On the Appropriateness of the Correlation Coefficient with a 0, 1 Dependent Variable

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Abstract
This article deals with the use and misuse of the correlation coefficient when the dependent variable is of a dichotomous 0,1 nature. It focuses particularly on problems relating to curvilinearity and the nature of the prediction being made. The prediction of consumer purchases from reported subjective probabilities provides a vehicle for illustrating problems discussed. It is noted that with a 0,1 dependent variable, the correlation ratio is likely to be a better measure of the degree of relationship than the coefficient of determination because it is free of restrictions on the functional form of the relationship. The article then considers the mean error probability and the average conditional entropy as alternative measures. Finally, the article emphasizes that the purpose for using the relation between the independent and dependent variable should govern the development of an appropriate model and the measure to be used for deciding which of several independent variables is best.

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