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…

Sampling errors limit the accuracy with which forms can be linked. Limitations on accuracy are especially important in testing programs in which a very large number of forms are employed. Standard inequalities in mathematical statistics may be used to establish lower bounds on the achievable inking accuracy. To illustrate results, a variety of…

This article describes two methods for obtaining the standard errors of two commonly used population invariance measures of equating functions: the root mean square difference of the subpopulation equating functions from the overall equating function and the root expected mean square difference. The delta method relies on an analytical…

Equating functions are supposed to be population invariant, meaning that the choice of subpopulation used to compute the equating function should not matter. The extent to which equating functions are population invariant is typically assessed in terms of practical difference criteria that do not account for equating functions' sampling…

This exploratory study was built on research spanning three decades. Petersen, Marco, and Stewart (1982) conducted a major empirical investigation of the efficacy of different equating methods. The studies reported in Dorans (1990) examined how different equating methods performed across samples selected in different ways. Recent population…

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

The sample invariant properties of five anchor test equating methods are addressed. Equating results across two sampling conditions--representative sampling and new-form matched sampling--are compared for Tucker and Levine equally reliable linear equating, item response theory true-score equating, and two equipercentile methods. (SLD)

Meehl's taxometric method was developed to distinguish categorical and continuous constructs. However, taxometric output can be difficult to interpret because expected results for realistic data conditions and differing procedural implementations have not been derived analytically or studied through rigorous simulations. By applying bootstrap…

Articles on equating test forms in this issue are reviewed and discussed. The results of these papers collectively indicate that matching on the anchor test does not result in more accurate equating. Implications for research are discussed. (SLD)

The articles in this issue that address the effect of matching samples on ability are reviewed. In spite of these examinations of equating methods and sampling plans, it is still hard to determine a definitive answer to the question of to match or not to match. Implications are discussed. (SLD)

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

This paper addresses the sample invariant properties of four equating methods (Tucker and Levine linear equating, equipercentile equating through an anchor test, and three-parameter item response theory equating). Data from several national administrations of the Scholastic Aptitude Test served as the source of data for the study. Equating results…

Using the characteristic curve method for dichotomously scored test items, the sampling distributions of equating coefficients were examined. Simulations indicate that for the equating conditions studied, the sampling distributions of the equating coefficients appear to have acceptable characteristics, suggesting confidence in the values obtained…

Two recent simulation studies were conducted to aid in the diagnosis and interpretation of equating differences found between random and matched (nonrandom) samples for four commonly used equating procedures: (1) Tucker; (2) Levine equally reliable; (3) Chained equipercentile observed-score; and (4) three-parameter, item response theory true-score…

Equating two parallel forms of the College Board Biology Achievement Test using three sampling strategies was examined. For each strategy, five equating procedures were studied: Tucker and Levine equally reliable linear equatings; frequency estimation equipercentile equatings; chained equipercentile curvilinear equatings; and three-parameter…