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I am trying to compare numbers in two sets (X and Y) to test if numbers in one of the set are statistically larger than the others. However, some of the numbers are paired, and some are not. For instance:

Set X: X1, X2, X3, X4, X5
Set Y: Y1, Y4, Y5, Y6, Y7

number in "X1" represent pairings, so (X 1, Y1), (X4, Y4) and (X5, Y5) are paired. While X2,X3, Y6 and Y7 are not paired. How can I perform a statistical test? The data is not normal, and ideally, I would like a non-parametric test.

avi
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    There was extensive discussion of the same problem but using $t$-tests in this Q&A http://stats.stackexchange.com/questions/25941/t-test-for-partially-paired-and-partially-unpaired-data so perhaps some of the insights there might help you with this different problem. – mdewey Jan 27 '17 at 13:31
  • Ignoring the pairing will not invalidate the statistical test, it will just reduce the power of the test. Are you concerned about finding the most powerful test? – Joel W. Jan 27 '17 at 13:57
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    @Joel would like the most powerful test, as the sample size is not large. – avi Jan 27 '17 at 19:26

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