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Table 3 Exact (CD) and approximate critical values of differences in rank sums, at the familywise error rate of α=.05

From: Exact p-values for pairwise comparison of Friedman rank sums, with application to comparing classifiers

k n max(d) Unadjusted Bonferroni-adjusted
   1 × N comparison N × N comparison
CD CD N CD CD N CD M CD CD N CD Q CD χ 2
5 5 20 11 10 13 13 13 14 15 14 16
10 40 15 14 18 18 18 20 20 20 22
25 100 23 22 29 28 28 32 33 31 35
50 200 32 31 40 40 39 45 45 44 49
100 400 45 44 57 56 55 64 63 61 69
10 5 45 20 19 27 27 26 30 32 31 40
10 90 27 27 38 38 37 44 45 43 56
25 225 43 42 60 60 58 70 70 68 89
50 450 60 60 85 84 82 99 99 96 125
100 900 85 84 120 119 115 141 140 136 177
25 5 120 46 46 70 72 69 83 88 86 141
10 240 65 65 100 102 98 121 124 121 199
25 600 103 102 160 161 154 194 196 191 315
50 1200 145 145 227 227 218 276 278 270 445
100 2400 205 204 321 321 308 392 392 381 629
50 5 245 91 91 146 152 145 175 190 185 376
10 490 128 128 210 215 205 258 268 261 531
25 1225 203 203 337 339 323 417 423 412 840
50 2450 287 286 478 479 457 595 599 582 1188
100 4900 405 405 677 678 646 844 846 824 1680
100 5 495 180 180 304 320 302 368 406 395 1019
10 990 255 255 441 452 427 548 573 559 1441
25 2475 403 403 708 714 676 891 906 883 2278
50 4950 569 569 1005 1010 955 1271 1281 1249 3221
100 9900 805 805 1425 1427 1350 1805 1812 1766 4555
  1. Note: The tabled values satisfy the relation P(D ≥ tabled value) <.05. For presentational purposes, the approximate critical differences were rounded up to the smallest integer that is not less than the calculated value. Italicized figures in the right-most column represent critical differences exceeding the maximum value of d, denoted max(d), implying that none of the rank sum differences is significant at the α=.05 level