Hypothesis Testing
Each row can be tested for significance with the following method. Since the correlations are sorted, saying that row is zero implies all further correlations are also zero. If we have independent observations in a sample and is the estimated correlation for . For the th row, the test statistic is:
which is asymptotically distributed as a chi-squared with degrees of freedom for large . Since all the correlations from to are logically zero (and estimated that way also) the product for the terms after this point is irrelevant.
Read more about this topic: Canonical Correlation
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—Ludwig Wittgenstein (1889–1951)
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—Bible: New Testament, 1 Corinthians 10:13.