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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

Dixon, W. D., Brown, M. B., Engleman, L., Frand, J. W., Hill, M. A., Jenrich, R. I., Toporek, J. D. (1983). BMDP statistical software, Los Angeles: University of California Press.Google Scholar
Eaton, M. L. (1983). Multivariate statistics, A vector space approach, New York: Wiley & Sons.Google Scholar
Heck, D. L. (1960). Charts of some upper percentage points of the distribution of the largest characteristic root. Annals of Mathematical Statistics, 31, 625–642.CrossRefGoogle Scholar
Hull, C. H., Nie, N. H. (1981). SPSS Update 7-9, New York: McGraw Hill.Google Scholar
Olson, C. L. (1976). On choosing a test statistic in multivariate analysis of variance. Psychological Bulletin, 83, 579–586.CrossRefGoogle Scholar
Roy, S. N. (1953). On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics, 24, 220–238.CrossRefGoogle Scholar
SAS Institute Inc. (1985). SAS User's Guide: Statistics Version 5 Edition,, Cary, NC: Author.Google Scholar
SPSS Inc. (1983). SPSSx User's Guide, New York: McGraw Hill.Google Scholar