The standardized and unstandardized canonical correlation coefficients

[Ad VanderVen]

TL;DR Summary

What exactly are the standardized and unstandardized canonical correlation coefficients and what is the difference between them?

The output of SPSS 27 Canonical Correlation gives the standardized and unstandardized canonical correlation coefficients.

What exactly are the standardized and unstandardized canonical correlation coefficients and what is the difference between them?

 

[fresh_42]

standardized:
$$
\operatorname{cov}\left(\dfrac{X-\mu_X}{\sigma_X}\, , \,\dfrac{Y-\mu_Y}{\sigma_Y}\right)=\dfrac{1}{\sigma_X\,\sigma_Y}\,\operatorname{cov}(X,Y)
$$

unstandardized:
$\operatorname{cov}(X,Y)$

 

[Ad VanderVen]

standardized:
$$
\operatorname{cov}\left(\dfrac{X-\mu_X}{\sigma_X}\, , \,\dfrac{Y-\mu_Y}{\sigma_Y}\right)=\dfrac{1}{\sigma_X\,\sigma_Y}\,\operatorname{cov}(X,Y)
$$

unstandardized:
$\operatorname{cov}(X,Y)$

You simply define the standardized and unstandardized correlation coefficient, but we are talking about the canonical correlation coefficient here.