% <html><head><title>Mann-whitney Tables</title>

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