Equating, Concordance, and Expectation

Abstract

How do scores from different tests relate to each other? Three types of score linkage are discussed: equating, concordance, and prediction of expected scores. Statistical indices, in conjunction with rational considerations, are needed to determine whether the highest level of linkage attainable between scores from two “tests” is the conceptual and statistical interchangeability sought by equating, the distributional similarity of concordance links, or the minimum squared loss attained by prediction of expected scores. Relationships among the different scales of the ACT and SAT I are described in the context of the conceptual framework developed herein. These relationships are used to evaluate the appropriateness of concordances and predictions of expected scores among various scores on these two prominent tests. Sums of scores, composite scores, and individual scores are examined. The importance of score reliability in assessing linkage possibilities is discussed.