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Back in Stackoverflow, I had asked this question but was redirected here for clarifications related to statistics. As mentioned in the question, I have about 200 brain anatomical measurements from two groups of individuals and would like to extract the most distinguishing features. Can someone please suggest me which statistical tests are best to try.

Some papers mentioned the KS test. In the KS 2 sample test, I am confused if the 2 samples are a brain anatomical measurement (such as thickness of cortex) of two patients one from each group? Or one patient from group 1 vs another patient from group 2 (taking all the different anatomical measurements at once)?

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    $\begingroup$ The purpose of the two-sample KS test is to test whether two distinct, one-dimensional samples have the same distribution. It is not an explicit method for feature selection (although I suppose you can use the results from the test to do that). Without knowing anything more about your experiment, I'd say you're probably looking for the case where you have measurements from one group in sample 1 and the other in sample 2. $\endgroup$ – Emil May 17 '18 at 7:57
  • $\begingroup$ How many features ? 200 ? how many people in each of two groups ? what and why do you want to discriminate ? $\endgroup$ – Subhash C. Davar May 17 '18 at 9:03
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The Kolmogorov-Smirnov 2 sample test tests for the hypothesis that two samples share the same distribution, without specifying what that distribution is.

It does so by computing the difference between the empirical CDFs of both samples.

More info here: https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ks2samp.htm

The test wouldn't allow you to compare two patients, but rather to test for the hypothesis that the two groups of patients share the same distributions of brain measurements.

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