Appendix 5. Wilcoxon Signed Rank Distribution
The lower tail of the distribution of the statistic is given below.
W | n = 4 | n = 5 | n = 6 | n = 7 | n = 8 |
0 | 0.06250 | 0.03125 | 0.01563 | 0.00781 | 0.00391 |
1 | 0.12500 | 0.06250 | 0.03125 | 0.01563 | 0.00781 |
2 | 0.18750 | 0.09375 | 0.04688 | 0.02344 | 0.01172 |
3 | 0.31250 | 0.15625 | 0.07813 | 0.03906 | 0.01953 |
4 | 0.43750 | 0.21875 | 0.10938 | 0.05469 | 0.02734 |
5 | 0.56250 | 0.31250 | 0.15625 | 0.07813 | 0.03906 |
6 | 0.68750 | 0.40625 | 0.21875 | 0.10938 | 0.05469 |
7 | 0.81250 | 0.50000 | 0.28125 | 0.14844 | 0.07422 |
8 | 0.87500 | 0.59375 | 0.34375 | 0.18750 | 0.09766 |
9 | 0.93750 | 0.68750 | 0.42188 | 0.23438 | 0.12500 |
10 | 1.00000 | 0.78125 | 0.50000 | 0.28906 | 0.15625 |
11 |
| 0.84375 | 0.57813 | 0.34375 | 0.19141 |
12 |
| 0.90625 | 0.65625 | 0.40625 | 0.23047 |
13 |
| 0.93750 | 0.71875 | 0.46875 | 0.27344 |
14 |
| 0.96875 | 0.78125 | 0.53125 | 0.32031 |
15 |
| 1.00000 | 0.84375 | 0.59375 | 0.37109 |
16 |
|
| 0.89063 | 0.65625 | 0.42188 |
17 |
|
| 0.92188 | 0.71094 | 0.47266 |
18 |
|
| 0.95313 | 0.76563 | 0.52734 |
19 |
|
| 0.96875 | 0.81250 | 0.57813 |
20 |
|
| 0.98438 | 0.85156 | 0.62891 |
W | n = 9 | n = 10 | n = 11 | n = 12 | n = 13 |
0 | 0.00195 | 0.00098 | 0.00049 | 0.00024 | 0.00012 |
1 | 0.00391 | 0.00195 | 0.00098 | 0.00049 | 0.00024 |
2 | 0.00586 | 0.00293 | 0.00146 | 0.00073 | 0.00037 |
3 | 0.00977 | 0.00488 | 0.00244 | 0.00122 | 0.00061 |
4 | 0.01367 | 0.00684 | 0.00342 | 0.00171 | 0.00085 |
5 | 0.01953 | 0.00977 | 0.00488 | 0.00244 | 0.00122 |
6 | 0.02734 | 0.01367 | 0.00684 | 0.00342 | 0.00171 |
7 | 0.03711 | 0.01855 | 0.00928 | 0.00464 | 0.00232 |
8 | 0.04883 | 0.02441 | 0.01221 | 0.00610 | 0.00305 |
9 | 0.06445 | 0.03223 | 0.01611 | 0.00806 | 0.00403 |
10 | 0.08203 | 0.04199 | 0.02100 | 0.01050 | 0.00525 |
11 | 0.10156 | 0.05273 | 0.02686 | 0.01343 | 0.00671 |
12 | 0.12500 | 0.06543 | 0.03369 | 0.01709 | 0.00854 |
13 | 0.15039 | 0.08008 | 0.04150 | 0.02124 | 0.01074 |
14 | 0.17969 | 0.09668 | 0.05078 | 0.02612 | 0.01331 |
15 | 0.21289 | 0.11621 | 0.06152 | 0.03198 | 0.01636 |
16 | 0.24805 | 0.13770 | 0.07373 | 0.03857 | 0.01990 |
17 | 0.28516 | 0.16113 | 0.08740 | 0.04614 | 0.02393 |
18 | 0.32617 | 0.18750 | 0.10303 | 0.05493 | 0.02869 |
19 | 0.36719 | 0.21582 | 0.12012 | 0.06470 | 0.03406 |
20 | 0.41016 | 0.24609 | 0.13916 | 0.07568 | 0.04016 |
21 | 0.45508 | 0.27832 | 0.16016 | 0.08813 | 0.04712 |
22 | 0.50000 | 0.31250 | 0.18262 | 0.10181 | 0.05493 |
W | n = 9 | n = 10 | n = 11 | n = 12 | n = 13 |
23 |
| 0.34766 | 0.20654 | 0.11670 | 0.06360 |
24 |
| 0.38477 | 0.23242 | 0.13306 | 0.07324 |
25 |
| 0.42285 | 0.25977 | 0.15063 | 0.08386 |
26 |
| 0.46094 | 0.28857 | 0.16968 | 0.09546 |
27 |
| 0.50000 | 0.31885 | 0.19019 | 0.10815 |
28 |
|
| 0.35010 | 0.21191 | 0.12195 |
29 |
|
| 0.38232 | 0.23486 | 0.13672 |
30 |
|
| 0.41553 | 0.25928 | 0.15271 |
31 |
|
| 0.44922 | 0.28467 | 0.16980 |
32 |
|
| 0.48291 | 0.31104 | 0.18787 |
33 |
|
| 0.51709 | 0.33862 | 0.20715 |
34 |
|
|
| 0.36670 | 0.22742 |
35 |
|
|
| 0.39551 | 0.24866 |
36 |
|
|
| 0.42505 | 0.27087 |
37 |
|
|
| 0.45483 | 0.29395 |
38 |
|
|
| 0.48486 | 0.31775 |
39 |
|
|
| 0.51514 | 0.34241 |
40 |
|
|
|
| 0.36768 |
41 |
|
|
|
| 0.39343 |
42 |
|
|
|
| 0.41968 |
43 |
|
|
|
| 0.44629 |
44 |
|
|
|
| 0.47302 |
45 |
|
|
|
| 0.50000 |