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A Note on Roy's Largest Root

Published online by Cambridge University Press:  01 January 2025

Warren F. Kuhfeld
Warren F. Kuhfeld*
Affiliation:
The University of North Carolina at Chapel Hill
*
Requests for reprints should be sent to Warren F. Kuhfeld, The L. L. Thurstone Psychometric Laboratory, Davie Hall 013-A, The University of North Carolina, Chapel Hill, NC 27514.
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Abstract

The name “Roy's largest root” and similar names are used in practice to label two different but functionally related statistics—one proportional to anF, and the other, a squared canonical correlation. This note presents the logic that leads to the two formulations, states which statistic some popular statistical packages use, and shows the possible source of this inconsistency in the original work of Roy (1953) and Heck (1960).

Keywords

Roy's largest rootMANOVAcanonical correlationmultivariate test statistics
Type
Computational Psychometrics
Information
Psychometrika , Volume 51 , Issue 3 , September 1986 , pp. 479 - 481
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

The author wishes to thank Lyle Jones, Mark Appelbaum, and Elliot Cramer, for their comments on an earlier version of this note.

SAS ® is a registered trademark of SAS Institute Inc, Cary, NC. SPSS ® is a registered trademark of SPSS Inc, Chicago IL. SPSS xTM is a trademark of SPSS Inc, Chicago, IL. BMDP ® is a registered trademark of BMDP Statistical Software, Los Angeles, CA.

References

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