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On Estimation and Hypothesis Testing Problems for Correlation Coefficients

Published online by Cambridge University Press:  01 January 2025

Helena Chmura Kraemer
Helena Chmura Kraemer*
Affiliation:
Stanford Medical School
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Abstract

A selection of statistical problems commonly encountered in psychological or psychiatric research concerning correlation coefficients are re-evaluated in the light of recently developed simplifications in the forms of the distribution theory of the intraclass correlation coefficient (exact theory), of the product-moment correlation coefficient and of the Spearman rank correlation coefficient (approximate).

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 4 , December 1975 , pp. 473 - 485
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

Helena Chmura Kraemer is Associate Professor of Biostat, istics in Psychiatry, Department of Psychiatry and Behavioral Science, Stanford Medical School, Stanford, California 94305.

References

Anderson, T. W.. Introduction to multivariate statistical analysis, 1958, New York: John Wiley and Sons, Inc..Google Scholar
Arrow, Kenneth J. et al. Decision theory and the choice of a level of significance for the t-test. In Olkin, I. et al (Eds.), Contributions to probability and statistics. Stanford: Stanford University Press. 1960, 70–78.Google Scholar
David, F. N.. Tables of the distribution of the correlation coefficients, 1938, London: Biometrika Office.Google Scholar
David, F. N.. Tables of the ordinates and probability integral of the distribution of the correlation coefficients in small samples, 1938, London: Cambridge University Press.Google Scholar
DeLury, D. B.. Note on correlations. Annals of Mathematical Statistics, 1938, 9, 149–151.Google Scholar
Fieller, E. C., Hartley, H. O., Pearson, E. S.. Tests for rank correlation coefficients, I. Biometrika, 1957, 44, 470–481.CrossRefGoogle Scholar
Fieller, E. C., Pearson, E. S.. Tests for rank corerlation coefficients, II. Biometrika, 1961, 48, 29–40.Google Scholar
Fisher, R. A.. On the ‘probable error’ of a coefficient of correlation deduced from a small sample. Metron, 1921, 1, 1–32.Google Scholar
Hsu, C. T.. On samples from a normal bivariate population. Annals of Mathematical Statistics, 1940, 11, 410–426.CrossRefGoogle Scholar
Kraemer, Helena Chmura. Improved approximation to the non-null distribution of the correlation coefficient. Journal of the American Statistical Association, 1974, 68, 1004–1008.CrossRefGoogle Scholar
Kraemer, Helena Chmura. The non-null distribution theory of the Spearman rank correlation coefficient. Journal of the American Statistical Association, 1974, 69, 114–117.CrossRefGoogle Scholar
Kristof, Walter. On a statistic arising in testing correlation. Psychometrika, 1972, 39, 377–384.CrossRefGoogle Scholar
Mehta, J. S., Gurland, John. Some properties and an application of a statistic arising in testing correlation. Annals of Mathematical Statistics, 1969, 40, 1736–1745.CrossRefGoogle Scholar
Olkin, Ingram. Correlations revisited. In Stanley, J. (Eds.), Improving experimental design and statistical analysis. Chicago: Rand McNally. 1967, 102–156.Google Scholar
Olkin, I., Siotani, M.. Testing for the equality of correlation coefficients for various multivariate models, 1964, Stanford: Stanford University Laboratory for Quantitative Research in Education.Google Scholar
Pearson, E. S., Hartley, H. O.. Biometrika tables for statisticians (Vol. 1), 1962, London: Cambridge University Press.Google Scholar
Samiudden, M.. On a test for an assigned value of correlation in a bivariate normal distribution. Biometrika, 1970, 57, 461–464.Google Scholar