The Effectiveness of Circular Equating as a Criterion for Evaluating Equating

Abstract

Circular equating—equating a test form to itself through a chain of equatings—has been widely used as a criterion to evaluate the adequacy of equating. In this paper, analytical methods and simulations showed that this criterion is generally invalid for evaluating the adequacy of equating. Three different designs were studied: (1) the random groups design implemented in the same year, (2) the random groups design implemented across different years, and (3) the common-item-nonequivalent-groups design. For Design 1, it was shown analytically that circular equating always resulted in the identity function (i.e., the perfect result), even with the presence of random and systematic equating errors. For Design 2, a heuristic argument showed that circular equating generally deviates from the identity function by some random sampling error. A simulation study for this design also showed that expected values of circular equating might deviate slightly from the identity function, but those deviations do not reflect the systematic error (bias) embedded in the equating. For Design 3, a simulation study again showed thatcircular equating cannot reflect the systematic error in equating. systematic error in equating.