This is a complex topic, there is a huge amount of literature available. And the answer depends on many details of your specific aims and your particular data. Instead of writing book-chapters here explaining all these things once more that are explained in so many courses and books, I suggest that you consult a statistician.

Dear Jochen, thank you by the comment. Eduard, thank you by the article. Best regards

For multivariate data distribution context you can use hotelling'T2 statistics may help you on favour of mahalanobis distances and probability distances.....after words you can use MANOVA .........

Actually I work with multivariate data .....like pca, pls technique.