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The devil rides again: Correlation as an index of fit.

Correlations between theoretical predictions and data can be higher for incorrect than for correct models, as illustrated by analyses of two sets of hypothetical data. This fact raises questions about the conclusions of recent studies that use correlation as an index of fit. Functional measurement provides a sounder basis for model evaluation by placing scaling in the context of model fitting and by testing deviations from prediction rather than concent rating an overall goodness of fit. Although widely recognized as an "instrument of the devil" when used to infer causation from confounded data, the correlation coefficient is still employed as an index of the fit of theoretical models. There are two serious criticisms of this usage. First, incorrect models can correlate highly with data (Anderson, 1971; Yntema & Torgerson, 1961). Second, based upon the assumption that the better model will correlate higher, investigators have recently used the correlation coefficient to compare the fit of rival models.3