% <html><head><title>Duncan's Multiple Range Test</title>

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\begin{document}
\begin{center}
  \textbf{Tables for Duncan's multiple range tests} \\
  Critical values $q'(p, df; 0.05)$ for Duncan's multiple range tests \\
\ \\
\begin{tabular}{rrrrrrrrrrrrrr}
$df\backslash p$ & \multicolumn{1}{c}{\ 2} & \multicolumn{1}{c}{\ 3} & 
\multicolumn{1}{c}{\ 4} & \multicolumn{1}{c}{\ 5} & \multicolumn{1}{c}{\ 6} &
\multicolumn{1}{c}{\ 7} & \multicolumn{1}{c}{\ 8} & \multicolumn{1}{c}{\ 9} &
\multicolumn{1}{c}{\ 10} & \multicolumn{1}{c}{\ 11} & \multicolumn{1}{c}{\ 12} &
\multicolumn{1}{c}{\ 15} & \multicolumn{1}{c}{\ 20} \\
1 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 & 17.969 \\
2 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 & 6.085 \\
3 & 4.501 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 & 4.516 \\
4 & 3.926 & 4.013 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 & 4.033 \\
5 & 3.635 & 3.749 & 3.796 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 & 3.814 \\
6 & 3.460 & 3.586 & 3.649 & 3.680 & 3.694 & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 & 3.697 \\
7 & 3.344 & 3.477 & 3.548 & 3.588 & 3.611 & 3.622 & 3.625 & 3.625 & 3.625 & 3.625 & 3.625 & 3.625 & 3.625 \\
8 & 3.261 & 3.398 & 3.475 & 3.521 & 3.549 & 3.566 & 3.575 & 3.579 & 3.579 & 3.579 & 3.579 & 3.579 & 3.579 \\
9 & 3.199 & 3.339 & 3.420 & 3.470 & 3.502 & 3.523 & 3.536 & 3.544 & 3.547 & 3.547 & 3.547 & 3.547 & 3.547 \\
10 & 3.151 & 3.293 & 3.376 & 3.430 & 3.465 & 3.489 & 3.505 & 3.516 & 3.522 & 3.525 & 3.525 & 3.525 & 3.525 \\
11 & 3.113 & 3.256 & 3.341 & 3.397 & 3.435 & 3.462 & 3.480 & 3.493 & 3.501 & 3.506 & 3.509 & 3.510 & 3.510 \\
12 & 3.081 & 3.225 & 3.312 & 3.370 & 3.410 & 3.439 & 3.459 & 3.474 & 3.484 & 3.491 & 3.495 & 3.498 & 3.498 \\
13 & 3.055 & 3.200 & 3.288 & 3.348 & 3.389 & 3.419 & 3.441 & 3.458 & 3.470 & 3.478 & 3.484 & 3.490 & 3.490 \\
14 & 3.033 & 3.178 & 3.268 & 3.328 & 3.371 & 3.403 & 3.426 & 3.444 & 3.457 & 3.467 & 3.474 & 3.484 & 3.484 \\
15 & 3.014 & 3.160 & 3.250 & 3.312 & 3.356 & 3.389 & 3.413 & 3.432 & 3.446 & 3.457 & 3.465 & 3.478 & 3.480 \\
16 & 2.998 & 3.144 & 3.235 & 3.297 & 3.343 & 3.376 & 3.402 & 3.422 & 3.437 & 3.449 & 3.458 & 3.473 & 3.477 \\
17 & 2.984 & 3.130 & 3.222 & 3.285 & 3.331 & 3.365 & 3.392 & 3.412 & 3.429 & 3.441 & 3.451 & 3.469 & 3.475 \\
18 & 2.971 & 3.117 & 3.210 & 3.274 & 3.320 & 3.356 & 3.383 & 3.404 & 3.421 & 3.435 & 3.445 & 3.465 & 3.474 \\
