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Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis

Published online by Cambridge University Press:  01 January 2025

Gwowen Shieh
Gwowen Shieh*
Affiliation:
National Chiao Tung University, Taiwan
*
Request for reprints should be sent to Gwowen Shieh, Department of Management Science, National Chiao Tung University, Hsinchu, Taiwan 30050, ROC. E-mail: gwshieh@mail.nctu.edu.tw
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Abstract

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple correlation coefficients. The inversion principle and monotonicity property of the proposed formulations are used to describe alternative approaches to the exact interval estimation, power calculation, and sample size determination for correlation coefficients.

Keywords

multiple correlationpartial-multiple correlationsimple correlation
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 3 , September 2006 , pp. 529 - 540
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

The author thanks the referees for their constructive comments and helpful suggestions and especially the associate editor for drawing attention to several critical results which led to substantial improvements of the exposition. The work for this paper was initiated while the author was visiting the Department of Statistics, Stanford University. This research was partially supported by National Science Council Grant NSC-94-2118-M-009-004.

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