I have done a canonical correlation analysis using the American Community Survey Dataset. The analysis is done between Ancestry and Educational Attainment variables. The values for canonical correlations are: {0.8140, 0.5716, 0.4708, 0.3946, 0.1465, 0.1365, 0.0409}.

The values for multivariate tests of significance for the first canonical function:

Statistic        Value    F-Value    df1    df2    P-Value
Wilk's Lambda    0.143    35.373     98    19754   0.000
Pillai's Trace   1.408    54.358     98    21896   0.000
Hotelling Trace  2.961    22.779     98    21842   0.000
Roy's Root       0.662

The redundancy analysis for the first canonical function:

For Educational Attainment variables

Average Squared Loading      Canonical R^2      Redundancy Index
   2.119                    0.666               1.411

For Ancestry variables

Average Squared Loading      Canonical R^2      Redundancy Index
   2.1514                    0.666               1.432

Please help me interpret these results. I understand the p-values are good (as they are very low); F-values seems good as well (as they are high), but I'm not sure how to interpret the values of Wilk's Lambda, Pillai's Trace, the Hotelling–Lawley Trace, and Roy's Largest Root.

According to my understanding of the analysis, the multivariate tests are statistically significant, but not practically significant according to redundancy analysis. Any help (a little explanation of the analysis) would be appreciated.

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    $\begingroup$ The multivariate tests are all those tests common in MANOVA. Any textbook on MANOVA will tell you what they are. But why should you interpret them? The only important about them is that your 1st canonical correlation (.666) is significant. $\endgroup$ – ttnphns May 30 '14 at 5:59
  • $\begingroup$ What made you dissatisfied with the redundancy analysis? $\endgroup$ – ttnphns May 30 '14 at 6:00
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    $\begingroup$ Thanks so much for the reply @ttnphns. According to my understanding of redundancy index, if it is a low value although the canonical correlation is high, it might mean that results are not practically significant. Please correct me if I am wrong. Looking at the article and the book, I feel the value of Wilk's lambda, p-value, F-statistic is good enough to say that the results are statistically significant. The canonical correlation is actually 0.814 and the square is 0.666. $\endgroup$ – Sherry May 31 '14 at 19:09

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