19 & 2.960 & 3.106 & 3.199 & 3.264 & 3.311 & 3.347 & 3.375 & 3.397 & 3.415 & 3.429 & 3.440 & 3.462 & 3.474 \\
20 & 2.950 & 3.097 & 3.190 & 3.255 & 3.303 & 3.339 & 3.368 & 3.390 & 3.409 & 3.423 & 3.435 & 3.459 & 3.473 
\end{tabular}
\end{center}

\newpage

\begin{center}
  \textbf{Tables for Duncan's multiple range tests} \\
  Critical values $q'(p, df; 0.05)$ for Duncan's multiple range tests
  \textit{(cont.)} \\
\ \\
\begin{tabular}{rrrrrrrrrrrrrr}
$df\backslash p$ & \multicolumn{1}{c}{\ 2} & \multicolumn{1}{c}{\ 3} & 
\multicolumn{1}{c}{\ 4} & \multicolumn{1}{c}{\ 5} & \multicolumn{1}{c}{\ 6} &
\multicolumn{1}{c}{\ 7} & \multicolumn{1}{c}{\ 8} & \multicolumn{1}{c}{\ 9} &
\multicolumn{1}{c}{\ 10} & \multicolumn{1}{c}{\ 11} & \multicolumn{1}{c}{\ 12} &
\multicolumn{1}{c}{\ 15} & \multicolumn{1}{c}{\ 20} \\
21 & 2.941 & 3.088 & 3.181 & 3.247 & 3.295 & 3.332 & 3.361 & 3.385 & 3.403 & 3.418 & 3.431 & 3.456 & 3.473 \\
22 & 2.933 & 3.080 & 3.173 & 3.239 & 3.288 & 3.326 & 3.355 & 3.379 & 3.398 & 3.414 & 3.427 & 3.453 & 3.472 \\
23 & 2.926 & 3.072 & 3.166 & 3.233 & 3.282 & 3.320 & 3.350 & 3.374 & 3.394 & 3.410 & 3.423 & 3.451 & 3.472 \\
24 & 2.919 & 3.066 & 3.160 & 3.226 & 3.276 & 3.315 & 3.345 & 3.370 & 3.390 & 3.406 & 3.420 & 3.449 & 3.472 \\
25 & 2.913 & 3.059 & 3.154 & 3.221 & 3.271 & 3.310 & 3.341 & 3.366 & 3.386 & 3.403 & 3.417 & 3.447 & 3.471 \\
26 & 2.907 & 3.054 & 3.149 & 3.216 & 3.266 & 3.305 & 3.336 & 3.362 & 3.382 & 3.400 & 3.414 & 3.445 & 3.471 \\
27 & 2.902 & 3.049 & 3.144 & 3.211 & 3.262 & 3.301 & 3.332 & 3.358 & 3.379 & 3.397 & 3.412 & 3.443 & 3.471 \\
28 & 2.897 & 3.044 & 3.139 & 3.206 & 3.257 & 3.297 & 3.329 & 3.355 & 3.376 & 3.394 & 3.409 & 3.442 & 3.470 \\
29 & 2.892 & 3.039 & 3.135 & 3.202 & 3.253 & 3.293 & 3.326 & 3.352 & 3.373 & 3.392 & 3.407 & 3.440 & 3.470 \\
30 & 2.888 & 3.035 & 3.131 & 3.199 & 3.250 & 3.290 & 3.322 & 3.349 & 3.371 & 3.389 & 3.405 & 3.439 & 3.470 \\
31 & 2.884 & 3.031 & 3.127 & 3.195 & 3.246 & 3.287 & 3.319 & 3.346 & 3.368 & 3.387 & 3.403 & 3.438 & 3.470 \\
32 & 2.881 & 3.028 & 3.123 & 3.192 & 3.243 & 3.284 & 3.317 & 3.344 & 3.366 & 3.385 & 3.401 & 3.436 & 3.470 \\
33 & 2.877 & 3.024 & 3.120 & 3.188 & 3.240 & 3.281 & 3.314 & 3.341 & 3.364 & 3.383 & 3.399 & 3.435 & 3.470 \\
34 & 2.874 & 3.021 & 3.117 & 3.185 & 3.238 & 3.279 & 3.312 & 3.339 & 3.362 & 3.381 & 3.398 & 3.434 & 3.469 \\
35 & 2.871 & 3.018 & 3.114 & 3.183 & 3.235 & 3.276 & 3.309 & 3.337 & 3.360 & 3.379 & 3.396 & 3.433 & 3.469 \\
