TABLE 6 - Critical values and P-values of U₅ for the Wilcoxon-Mann-Whitney

Oct 12, 2026

Table 6 provides selected critical values of the U₅ statistic in bold and the corresponding P-values in italics for the Wilcoxon-Mann-Whitney test under a non-directional alternative. Because the null distribution is discrete, values are given for multiple sample-size combinations (n and n′) and for several significance levels such as 0.20, 0.10, 0.05, 0.025, 0.01, and 0.005. Directional P-values are obtained by dividing the numbers in italics in half.

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TABLE 6 Critical values and P-values of U₅for the Wilcoxon-Mann-Whitney test

## TABLE 6 Critical values and P-values of U₅for the Wilcoxon-Mann-Whitneytest Note:Because the Wilcoxon-Mann-Whitney test null distribution is discrete,this table provides selected values of the test ## statistic U₅in bold type and corresponding P-values for a non-directional alternative in italics.Directional P-values are | found by dividing the numbers in italics in half. | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | n | n' | 0.20 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | | 3 | 2 | 60.200 | | | | | | | | 3 | 80.200 | 90.100 | | | | | | 4 | 2 | 80.133 | | | | | | | | 3 | 110.114 | 120.057 | | | | | | | 4 | 130.200 | 150.057 | 160.029 | | | | | 5 | 2 | 90.191 | 100.095 | | | | | | | 3 | 130.143 | 140.071 | 150.036 | | | | | | 4 | 160.191 | 180.064 | 190.032 | 200.016 | | | | | 5 | 200.151 | 210.095 | 230.032 | 240.016 | 250.0079 | | | 6 | 2 | 110.143 | 120.071 | | | | | | | 3 | 150.167 | 160.095 | 170.048 | 180.024 | | | | | 4 | 190.171 | 210.067 | 220.038 | 230.019 | 240.0095 | | | | 5 | 230.178 | 250.082 | 270.030 | 280.017 | 290.0087 | 300.0043 | | | 6 | 270.180 | 290.093 | 310.041 | 330.015 | 340.0087 | 350.0043 | | 7 | 2 | 130.111 | 140.056 | | | | | | | 3 | 170.183 | 190.067 | 200.033 | 210.017 | | | | | 4 | 220.164 | 240.072 | 250.042 | 260.024 | 280.0061 | | | | 5 | 270.149 | 290.073 | 300.048 | 320.018 | 340.0051 | 350.0025 | | | 6 | 310.181 | 340.073 | 360.035 | 370.022 | 390.0082 | 400.0047 | | | 7 | 360.165 | 380.097 | 410.038 | 430.018 | 450.0070 | 460.0041 | | 8 | 2 | 140.178 | 150.089 | 160.044 | | | | | | 3 | 190.194 | 210.085 | 220.049 | 230.024 | | | | | 4 | 250.154 | 270.073 | 280.049 | 300.016 | 310.0081 | 320.0040 | | | 5 | 300.171 | 320.093 | 340.045 | 360.019 | 380.0062 | 390.0031 | | | 6 | 350.181 | 380.081 | 400.043 | 420.020 | 440.0080 | 450.0047 | | | 7 | 400.189 | 430.094 | 460.041 | 480.021 | 500.0093 | 520.0037 | | | 8 | 450.195 | 490.083 | 510.050 | 540.021 | 570.0070 | 580.0047 | | 9 | 2 | 160.146 | 170.073 | 180.036 | | | | | | 3 | 220.146 | 230.100 | 250.036 | 260.018 | 270.0091 | | | | 4 | 270.199 | 300.076 | 320.034 | 330.020 | 350.0056 | 360.0028 | | | 5 | 330.190 | 360.083 | 380.042 | 400.019 | 420.0070 | 430.0040 | | | 6 | 390.181 | 420.088 | 440.050 | 470.018 | 490.0076 | 500.0048 | | | 7 | 450.174 | 480.091 | 510.042 | 530.023 | 560.0079 | 580.0033 | | | 8 | 500.200 | 540.093 | 570.046 | 600.021 | 630.0079 | 650.0037 | | | 6 | 560.190 | 600.094 | 640.040 | 660.024 | 700.0078 | 720.0040 | | 10 | 2 | 170.182 | 190.061 | 200.030 | | | | | | 3 | 240.161 | 260.077 | 270.049 | 290.014 | 300.0070 | | | | 4 | 300.188 | 330.076 | 350.036 | 360.024 | 380.0080 | 390.0040 | | | 5 | 370.165 | 390.099 | 420.040 | 440.019 | 460.0080 | 470.0047 | | | 6 | 430.181 | 460.093 | 490.042 | 510.023 | 540.0075 | 550.0047 | | | 7 | 490.193 | 530.088 | 560.043 | 580.025 | 610.0097 | 630.0046 | | | 8 | 560.173 | 600.083 | 630.043 | 660.021 | 690.0085 | 710.0044 | | | 9 | 620.182 | 660.095 | 700.044 | 730.022 | 770.0076 | 790.0041 | | | 10 | 680.190 | 730.089 | 770.043 | 80.0.023 | 840.0089 | 870.0039 | # TABLE 6 Critical values and P-values of U₅for the Wilcoxon-Mann-Whitney | test(continued) | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | n | n' | 0.20 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | | 11 | 2 | 190.154 |

FAQs

What does Table 6 report for the Wilcoxon-Mann-Whitney test?

It lists critical values of the U₅ statistic (in bold) and corresponding P-values (in italics) for a non-directional alternative.

Why does the table provide selected values?

Because the null distribution of the Wilcoxon-Mann-Whitney test is discrete.

How are directional P-values obtained?

Directional P-values are found by dividing the numbers in italics in half.

Oct 12, 2026

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