Skip Navigation

Biometrika 1976 63(1):214-215; doi:10.1093/biomet/63.1.214
© 1976 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by WOLFE, D. A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Miscellanea

On testing equality of related correlation coefficients

DOUGLAS A. WOLFE

Department of Statistics, Ohio State University

Let (X1, X2, X3) have a trivariate distribution with mean vector µ and covariance matrix {Sigma} having (i, j)th element {sigma}ij={rho}ij{sigma}i{sigma}j with {rho}ij= 1(i, j=1, 2, 3). If we are interested in testing the hypothesis H:{rho}12={rho}13 against appropriate alternatives under a variety of assumptions about the form of the trivariate distribution, but with no further restrictions on {Sigma}, we could use one of the many asymptotic or conditional procedures that are available; see, for example, Aitkin, Nelson & Reinfurt (1968), Corsten (1970) and Dunn & Clark (1969). On the other hand, an exact, small-sample, unconditional test of H does not appear to be tractable for this general {Sigma}. We show that by placing a mild restriction on {Sigma}, such a small-sample test of H can be based on a simple, single product-moment correlation coefficient between the variables X1 and X3–X2 provided that the conditional distribution of X1 given X3–X2, is normal.

Key Words: Covariance matrices • Equality of regressions • Exact tests • Related correlation coefficients


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Am J EpidemiolHome page
B. Rosner and R. Gore
Measurement Error Correction in Nutritional Epidemiology based on Individual Foods, with Application to the Relation of Diet to Breast Cancer
Am. J. Epidemiol., November 1, 2001; 154(9): 827 - 835.
[Abstract] [Full Text] [PDF]

Home page
 JOURNAL OF EDUCATIONAL AND BEHAVIORAL STATISTICSHome page
J. E. Boyer Jr., A. D. Palachek, and W. R. Schucany
An Empirical Study of Related Correlation Coefficients
Journal of Educational and Behavioral Statistics, January 1, 1983; 8(1): 75 - 86.
[Abstract] [PDF]


Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.