This paper describes a computer program, CORFREE, which computes the ordinal correlations discussed by Freeman. The correlation coefficients are calculated for the sample data, and the population values are estimated by a combination of the jackknife with robust/resistant methods. The sampling variance of each correlation coefficient is estimated by robust/resistant methods. The program computes one- and two-tailed significance tests of the null hypothesis by randomization methods. The program is useful for calculating the descriptive family of ordinal correlation coefficients described by Freeman, and for finding their significance levels. The program uses computer intensive methods to reduce errors or biases in estimating the population coefficients or their sampling variances. Program outputs can be further analyzed by other programs.
Get full access to this article
View all access options for this article.
References
1.
Agresti, A. (1976). The effect of category choice on some ordinal measures of association. Journal of the American Statistical Association, 71, 49-55.
2.
Balloun, J. L. and Oumlil, A. B. (1988). Comparing the results of nonmetric multidimensional scaling and principal components analysis. Journal of Business Research, 17(1), 5-14.
3.
Berry, K. J. , Jacobsen, R. B., and Martin, T. W. (1976). Clarifying the use of chi-square: Testing the significance of Goodman and Kruskal's gamma. Social Science Quarterly, 56, 687-690.
4.
Berry, K. J. , Mielke, P. W., Jr., and Jacobsen, R. B. (1977). A large sample procedure for testing coefficients of ordinal association: Goodman and Kruskal's gamma and Somers' dba and dab. Educational and Psychological Management37(3), 791-794.
5.
Carroll, J. B. (1945). The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 10, 1-19.
6.
Carroll, J. B. (1961). The nature of the data, or how to choose a correlation coefficient. Psychometrika, 26, 347-372.
7.
Devlin, S. J. , Gnanadesikan, R., and Kettenring, J. R. (1981). Robust estimation of dispersion matrices and principal components. Journal of the American Statistical Association, 76(374), 354-362.
8.
Efron, B. (1979a). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.
9.
Efron, B. (1979b). Computers and the theory of statistics: Thinking the unthinkable. Society for Industrial and Applied Mathematics Review, 21, 460-480.
10.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Philadelphia: Society for Industrial and Applied Mathematics.
11.
Fisher, R. A. (1970). Statistical methods for research workers. (14th ed.). New York: Hafner.
12.
Freeman, L. C. (1986). Order-based statistics and monotonicity: A family of ordinal measures of association. Journal of Mathematical Sociology, 12, 49-69.
13.
Gans, L. P. and Robertson, C. A. (1981). Distribution of Goodman and Kruskal's Gamma and Spearman's Rho in 2 × 2 tables for small and moderate sample sizes. Journal of the American Statistical Association, 76, 942-946.
14.
Goodman, L. A. and Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732-764.
15.
Hildebrand, D. K. , Laing, J. D., and Rosenthal, H. (1977). Analysis of ordinal data. Beverly Hills: Sage.
16.
IBM (1968). 1130 scientific subroutine package. (1130-CM-02X): Programmer's manual (4th ed.). White Plains, N.Y.: Author.
17.
Kendall, M. G. (1962). Rank correlation methods. London: Griffin.
18.
Kim, J. O. (1971). Predictive measures of ordinal association. American Journal of Sociology, 76, 891-907.
19.
Mosteller, F. and Tukey, J. W. (1977). Data analysis and regression: A second course in statistics. Menlo Park, Ca.: Addison-Wesley, pp. 203-219.
20.
Nelson, T. O. (1984). A comparison of current measures of the accuracy of feeling-of-knowing predictions. Psychological Bulletin, 95, 109-133.
21.
Nelson, T. O. (1986). BASIC programs for computation of the Goodman-Kruskal gamma coefficient. Bulletin of the Psychonomic Society, 24, 281-283.
22.
Noreen, E. W. (1989). Computer intensive methods for testing hypotheses. New York: Wiley.
23.
Quade, D. (1974). Nonparametric partial correlation. In Blalock, H. M., Jr. (Ed.) Measurement in the social sciences. Chicago: Aldine, pp. 369-398.
24.
Reynolds, H. T. (1974). Ordinal partial correlation and causal inferences. In Blalock, H. M., Jr. (Ed.) Measurement in the social sciences. Chicago: Aldine, pp. 399-423.
25.
Rosenthal, I. (1966). Distribution of the sample version of the measure of association, gamma. Journal of the American Statistical Association, 61, 440-455.
Wilson, T. P. (1974). Measures of association for bivariate ordinal hypotheses. In Blalock, H. M., Jr. (Ed.) Measurement in the social sciences. Chicago: Aldine, pp. 327-342.
