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Estimation of a Correlation Coefficient from an Uncertainty Measure

Published online by Cambridge University Press:  01 January 2025

William H. Pearson
William H. Pearson*
Affiliation:
Aerospace Medical, Research Laboratories Wright-Patterson Air Force Base, Ohio
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Abstract

In this paper graphs are given for estimating a correlation ρXY from a double-entry table. 2 Hr, twice the statistic Hr, “relative uncertainty” (the average of the ratios of the conditional uncertainty of each variable to its uncertainty) was computed. Mean 2 Hr's were computed from 100 samples for each of several sample sizes and numbers of categories. Graphs relating mean 2 Hr to \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat r_H$$\end{document}, the estimated correlation, for 3–17 categories to each variable and 3 sample sizes—50, 100, and 500—were constructed. 2.5 per cent and 97.5 per cent fiducial limits curves were constructed for establishing confidence limits on ρXY and \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat r_H$$\end{document}.

Type
Original Paper
Information
Psychometrika , Volume 31 , Issue 3 , September 1966 , pp. 421 - 433
Copyright
Copyright © 1966 Psychometric Society

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Footnotes

*

The research reported in this paper was conducted by personnel of the Aerospace Medical Research Laboratories, Aerospace Medical Division, Air Force Systems Command, Wright-Patterson AFB, Ohio. Further reproduction is authorized to satisfy the needs of the U. S. Government. This paper has been identified by the Aerospace Medical Research Laboratories as AMRL-TR-66-54.

References

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