# Short proof of Miss Harley's theorem on the correlation coefficient

## Short proof of Miss Harley's theorem on the correlation coefficient

Abstract

In conclusion, it is a pleasure to acknowledge the help I have received from my students in the preparation of the tables. Particular mention must be made of Mr G. Balakrishnan, Mr R. Raman, Mr S. Rajagopalan, Mr V. Sivakumaran and Mr S. R. Srinivasavaradan. I also wish to express my sincere thanks to Prof. E. S. Pearson for his helpful comments on earlier versions of the paper. REFERENCES CRAMEB, H. (1951). Mathematical Methods of Statistics. Princeton University Press. HABLEY, B. I. (1954). Biometrika, 41, 278. HARLEY, B. I. (1956). Biometrika, 43, 219. HOTEIXING, H. (1953). J.R. Statist. Soc. B, 15, 193. PILLAI, K. C. S. (1946). Sankhya, 7, 418. Downloaded from biomet.oxfordjournals.org at Infovell on November 16, 2010 Short proof of Miss Harley's theorem on the correlation coefficient BY H. E. DANIELS, University of Birmingham AND M. G. KENDALL, Research Techniques Unit, London School of Economics 1. In considering the correlation coefficient r based on a sample of n values from a, bivariate normal population with correlation parameter p, Hotelling (1953) discussed the question: does there exist a function ^(r), independent of n, such that Erp-(r) = i/r(p) for all n? He showed that for functions expressible
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Title
Short proof of Miss Harley's theorem on the correlation coefficient
Author(s)
H. E. DANIELS and M. G. KENDALL
Journal
Biometrika , Volume 45 ( 3-4 ): 571 Oxford University Press – Dec 1, 1958
Publisher
American Physiological Society