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  {\Large\textbf{Critical values of $R$ for the}}
  {\Large\textbf{Mann-Whitney rank-sum test}}
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\noindent
The pairs of values below are approximate critical values of R for
two-tailed tests at levels $P=0.10$ (upper pair) and $P=0.05$ 
(lower pair).

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\noindent
(Use relevant $P=0.10$ entry for one-tailed test at level $0.05$).

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  \begin{tabular}{lc|ccccccc}
    &amp; &amp; \multicolumn{7}{c}{larger sample size, $n_2$} \\
    &amp; &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; 8 &amp; 9 &amp; 10 \\ \hline
smaller sample &amp; 4 &amp; 12,24 &amp; 13,27 &amp; 14,30 &amp; 15,33 &amp; 16,36 &amp; 17,39 &amp; 18,42 \\
size $n_1$ &amp;   &amp; 11,25 &amp; 12,28 &amp; 12,32 &amp; 13,35 &amp; 14,38 &amp; 15,41 &amp; 16,44 \\
           \hline
           &amp; 5 &amp;       &amp; 19,36 &amp; 20,40 &amp; 22,43 &amp; 23,47 &amp; 25,50 &amp; 26,54 \\
           &amp;   &amp;       &amp; 18,37 &amp; 19,41 &amp; 20,45 &amp; 21,49 &amp; 22,53 &amp; 24,56 \\
           \hline
           &amp; 6 &amp;       &amp;       &amp; 28,50 &amp; 30,54 &amp; 32,58 &amp; 33,63 &amp; 35,67 \\
           &amp;   &amp;       &amp;       &amp; 26,52 &amp; 28,56 &amp; 29,61 &amp; 31,65 &amp; 33,69 \\
           \hline
           &amp; 7 &amp;       &amp;       &amp;       &amp; 39,66 &amp; 41,71 &amp; 43,76 &amp; 46,80 \\
           &amp;   &amp;       &amp;       &amp;       &amp; 37,68 &amp; 39,73 &amp; 41,78 &amp; 43,83 \\
           \hline
           &amp; 8 &amp;       &amp;       &amp;       &amp;       &amp; 52,84 &amp; 54,90 &amp; 57,95 \\
           &amp;   &amp;       &amp;       &amp;       &amp;       &amp; 49,87 &amp; 51,93 &amp; 54,98 \\
           \hline
           &amp; 9 &amp;       &amp;       &amp;       &amp;       &amp;       &amp; 66,105 &amp; 69,111 \\
           &amp;   &amp;       &amp;       &amp;       &amp;       &amp;       &amp; 63,108 &amp; 66,114 \\
           \hline
           &amp; 10 &amp;      &amp;       &amp;       &amp;       &amp;       &amp;        &amp; 83,127 \\
           &amp;   &amp;       &amp;       &amp;       &amp;       &amp;       &amp;        &amp; 79,131 \\
           \hline
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