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New Results on the Linear Equating Methods for the Non-Equivalent-Groups Design

The two most common observed-score equating functions are the linear and equipercentile functions. These are often seen as different methods, but von Davier, Holland, and Thayer showed that any equipercentile equating function can be decomposed into linear and nonlinear parts. They emphasized the dominant role of the linear part of the nonlinear equating function and gave conditions under which the equipercentile methods in the non-equivalent-groups anchor test (NEAT) design give identical results. Consequently, this article focuses on linear equating methods in a NEAT design—the Tucker, chained, and Levine observed-score functions—and describes the theoretical conditions under which these methods produce the same equating function. Constructed examples illustrate the theoretical results.