% <html><head><title>Upper Critical Values for Friedman Test</title>

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  {\Large\textbf{Upper Critical Values for the Friedman Test}} \\
  \textbf{($k$ treatments and $b$ blocks)}
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  \begin{tabular}{rl}
    Notes 1. & In the table below, the critical values give significance
               levels as close as \\
             & possible to, but not exceeding the nominal $\alpha$. \\
   \ \\
          2. & For values of $k$ and $b$ beyond the range of the table 
               below, various \\
             & approximations are available.
  \end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline
& \multicolumn{2}{c|}{$k=3$} & \multicolumn{2}{c|}{$k=4$}
& \multicolumn{2}{c|}{$k=5$} & \multicolumn{2}{c|}{$k=6$} \\ \hline 
$b$&  0.05 &  0.01 &  0.05 &  0.01 &  0.05 &  0.01 &  0.05 &  0.01 \\ \hline
 2 &   -   &   -   & 6.000 &   -   & 7.600 & 8.000 & 9.143 & 9.714 \\
 3 & 6.000 &   -   & 7.400 & 9.000 & 8.533 & 10.13 & 9.857 & 11.76 \\
 4 & 6.500 & 8.000 & 7.800 & 9.600 & 8.800 & 11.20 & 10.29 & 12.71 \\
 5 & 6.400 & 8.400 & 7.800 & 9.960 & 8.960 & 11.68 & 10.49 & 13.23 \\
 6 & 7.000 & 9.000 & 7.600 & 10.20 & 9.067 & 11.87 & 10.57 & 13.62 \\
 7 & 7.143 & 8.857 & 7.800 & 10.54 & 9.143 & 12.11 &  &  \\
 8 & 6.250 & 9.000 & 7.650 & 10.50 & 9.200 & 12.30 &  &  \\
 9 & 6.222 & 9.556 & 7.667 & 10.73 & 9.244 & 12.44 &  &  \\
10 & 6.200 & 9.600 & 7.680 & 10.68 &  &  &  &  \\
11 & 6.545 & 9.455 & 7.691 & 10.75 &  &  &  &  \\
12 & 6.500 & 9.500 & 7.700 & 10.80 &  &  &  &  \\
13 & 6.615 & 9.385 & 7.800 & 10.85 &  &  &  &  \\
14 & 6.143 & 9.143 & 7.714 & 10.89 &  &  &  &  \\
15 & 6.400 & 8.933 & 7.720 & 10.92 &  &  &  &  \\
16 & 6.500 & 9.375 & 7.800 & 10.95 &  &  &  &  \\
17 & 6.118 & 9.294 & 7.800 & 11.05 &  &  &  &  \\
18 & 6.333 & 9.000 & 7.733 & 10.93 &  &  &  &  \\
19 & 6.421 & 9.579 & 7.863 & 11.02 &  &  &  &  \\
20 & 6.300 & 9.300 & 7.800 & 11.10 &  &  &  &  \\
21 & 6.095 & 9.238 & 7.800 & 11.06 &  &  &  &  \\
22 & 6.091 & 9.091 & 7.800 & 11.07 &  &  &  &  \\
23 & 6.348 & 9.391 &  &  &  &  &  &  \\
24 & 6.250 & 9.250 &  &  &  &  &  &  \\ \hline
\end{tabular}
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\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline
& \multicolumn{2}{c|}{$k=3$} & \multicolumn{2}{c|}{$k=4$}
& \multicolumn{2}{c|}{$k=5$} & \multicolumn{2}{c|}{$k=6$} \\ \hline 
$b$&  0.05 &  0.01 &  0.05 &  0.01 &  0.05 &  0.01 &  0.05 &  0.01 \\ \hline
25 & 6.080 & 8.960 &  &  &  &  &  &  \\
26 & 6.077 & 9.308 &  &  &  &  &  &  \\
27 & 6.000 & 9.407 &  &  &  &  &  &  \\
28 & 6.500 & 9.214 &  &  &  &  &  &  \\
29 & 6.276 & 9.172 &  &  &  &  &  &  \\
30 & 6.200 & 9.267 &  &  &  &  &  &  \\
31 & 6.000 & 9.290 &  &  &  &  &  &  \\
32 & 6.063 & 9.250 &  &  &  &  &  &  \\
33 & 6.061 & 9.152 &  &  &  &  &  &  \\
34 & 6.059 & 9.176 &  &  &  &  &  &  \\
35 & 6.171 & 9.314 &  &  &  &  &  &  \\
36 & 6.167 & 9.389 &  &  &  &  &  &  \\
37 & 6.054 & 9.243 &  &  &  &  &  &  \\
38 & 6.158 & 9.053 &  &  &  &  &  &  \\
39 & 6.000 & 9.282 &  &  &  &  &  &  \\
40 & 6.050 & 9.150 &  &  &  &  &  &  \\
41 & 6.195 & 9.366 &  &  &  &  &  &  \\
42 & 6.143 & 9.190 &  &  &  &  &  &  \\
43 & 6.186 & 9.256 &  &  &  &  &  &  \\
44 & 6.318 & 9.136 &  &  &  &  &  &  \\
45 & 6.178 & 9.244 &  &  &  &  &  &  \\
46 & 6.043 & 9.435 &  &  &  &  &  &  \\
47 & 6.128 & 9.319 &  &  &  &  &  &  \\
48 & 6.167 & 9.125 &  &  &  &  &  &  \\
49 & 6.041 & 9.184 &  &  &  &  &  &  \\
50 & 6.040 & 9.160 &  &  &  &  &  &  \\ \hline
\end{tabular}
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