Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…

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…

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…

The selection of bandwidth in kernel equating is important because it has a direct impact on the equated test scores. The aim of this article is to examine the use of double smoothing when selecting bandwidths in kernel equating and to compare double smoothing with the commonly used penalty method. This comparison was made using both an equivalent…

Preequating is in demand because it reduces score reporting time. In this article, we evaluated an observed-score preequating method: the empirical item characteristic curve (EICC) method, which makes preequating without item response theory (IRT) possible. EICC preequating results were compared with a criterion equating and with IRT true-score…

In this article, we introduce a section preequating (SPE) method (linear and nonlinear) under the randomly equivalent groups design. In this equating design, sections of Test X (a future new form) and another existing Test Y (an old form already on scale) are administered. The sections of Test X are equated to Test Y, after adjusting for the…

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

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…

While agreeing with van der Linden (this issue) that test equating needs better theoretical underpinnings, my comments criticize several aspects of his article. His examples are, for the most part, worthless; he does not use well-established terminology correctly; his view of 100 years of attempts to give a theoretical basis for equating is…

van der Linden (this issue) uses words differently than Holland and Dorans. This difference in language usage is a source of some confusion in van der Linden's critique of what he calls equipercentile equating. I address these differences in language. van der Linden maintains that there are only two requirements for score equating. I maintain…

Based on Lord's criterion of equity of equating, van der Linden (this issue) revisits the so-called local equating method and offers alternative as well as new thoughts on several topics including the types of transformations, symmetry, reliability, and population invariance appropriate for equating. A remarkable aspect is to define equating…

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…

The van der Linden article (this issue) provides a roadmap for future research in equating. My belief is that the roadmap begins and ends with collecting auxiliary data that can be utilized to provide improved equating, especially when data are sparse or equating beyond simple moments is desired.

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…