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Say, I have two vector of percentages (in this particular case, percentages represent a proportion of certain cell types in blood samples). Both vectors sum up to 1.

For example, there are vectors A = [0.1, 0.15, 0.15, 0.20, 0.25, 0.15] and B = [0.05, 0.2, 0.15, 0.15, 0.2, 0.25], where A[1] and B[1] represent a proportion of cell type #1, etc.

What I want to do here is to find out whether the "composition" of cell types is similar between A and B. What would be the right statistical test to do this?

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The data you have is two probability distributions over the 6 categories: they are all non-negative and they sum up to 1.

To tell if two distributions are the same over a set of categories (this is what you can call 'similar') you can use the Chi-squared test:

https://en.wikipedia.org/wiki/Chi-squared_test#Example_chi-squared_test_for_categorical_data

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    $\begingroup$ @sus_mlm: But please notice that you will need to know the size of the samples. $\endgroup$ – Pere Sep 19 '16 at 14:35

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