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How do you perform a rank test when there are duplicates in the data?

that is, we have a dataset with numbers $1,1,1,1,3,3,3,3,4,4,4,4.$ and another dataset also with duplicates.... Is the sum of the ranks for the first data set, $1+1+1+1+2+2+2+2+3+3+3+3?$

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This would be called ties, according to wiki "https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test Ties receive a rank equal to the average of the ranks they span." So for your case

1,1,1,1,3,3,3,3,4,4,4,4 will give ranks 2.5, 2.5, 2.5, 2.5, 6.5, 6.5, 6.5, 6.5, 10.5, 10.5, 10.5, 10.5

Notice that the sum of ranks 1, 2, ... 12, is the same as the sum of these tied ranks

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  • $\begingroup$ How did you calculate 2.5? $\endgroup$ – user271077 Jan 20 '20 at 23:16
  • $\begingroup$ (1+2+3+4)/4 i.e. mean rank of ones $\endgroup$ – rep_ho Jan 20 '20 at 23:34
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    $\begingroup$ With so many ties in such a small data set, it's important not to ignore the effect of ties on the distribution, however. $\endgroup$ – Glen_b Jan 21 '20 at 4:56

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