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I have just performed a K-means clustering analysis on 43 variables and as a result I have 2 cluster. Now I want to test if the cluster means for each variable are significantly different between the 2 clusters. Rather then doing 43 individual t-tests, is there a better way to test statistical significance in this case?

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    $\begingroup$ You can do MANOVA and what not.. But what is the reason? Because clustering (classic methods such as k-means) by definition will split your data into nonoverlapping groups those groups are expected to differ "significantly" by many if not all of the attributes used in the clustering. $\endgroup$
    – ttnphns
    Jul 24, 2018 at 12:57

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It's deceptive to perform this kind of tests. You'd need to perform some clever cross validation, such as using only 42 attributes for clustering, then testing the withheld attribute.

Because if you use the same attributes/samples for clustering and for splitting, this will overfit. You can get highly "significant" differences even on random data.

See the discussion of the **Calinski-Harabasz Variance-Ratio-Criterion ** on why you can't just apply the usual significance thresholds here.

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