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Suppose I have n columns in a matrix (example below has n= 4).

Is there a test I can check that the rankings over columns are the same? Specifically, if the rankings in column 1 are "similar" to that of column 2, etc etc..

For two columns I can possibly do something like the morisita index but I need n columns and a p-value hopefully.

Thanks!

      [,1] [,2] [,3] [,4]
 [1,]    5   42   17   46
 [2,]   39   49   16   17
 [3,]   46   28   21   26
 [4,]   17    3   28    5
 [5,]   40   45   46   25
 [6,]   13   11    7   11
 [7,]   25    8   32   13
 [8,]   47   18    6   43
 [9,]   37   16   25   22
[10,]   41   17   12   34
[11,]    8   26   24   36
[12,]    1    5   34   28
[13,]   21   46   48   14
[14,]   34   35   37   10
[15,]   24    9   49   39
[16,]    3   41   31    3
[17,]   43   19   36   18
[18,]   42   48   15   37
[19,]   36   37   43   30
[20,]   30   31   10   45
[21,]   26   29   30   50
[22,]   20   43   11   31
[23,]   14   13   45   33
[24,]    4   21    9   49
[25,]   23   34    1   12
[26,]   33   20   42   48
[27,]   31   10   26    9
[28,]   11   12   29   21
[29,]   48    6   22   41
[30,]   12    2    5   16
[31,]    7   27   38    2
[32,]   19   15    8    7
[33,]   44    1    3    6
[34,]   49   24   13   44
[35,]   29   47   41   15
[36,]   27   30   44    1
[37,]    9   32   20   24
[38,]   10   25   23   47
[39,]   50   22   27   27
[40,]   16   39   35   38
[41,]   35    7   18    8
[42,]    2    4    4   29
[43,]   28   50   33   35
[44,]    6   33   14   40
[45,]   38   40   50   19
[46,]   18   38   40   20
[47,]   22   23   19   42
[48,]   15   36   39   32
[49,]   45   44    2   23
[50,]   32   14   47    4
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This rank-based procedure has been recommended as being robust to non-normal errors, resistant to outliers, and highly efficient for many distributions. It may result in a known statistic (e.g., in the two independent samples layout ranking)

In this problem i suggest you to run the test in the Wilcoxon rank-sum / Mann–Whitney U test

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  • $\begingroup$ This just looks at 2 related samples. Then I would have to do all pairwise comparisons.. $\endgroup$ – user1357015 Oct 18 '14 at 4:59
  • $\begingroup$ Isn't that what you are asking for in the question? $\endgroup$ – whuber Oct 18 '14 at 5:20
  • $\begingroup$ @user1357015 if you wanna do for n columns just run the kruskal-Wallis H test for several n independent column. $\endgroup$ – valerie Oct 18 '14 at 5:24

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