Appendix 5. Wilcoxon Signed Rank Distribution

The lower tail of the distribution of the statistic is given below.

Wn = 4n = 5n = 6n = 7n = 8
00.062500.031250.015630.007810.00391
10.125000.062500.031250.015630.00781
20.187500.093750.046880.023440.01172
30.312500.156250.078130.039060.01953
40.437500.218750.109380.054690.02734
50.562500.312500.156250.078130.03906
60.687500.406250.218750.109380.05469
70.812500.500000.281250.148440.07422
80.875000.593750.343750.187500.09766
90.937500.687500.421880.234380.12500
101.000000.781250.500000.289060.15625
11
0.843750.578130.343750.19141
12
0.906250.656250.406250.23047
13
0.937500.718750.468750.27344
14
0.968750.781250.531250.32031
15
1.000000.843750.593750.37109
16

0.890630.656250.42188
17

0.921880.710940.47266
18

0.953130.765630.52734
19

0.968750.812500.57813
20

0.984380.851560.62891
Wn = 9n = 10n = 11n = 12n = 13
00.001950.000980.000490.000240.00012
10.003910.001950.000980.000490.00024
20.005860.002930.001460.000730.00037
30.009770.004880.002440.001220.00061
40.013670.006840.003420.001710.00085
50.019530.009770.004880.002440.00122
60.027340.013670.006840.003420.00171
70.037110.018550.009280.004640.00232
80.048830.024410.012210.006100.00305
90.064450.032230.016110.008060.00403
100.082030.041990.021000.010500.00525
110.101560.052730.026860.013430.00671
120.125000.065430.033690.017090.00854
130.150390.080080.041500.021240.01074
140.179690.096680.050780.026120.01331
150.212890.116210.061520.031980.01636
160.248050.137700.073730.038570.01990
170.285160.161130.087400.046140.02393
180.326170.187500.103030.054930.02869
190.367190.215820.120120.064700.03406
200.410160.246090.139160.075680.04016
210.455080.278320.160160.088130.04712
220.500000.312500.182620.101810.05493
Wn = 9n = 10n = 11n = 12n = 13
23
0.347660.206540.116700.06360
24
0.384770.232420.133060.07324
25
0.422850.259770.150630.08386
26
0.460940.288570.169680.09546
27
0.500000.318850.190190.10815
28

0.350100.211910.12195
29

0.382320.234860.13672
30

0.415530.259280.15271
31

0.449220.284670.16980
32

0.482910.311040.18787
33

0.517090.338620.20715
34


0.366700.22742
35


0.395510.24866
36


0.425050.27087
37


0.454830.29395
38


0.484860.31775
39


0.515140.34241
40



0.36768
41



0.39343
42



0.41968
43



0.44629
44



0.47302
45



0.50000