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Costner (1965) showed that many of the most commonly used measures of association may be conceptually interpreted as indicating proportional reduction in prediction error. But because it is verbally cumbersome, and conceptually complex for some measures, the proportional reduction in error interpretation has not been widely incorporated in research reports where appropriate. Instead, measures of association continue to be interpreted in abstract terms distinguishing between broad levels of strength. This paper demonstrates that all proportional reduction in error measures of association may be alternately interpreted as indicating the percent of variation explained. Because this interpretation is conceptually meaningful in a manner highly relevant for scientific investigation, more convenient to apply in research reports, and already familiar to most social scientists, it is argued that it be standardly applied to all proportional reduction in error measures. [ABSTRACT FROM AUTHOR]

The theory of regular equivalence has advanced over the last 15 years on a number of different fronts. Notation and terminology have developed often making it difficult to obtain a coherent view of the area as a whole. This paper attempts to provide a framework in which to develop and explore the general mathematical theory of regular equivalence and to place a number of the more important results into that framework. [ABSTRACT FROM AUTHOR]