In the framework of the observed-score equating methods for the nonequivalent groups with anchor test design, there are 3 fundamentally different ways of using the information provided by the anchor scores to equate the scores of a new form to those of an old form. One method uses the anchor scores as a conditioning variable, such as the Tucker method and poststratification equating. A second way to use the anchor scores is as the middle link in a chain of linking relationships, such as chain linear equating and chain equating. The third way to use the anchor scores is in conjunction with the classical test theory, such as Levine observed-score equating and the newly created hybrid Levine equipercentile equating and poststratification equating based on true anchor scores. The purpose of this paper is to demonstrate that with real data, under certain conditions, hybrid Levine equipercentile equating and poststratification equating based on true anchor scores outperform both poststratification equating and chain equating.