36 & 2.868 & 3.015 & 3.111 & 3.180 & 3.232 & 3.274 & 3.307 & 3.335 & 3.358 & 3.378 & 3.395 & 3.432 & 3.469 \\
37 & 2.865 & 3.013 & 3.109 & 3.178 & 3.230 & 3.272 & 3.305 & 3.333 & 3.356 & 3.376 & 3.393 & 3.431 & 3.469 \\
38 & 2.863 & 3.010 & 3.106 & 3.175 & 3.228 & 3.270 & 3.303 & 3.331 & 3.355 & 3.375 & 3.392 & 3.431 & 3.469 \\
39 & 2.861 & 3.008 & 3.104 & 3.173 & 3.226 & 3.268 & 3.301 & 3.330 & 3.353 & 3.373 & 3.391 & 3.430 & 3.469 \\
40 & 2.858 & 3.005 & 3.102 & 3.171 & 3.224 & 3.266 & 3.300 & 3.328 & 3.352 & 3.372 & 3.389 & 3.429 & 3.469 \\
48 & 2.843 & 2.991 & 3.087 & 3.157 & 3.211 & 3.253 & 3.288 & 3.318 & 3.342 & 3.363 & 3.382 & 3.424 & 3.468 \\
60 & 2.829 & 2.976 & 3.073 & 3.143 & 3.198 & 3.241 & 3.277 & 3.307 & 3.333 & 3.355 & 3.374 & 3.419 & 3.468 \\
80 & 2.814 & 2.961 & 3.059 & 3.130 & 3.185 & 3.229 & 3.266 & 3.297 & 3.323 & 3.346 & 3.366 & 3.414 & 3.467 \\
120 & 2.800 & 2.947 & 3.045 & 3.116 & 3.172 & 3.217 & 3.254 & 3.286 & 3.313 & 3.337 & 3.358 & 3.409 & 3.466 \\
240 & 2.786 & 2.933 & 3.031 & 3.103 & 3.159 & 3.205 & 3.243 & 3.276 & 3.304 & 3.329 & 3.350 & 3.404 & 3.466 \\
$\infty$ & 2.772 & 2.918 & 3.017 & 3.089 & 3.146 & 3.193 & 3.232 & 3.265 & 3.294 & 3.320 & 3.343 & 3.399 & 3.466 
\end{tabular}
\end{center}

\newpage

\begin{center}
  \textbf{Tables for Duncan's multiple range tests} \\
  Critical values $q'(p, df; 0.01)$ for Duncan's multiple range tests \\
\ \\
\begin{tabular}{rrrrrrrrrrrrrr}
$df\backslash p$ & \multicolumn{1}{c}{\ 2} & \multicolumn{1}{c}{\ 3} & 
\multicolumn{1}{c}{\ 4} & \multicolumn{1}{c}{\ 5} & \multicolumn{1}{c}{\ 6} &
\multicolumn{1}{c}{\ 7} & \multicolumn{1}{c}{\ 8} & \multicolumn{1}{c}{\ 9} &
\multicolumn{1}{c}{\ 10} & \multicolumn{1}{c}{\ 11} & \multicolumn{1}{c}{\ 12} &
\multicolumn{1}{c}{\ 15} & \multicolumn{1}{c}{\ 20} \\
1 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 & 90.024 \\
2 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 & 14.036 \\
3 & 8.260 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 & 8.321 \\
4 & 6.511 & 6.677 & 6.740 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 & 6.755 \\
5 & 5.702 & 5.893 & 5.989 & 6.040 & 6.065 & 6.074 & 6.074 & 6.074 & 6.074 & 6.074 & 6.074 & 6.074 & 6.074 \\
6 & 5.243 & 5.439 & 5.549 & 5.614 & 5.655 & 5.680 & 5.694 & 5.701 & 5.703 & 5.703 & 5.703 & 5.703 & 5.703 \\
7 & 4.949 & 5.145 & 5.260 & 5.333 & 5.383 & 5.416 & 5.439 & 5.454 & 5.464 & 5.470 & 5.472 & 5.472 & 5.472 \\
