A The standardized and unstandardized canonical correlation coefficients

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Standardized canonical correlation coefficients are calculated by normalizing the variables, allowing for comparison across different scales, while unstandardized coefficients reflect the raw relationships between the variables without scaling. The standardized coefficients provide insights into the strength of the relationship in a standardized context, whereas unstandardized coefficients indicate the actual magnitude of the relationship. The distinction is crucial for interpreting results in canonical correlation analysis, as standardized coefficients are often more useful for understanding the relative importance of variables. Canonical correlation analysis in SPSS 27 outputs both types of coefficients, enabling researchers to choose the most appropriate for their analysis. Understanding these differences enhances the interpretation of the relationships between sets of variables.
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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?
 
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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)##
 
fresh_42 said:
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.
 

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