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252Wilcoxonpval 8/23/05
TABLE 5: Simplified Wilcoxon-Mann-Whitney Rank Sum Test for Two
Independent Samples
This table gives the p-value corresponding to the rank sum of the smaller sample when ranking is done starting from the end where the smaller sample is concentrated. p-values are doubled for two-sided tests. For example, suppose we are testing equality of medians for , and , and that . The p-value for 8 is .0476, which we double to .0952. Since this is above , we do not reject the null hypothesis.
Larger Sample size
Smaller Sample Size
1 2
W / p / W / p1 / .3333 / 3 / .1667
4 / .3333
Larger Sample size
Smaller Sample Size
1 2 3
W / p / W / p / W / p1 / .2500 / 3 / .1000 / 6 / .0500
2 / .5000 / 4 / .2000 / 7 / .1000
5 / .4000 / 8 / .2000
6 / .6000 / 9 / .3500
10 / .5000
Larger Sample size
Smaller Sample Size
1 2 3 4
W / p / W / p / W / p / W / p1 / .2000 / 3 / .0667 / 6 / .0286 / 10 / .0143
2 / .4000 / 4 / .1333 / 7 / .0571 / 11 / .0286
3 / .6000 / 5 / .2667 / 8 / .1143 / 12 / .0571
6 / .4000 / 9 / .2000 / 13 / .1000
7 / .6000 / 10 / .3143 / 14 / .1714
11 / .4286 / 15 / .2429
12 / .5714 / 16 / .3429
17 / .4429
18 / .5571
Larger Sample size
Smaller Sample Size
1 2 3 4 5
W / p / W / p / W / p / W / p / W / p1 / .1667 / 3 / .0476 / 6 / .0179 / 10 / .0079 / 15 / .0040
2 / .3333 / 4 / .0952 / 7 / .0357 / 11 / .0159 / 16 / .0079
3 / .5000 / 5 / .1905 / 8 / .0714 / 12 / .0317 / 17 / .0159
6 / .2857 / 9 / .1250 / 13 / .0556 / 18 / .0278
7 / .4286 / 10 / .1964 / 14 / .0952 / 19 / .0476
8 / .5714 / 11 / .2857 / 15 / .1429 / 20 / .0754
12 / .3929 / 16 / .2063 / 21 / .1111
13 / .5000 / 17 / .2778 / 22 / .1548
18 / .3651 / 23 / .2103
19 / .4524 / 24 / .2738
20 / .5476 / 25 / .3452
26 / .4206
27 / .5000
Pg. 20
252table5 TABLE 5
Simplified Wilcoxon-Mann-Whitney Rank Sum Test for Two Independent Samples(ctd)
Larger Sample size
Smaller Sample Size
1 2 3 4 5 6
W / p / W / p / W / p / W / p / W / P / W / p1 / .1429 / 3 / .0357 / 6 / .0119 / 10 / .0048 / 15 / .0022 / 21 / .0011
2 / .2857 / 4 / .0714 / 7 / .0238 / 11 / .0095 / 16 / .0043 / 22 / .0022
3 / .4286 / 5 / .1429 / 8 / .0476 / 12 / .0190 / 17 / .0087 / 23 / .0043
4 / .5714 / 6 / .2143 / 9 / .0833 / 13 / .0333 / 18 / .0152 / 24 / .0076
7 / .3214 / 10 / .1310 / 14 / .0571 / 19 / .0260 / 25 / .0130
8 / .4286 / 11 / .1905 / 15 / .0857 / 20 / .0411 / 26 / .0206
9 / .5714 / 12 / .2738 / 16 / .1286 / 21 / .0628 / 27 / .0325
13 / .3571 / 17 / .1762 / 22 / .0887 / 28 / .0465
14 / .4524 / 18 / .2381 / 23 / .1234 / 29 / .0660
15 / .5476 / 19 / .3048 / 24 / .1645 / 30 / .0898
20 / .3810 / 25 / .2143 / 31 / .1201
21 / .4571 / 26 / .2684 / 32 / .1548
22 / .5429 / 27 / .3312 / 33 / .1970
28 / .3961 / 34 / .2424
29 / .4654 / 35 / .2944
30 / .5346 / 36 / .3596
37 / .4091
38 / .4686
39 / .5314
Larger Sample size
Smaller Sample Size
1 2 3 4 5 6 7
W / p / W / p / W / p / W / p / W / p / W / p / W / p1 / .1250 / 3 / .0278 / 6 / .0083 / 10 / .0030 / 15 / .0013 / 21 / .0006 / 28 / .0003
2 / .2500 / 4 / .0556 / 7 / .0167 / 11 / .0061 / 16 / .0025 / 22 / .0012 / 29 / .0006
3 / .3750 / 5 / .1111 / 8 / .0333 / 12 / .0121 / 17 / .0051 / 23 / .0023 / 30 / .0012
4 / .5000 / 6 / .1667 / 9 / .0583 / 13 / .0212 / 18 / .0088 / 24 / .0041 / 31 / .0020
7 / .2500 / 10 / .0917 / 14 / .0364 / 19 / .0152 / 25 / .0070 / 32 / .0035
8 / .3333 / 11 / .1333 / 15 / .0545 / 20 / .0240 / 26 / .0111 / 33 / .0055
9 / .4444 / 12 / .1917 / 16 / .0818 / 21 / .0366 / 27 / .0175 / 34 / .0087
10 / .5556 / 13 / .2583 / 17 / .1152 / 22 / .0530 / 28 / .0256 / 35 / .0131
14 / .3333 / 18 / .1576 / 23 / .0745 / 29 / .0367 / 36 / .0189
15 / .4167 / 19 / .2061 / 24 / .1010 / 30 / .0507 / 37 / .0265
16 / .5000 / 20 / .2636 / 25 / .1338 / 31 / .0688 / 38 / .0364
21 / .3242 / 26 / .1717 / 32 / .0903 / 39 / .0487
22 / .3939 / 27 / .2159 / 33 / .1171 / 40 / .0641
23 / .4636 / 28 / .2652 / 34 / .1474 / 41 / .0825
24 / .5364 / 29 / .3194 / 35 / .1830 / 42 / .1043
30 / .3775 / 36 / .2226 / 43 / .1297
31 / .4381 / 37 / .2669 / 44 / .1588
32 / .5000 / 38 / .3141 / 45 / .1914
39 / .3654 / 46 / .2279
40 / .4178 / 47 / .2675
41 / .4726 / 48 / .3100
42 / .5274 / 49 / .3552
50 / .4024
51 / .4508
52 / .5000
Pg. 22