Finding a Correction for the Sampling Error in Multivariate Measures of Relationship: A Monte Carlo Study

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Abstract
Canonical correlation analysis is a powerful statistical method subsuming other parametric significance tests as special cases, and which can often best honor the complex reality to which most researchers wish to generalize. However, it has been suggested that the canonical correlation coefficient is positively biased. A Monte Carlo study involving 1,000 random samples from each of 64 different population matrices was conducted to investigate bias in both canonical correlation and redundancy coefficients, and to provide an empirical basis for isolating an appropriate correction formula. Results indicate that the Wherry correction, first suggested for use with the multiple correlation coefficient, provides a reasonable correction that is sensitive to those factors most affecting bias. The results also indicate that canonical results are not as positively biased as some researchers have believed, especially if sample size is at least 10 subjects per variable or effect sizes are moderate or large.

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