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The Nature of the Data, or How to Choose a Correlation Coefficient

Published online by Cambridge University Press:  01 January 2025

John B. Carroll*
Affiliation:
Harvard University

Abstract

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Type
Original Paper
Copyright
Copyright © 1961 The Psychometric Society

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Footnotes

*

Presidential address delivered to the Psychometric Society, New York City, September 6, 1961.

References

Binder, A. Consideration of the place of assumptions in correlational analysis. Amer. Psychologist, 1959, 14, 504510.CrossRefGoogle Scholar
Carroll, J. B. A factor analysis of verbal abilities. Psychometrika, 1941, 6, 279307.CrossRefGoogle Scholar
Carroll, J. B. The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 1945, 10, 119.CrossRefGoogle Scholar
Cattell, R. B. Factor analysis, New York: Harper, 1952.Google Scholar
Cureton, E. E. Note on φ/φmax. Psychometrika, 1959, 24, 8991.CrossRefGoogle Scholar
DeSoto, C. B. and Kuethe, J. L. On the relation between two variables. Educ. psychol. Measmt, 1960, 20, 743749.CrossRefGoogle Scholar
Dingman, H. F. The relation between coefficients of correlation and difficulty factors. Brit. J. statist. Psychol., 1958, 11, 1317.CrossRefGoogle Scholar
Dunlap, J. W. Psychometrics—a special case of the Brahman theory. Psychometrika, 1961, 26, 6571.CrossRefGoogle Scholar
Ferguson, G. A. The factorial interpretation of test difficulty. Psychometrika, 1941, 6, 323329.CrossRefGoogle Scholar
Furfey, P. H. Comment on “The needless assumption of normality in Pearson'sr.”. Amer. Psychologist, 1958, 13, 545546.CrossRefGoogle Scholar
Gage, N. L. and Damrin, D. E. Reliability, homogeneity, and number of choices. J. educ. Psychol., 1950, 41, 385404.CrossRefGoogle Scholar
Gourlay, N. Difficulty factors arising from the use of tetrachoric correlations in factor analysis. Brit. J. statist. Psychol., 1951, 4, 6573.CrossRefGoogle Scholar
Guilford, J. P. The difficulty of a test and its factor composition. Psychometrika, 1941, 6, 6777.CrossRefGoogle Scholar
Guttman, L. Metricizing rank-ordered or unordered data for a linear factor analysis. Sankhyā, 1959, 21, 257268.Google Scholar
Heath, H. A. An empirical study of correlation involving a half-normal distribution. Psychol. Rep., 1961, 9, 8586.CrossRefGoogle Scholar
John, E. and Burt, C. A reply to Mr. Gourlay's criticisms. Brit. J. statist. Psychol., 1951, 4, 7376.CrossRefGoogle Scholar
Kruskal, W. H. Ordinal measures of association. J. Amer. statist. Ass., 1958, 53, 814861.CrossRefGoogle Scholar
LaForge, R. Comment on “The needless assumption of normality in Pearson'sr.”. Amer. Psychologist, 1958, 13, 546546.CrossRefGoogle Scholar
Loevinger, J. A systematic approach to the construction and evaluation of tests of ability. Psychol. Monogr., 1947, 61(4), 149.CrossRefGoogle Scholar
Luce, R. D. On the possible psychophysical laws. Psychol. Rev., 1959, 66, 8195.CrossRefGoogle ScholarPubMed
Milholland, J. E. Comment on “The needless assumption of normality in Pearson'sr.”. Amer. Psychologist, 1958, 13, 544545.CrossRefGoogle Scholar
Nefzger, M. D. and Drasgow, J. The needless assumption of normality in Pearson'sr. Amer. Psychologist, 1957, 12, 623625.CrossRefGoogle Scholar
Norris, R. C. and Hjelm, H. F. Non-normality and product-moment correlation. J. exp. Educ., 1961, 29, 261270.CrossRefGoogle Scholar
Schuell, H. and Jenkins, J. J. The nature of language deficit in aphasia. Psychol. Rev., 1959, 66, 4567.CrossRefGoogle ScholarPubMed
Senders, V. L. Measurement and statistics. New York: Oxford, 1958..Google Scholar
Siegel, S. Nonparametric statistics for the behavioral sciences, New York: McGraw-Hill, 1956.Google Scholar
Stevens, S. S. Mathematics, measurement, and psychophysics. In Stevens, S. S. (Eds.), Handbook of experimental psychology. New York: Wiley, 1951, 149..Google Scholar
Thomson, G. H. The factorial analysis of human ability (5th ed.), Boston: Houghton-Mifflin, 1951.Google Scholar
Thurstone, L. L. Primary mental abilities, Chicago: Univ. Chicago Press, 1938.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar