The effectiveness of circular equating as a criterion for evaluating equating

Circular equating-equating a test form to itself through a chain of equatin gs-has been widely used as a criterion to evaluate the adequacy of equating . In this paper, analytical methods and simulations showed that this criter ion is generally invalid for evaluating the adequacy of equating. Three dif ferent designs were studied: (1) the random groups design implemented in th e same year, (2) the random groups design implemented across different year s, and (3) the common-item-nonequivalent-groups design. For Design 1, it wa s 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 ran dom sampling error. A simulation study for this design also showed that exp ected values of circular equating might deviate slightly from the identity function, but those deviations do not reflect the systematic error (bias) e mbedded in the equating. For Design 3, a simulation study again showed that circular equating cannot reflect the systematic error in equating.