8 & 4.745 & 4.939 & 5.056 & 5.134 & 5.189 & 5.227 & 5.256 & 5.276 & 5.291 & 5.302 & 5.309 & 5.317 & 5.317 \\
9 & 4.596 & 4.787 & 4.906 & 4.986 & 5.043 & 5.086 & 5.117 & 5.142 & 5.160 & 5.174 & 5.185 & 5.202 & 5.206 \\
10 & 4.482 & 4.671 & 4.789 & 4.871 & 4.931 & 4.975 & 5.010 & 5.036 & 5.058 & 5.074 & 5.087 & 5.112 & 5.124 \\
11 & 4.392 & 4.579 & 4.697 & 4.780 & 4.841 & 4.887 & 4.923 & 4.952 & 4.975 & 4.994 & 5.009 & 5.039 & 5.059 \\
12 & 4.320 & 4.504 & 4.622 & 4.705 & 4.767 & 4.815 & 4.852 & 4.882 & 4.907 & 4.927 & 4.944 & 4.978 & 5.005 \\
13 & 4.260 & 4.442 & 4.560 & 4.643 & 4.706 & 4.754 & 4.793 & 4.824 & 4.850 & 4.871 & 4.889 & 4.927 & 4.960 \\
14 & 4.210 & 4.391 & 4.508 & 4.591 & 4.654 & 4.703 & 4.743 & 4.775 & 4.802 & 4.824 & 4.843 & 4.884 & 4.921 \\
15 & 4.167 & 4.346 & 4.463 & 4.547 & 4.610 & 4.660 & 4.700 & 4.733 & 4.760 & 4.783 & 4.803 & 4.846 & 4.887 \\
16 & 4.131 & 4.308 & 4.425 & 4.508 & 4.572 & 4.622 & 4.662 & 4.696 & 4.724 & 4.748 & 4.768 & 4.813 & 4.858 \\
17 & 4.099 & 4.275 & 4.391 & 4.474 & 4.538 & 4.589 & 4.630 & 4.664 & 4.692 & 4.717 & 4.737 & 4.785 & 4.832 \\
18 & 4.071 & 4.246 & 4.361 & 4.445 & 4.509 & 4.559 & 4.601 & 4.635 & 4.664 & 4.689 & 4.710 & 4.759 & 4.808 \\
19 & 4.046 & 4.220 & 4.335 & 4.418 & 4.483 & 4.533 & 4.575 & 4.610 & 4.639 & 4.664 & 4.686 & 4.736 & 4.788 \\
20 & 4.024 & 4.197 & 4.312 & 4.395 & 4.459 & 4.510 & 4.552 & 4.587 & 4.617 & 4.642 & 4.664 & 4.716 & 4.769 
\end{tabular}
\end{center}

\newpage

\begin{center}
  \textbf{Tables for Duncan's multiple range tests} \\
  Critical values $q'(p, df; 0.05)$ for Duncan's multiple range tests
  \textit{(cont.)} \\
\ \\
\begin{tabular}{rrrrrrrrrrrrrr}
$df\backslash p$ & \multicolumn{1}{c}{\ 2} & \multicolumn{1}{c}{\ 3} & 
\multicolumn{1}{c}{\ 4} & \multicolumn{1}{c}{\ 5} & \multicolumn{1}{c}{\ 6} &
\multicolumn{1}{c}{\ 7} & \multicolumn{1}{c}{\ 8} & \multicolumn{1}{c}{\ 9} &
\multicolumn{1}{c}{\ 10} & \multicolumn{1}{c}{\ 11} & \multicolumn{1}{c}{\ 12} &
\multicolumn{1}{c}{\ 15} & \multicolumn{1}{c}{\ 20} \\
21 & 4.004 & 4.177 & 4.291 & 4.374 & 4.438 & 4.489 & 4.531 & 4.567 & 4.597 & 4.622 & 4.645 & 4.697 & 4.752 \\
22 & 3.986 & 4.158 & 4.272 & 4.355 & 4.419 & 4.470 & 4.513 & 4.548 & 4.578 & 4.604 & 4.627 & 4.680 & 4.737 \\
23 & 3.970 & 4.141 & 4.254 & 4.337 & 4.402 & 4.453 & 4.496 & 4.531 & 4.562 & 4.588 & 4.611 & 4.665 & 4.723 \\
24 & 3.955 & 4.126 & 4.239 & 4.322 & 4.386 & 4.437 & 4.480 & 4.516 & 4.546 & 4.573 & 4.596 & 4.651 & 4.710 \\
