Many measures of predictive power have been recommended. These include Mean Cost Rating (MCR), P(A), (from Signal Detection Theory), Kendall's rank correlation coefficient tau, and Goodman and Kruskal's gamma. It is shown that these four measures are related as all are merely different transformations of the statistic S. By reference to S, whose distribution is known, hypothesis testing is made possible. Of the four measures considered gamma is generally to be preferred. Remarks made here apply equally to measures of association for ordered contingency tables.
Get full access to this article
View all access options for this article.
References
1.
Copas, J. B. and Whiteley, J. S.Predicting success in the treatment of psychopaths. British Journal of Psychiatry, 1976, 129, 388-392.
2.
Duncan, O. D. , Ohlin, L. E., Reiss, A. J. and Stanton, H. R.Formal devices for making selection decisions. American Journal of Sociology, 1953, 58, 573-584.
3.
Fergusson, D. M. , Fifield, J. K., and Slater, S. W.Signal detectability theory and the evaluation of prediction tables. Journal of Research in Crime and Delinquency, 1977, 14, 237-246.
4.
Goodman, L. A. and Kruskal, W. H.Measures of association for cross classifications I. Journal of the American Statistical Association, 1954, 49, 732-764.
5.
Goodman, L. A. and Kruskal, W. H.Measures of association for cross classifications II. Journal of the American Statistical Association, 1959, 54, 123-163.
6.
Goodman, L. A. and Kruskal, W. H.Measures of association for cross classifications III. Journal of the American Statistical Association, 1963, 58, 310-364.
7.
Goodman, L. A. and Kruskal, W. H.Measures of association for cross classifications IV. Journal of the American Statistical Association, 1972, 67, 415-421.
8.
Kendall, M. G.Rank correlation methods. London: Griffin, 1970.
9.
Kendall, M. G. and Stuart, A.The advanced theory of statistics Vol. 2 London: Griffin, 1973.
10.
Lancucki, L. and Tarling, R.The relationship between Mean Cost Rating (MCR) and Kendall's Rank Correlation Coefficient Tau. Social Science Research, 1978, 7, 81-87.
11.
Simon, F. H.Prediction methods in criminology. London: HMSO, 1971.
12.
Stuart, A.The estimation and comparison of strengths of association in contingency tables . Biometrika, 1953, 40, 105-110.
