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I have four samples under four treatment conditions, and I want to test the hypothesis that they increase in such a way that the relative differences between them stay the same.

Pearson correlation coefficient and cosine distance would both be informative, but both only give pairwise comparisons between samples. Is it appropriate to do all 16 possible pairwise comparisons and then average or sum the values to give a total correlation value? Or is there a better test for this?

kjetil b halvorsen
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Geoff
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  • What is important in your comparison: vector lengths, vector directions or both? – Vladislavs Dovgalecs Apr 09 '15 at 00:21
  • Only vector directions are important. – Geoff Apr 09 '15 at 00:27
  • So use some test from directional statistics? Since vector length is unimportant, start with standardizing the vectors so all stay on the unit sphere (of some dimension), and then go to directional statistics: https://stats.stackexchange.com/questions/259324/most-accessible-introduction-to-directional-statistics – kjetil b halvorsen Sep 19 '18 at 13:21

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