties frequently reflect equal mean and spread of item difficulty. Sinharay and Holland (2007) suggested that the requirement for equal spread of difficulty may be too…

A goal for any linking or equating of two or more tests is that the linking function be invariant to the population used in conducting the linking or equating. Violations of population invariance in linking and equating jeopardize the fairness and validity of test scores, and pose particular problems for test-based accountability programs that…

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…

In this study we investigated when an equating conversion line is problematic in terms of gaps and clumps. We suggest using the conditional standard error of measurement (CSEM) to measure the scale scores that are inappropriate in the overall raw-to-scale transformation.

In spite of all of the technical progress in observed-score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test-theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's…

In his thoughtful focus article, Haertel (this issue) pushes testing experts to broaden the scope of their validation efforts and to invite scholars from other disciplines to join them. He credits existing validation frameworks for helping the measurement community to identify incomplete or nonexistent validity arguments. However, he notes his…

Differential item functioning (DIF) analysis is an important step in the data analysis of large-scale testing programs. Nowadays, many such programs endorse matrix sampling designs to reduce the load on examinees, such as the balanced incomplete block (BIB) design. These designs pose challenges to the traditional DIF analysis methods. For example,…

When good model-data fit is observed, the Many-Facet Rasch (MFR) model acts as a linking and equating model that can be used to estimate student achievement, item difficulties, and rater severity on the same linear continuum. Given sufficient connectivity among the facets, the MFR model provides estimates of student achievement that are equated to…

This manual contains technical information about the ACT® college readiness assessment. The principal purpose of this manual is to document the technical characteristics of the ACT in light of its intended purposes. ACT regularly conducts research as part of the ongoing formative evaluation of its programs. The research is intended to ensure that…

Local equating (LE) is based on Lord's criterion of equity. It defines a family of true transformations that aim at the ideal of equitable equating. van der Linden (this issue) offers a detailed discussion of common issues in observed-score equating relative to this local approach. By assuming an underlying item response theory model, one of…