25 & 3.942 & 4.112 & 4.224 & 4.307 & 4.371 & 4.423 & 4.466 & 4.502 & 4.532 & 4.559 & 4.582 & 4.638 & 4.698 \\
26 & 3.930 & 4.099 & 4.211 & 4.294 & 4.358 & 4.410 & 4.452 & 4.489 & 4.520 & 4.546 & 4.570 & 4.626 & 4.687 \\
27 & 3.918 & 4.087 & 4.199 & 4.282 & 4.346 & 4.397 & 4.440 & 4.477 & 4.508 & 4.535 & 4.558 & 4.615 & 4.677 \\
28 & 3.908 & 4.076 & 4.188 & 4.270 & 4.334 & 4.386 & 4.429 & 4.465 & 4.497 & 4.524 & 4.548 & 4.604 & 4.667 \\
29 & 3.898 & 4.065 & 4.177 & 4.260 & 4.324 & 4.376 & 4.419 & 4.455 & 4.486 & 4.514 & 4.538 & 4.595 & 4.659 \\
30 & 3.889 & 4.056 & 4.168 & 4.250 & 4.314 & 4.366 & 4.409 & 4.445 & 4.477 & 4.504 & 4.528 & 4.586 & 4.650 \\
31 & 3.881 & 4.047 & 4.159 & 4.241 & 4.305 & 4.357 & 4.400 & 4.436 & 4.468 & 4.495 & 4.519 & 4.577 & 4.643 \\
32 & 3.873 & 4.039 & 4.150 & 4.232 & 4.296 & 4.348 & 4.391 & 4.428 & 4.459 & 4.487 & 4.511 & 4.570 & 4.635 \\
33 & 3.865 & 4.031 & 4.142 & 4.224 & 4.288 & 4.340 & 4.383 & 4.420 & 4.452 & 4.479 & 4.504 & 4.562 & 4.629 \\
34 & 3.859 & 4.024 & 4.135 & 4.217 & 4.281 & 4.333 & 4.376 & 4.413 & 4.444 & 4.472 & 4.496 & 4.555 & 4.622 \\
35 & 3.852 & 4.017 & 4.128 & 4.210 & 4.273 & 4.325 & 4.369 & 4.406 & 4.437 & 4.465 & 4.490 & 4.549 & 4.616 \\
36 & 3.846 & 4.011 & 4.121 & 4.203 & 4.267 & 4.319 & 4.362 & 4.399 & 4.431 & 4.459 & 4.483 & 4.543 & 4.611 \\
37 & 3.840 & 4.005 & 4.115 & 4.197 & 4.260 & 4.312 & 4.356 & 4.393 & 4.425 & 4.452 & 4.477 & 4.537 & 4.605 \\
38 & 3.835 & 3.999 & 4.109 & 4.191 & 4.254 & 4.306 & 4.350 & 4.387 & 4.419 & 4.447 & 4.471 & 4.531 & 4.600 \\
39 & 3.830 & 3.993 & 4.103 & 4.185 & 4.249 & 4.301 & 4.344 & 4.381 & 4.413 & 4.441 & 4.466 & 4.526 & 4.595 \\
40 & 3.825 & 3.988 & 4.098 & 4.180 & 4.243 & 4.295 & 4.339 & 4.376 & 4.408 & 4.436 & 4.461 & 4.521 & 4.591 \\
48 & 3.793 & 3.955 & 4.064 & 4.145 & 4.209 & 4.261 & 4.304 & 4.341 & 4.374 & 4.402 & 4.427 & 4.489 & 4.561 \\
60 & 3.762 & 3.922 & 4.030 & 4.111 & 4.174 & 4.226 & 4.270 & 4.307 & 4.340 & 4.368 & 4.394 & 4.456 & 4.530 \\
80 & 3.732 & 3.890 & 3.997 & 4.077 & 4.140 & 4.192 & 4.236 & 4.273 & 4.306 & 4.335 & 4.360 & 4.424 & 4.500 \\
120 & 3.702 & 3.858 & 3.964 & 4.044 & 4.107 & 4.158 & 4.202 & 4.239 & 4.272 & 4.301 & 4.327 & 4.392 & 4.469 \\
240 & 3.672 & 3.827 & 3.932 & 4.011 & 4.073 & 4.125 & 4.168 & 4.206 & 4.239 & 4.268 & 4.294 & 4.359 & 4.439 \\
$\infty$ & 3.643 & 3.796 & 3.900 & 3.978 & 4.040 & 4.091 & 4.135 & 4.172 & 4.205 & 4.235 & 4.261 & 4.327 & 4.408
\end{tabular}
\end{center}
\end{document}

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