Standard Article

Canonical Correlation

  1. Shubhabrata Das1,
  2. Pranab K. Sen2

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a13005

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Das, S. and Sen, P. K. 2005. Canonical Correlation. Encyclopedia of Biostatistics. 1.

Author Information

  1. 1

    Indian Institute Of Management Bangalore, Bangalore, India

  2. 2

    University of North Carolina, Chapel Hill, NC, USA

Publication History

  1. Published Online: 15 JUL 2005


The article starts with the genesis of canonical correlation from the product moment correlation and defines canonical correlation from the various angles including algebraic and geometric approaches. The different issues related to interpreting canonical correlation analysis, for example, canonical coefficients, canonical loadings, and redundancy coefficients are highlighted. Relationship with other multivariate methods like principal component analysis, factor analysis, and MANOVA have also been outlined. Then the article dwells on the sampling distribution of the sample canonical correlation and the related inference problems, while touching upon the relevant resampling methods in this context. Various generalizations and extensions are taken up next, with emphasis on the treatment of dependence between more than two sets of variables as well as constrained dependence under problem specific restrictions on the coefficients. The article concludes with a narration of issues related to applications, specially in the field of Biostatistics and a reference to key articles in this domain.


  • canonical coefficients;
  • canonical loadings;
  • characteristic root;
  • distribution;
  • restricted canonical correlation