Critical values q'(p, nu; 0.05) for Duncan's multiple range tests
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nu p-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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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 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 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 4.516 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 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 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 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 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 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 3.547 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 3.525 3.525 3.525 3.525 3.525 3.525
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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 3.510 3.510 3.510 3.510 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 3.498 3.498 3.498 3.498 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 3.488 3.490 3.490 3.490 3.490 3.490 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 3.479 3.482 3.484 3.484 3.484 3.484 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 3.471 3.476 3.478 3.480 3.480 3.480 3.480 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 3.465 3.470 3.473 3.476 3.477 3.477 3.477 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 3.459 3.465 3.469 3.472 3.474 3.475 3.475 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 3.454 3.460 3.465 3.469 3.472 3.473 3.474 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 3.449 3.456 3.462 3.466 3.469 3.472 3.473 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 3.445 3.452 3.459 3.463 3.467 3.470 3.472 3.473
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nu p-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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21 2.941 3.088 3.181 3.247 3.295 3.332 3.361 3.385 3.403 3.418 3.431 3.441 3.449 3.456 3.461 3.465 3.469 3.471 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 3.437 3.446 3.453 3.459 3.464 3.467 3.470 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 3.434 3.443 3.451 3.457 3.462 3.466 3.469 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 3.431 3.441 3.449 3.455 3.461 3.465 3.469 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 3.429 3.439 3.447 3.454 3.459 3.464 3.468 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 3.426 3.436 3.445 3.452 3.458 3.463 3.468 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 3.424 3.434 3.443 3.451 3.457 3.463 3.467 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 3.422 3.433 3.442 3.450 3.456 3.462 3.467 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 3.420 3.431 3.440 3.448 3.455 3.461 3.466 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 3.418 3.429 3.439 3.447 3.454 3.460 3.466 3.470
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31 2.884 3.031 3.127 3.195 3.246 3.287 3.319 3.346 3.368 3.387 3.403 3.416 3.428 3.438 3.446 3.454 3.460 3.465 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 3.415 3.426 3.436 3.445 3.453 3.459 3.465 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 3.413 3.425 3.435 3.444 3.452 3.459 3.465 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 3.412 3.424 3.434 3.443 3.451 3.458 3.464 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 3.410 3.423 3.433 3.443 3.451 3.458 3.464 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 3.409 3.421 3.432 3.442 3.450 3.457 3.464 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 3.408 3.420 3.431 3.441 3.449 3.457 3.463 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 3.407 3.419 3.431 3.440 3.449 3.456 3.463 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 3.406 3.418 3.430 3.440 3.448 3.456 3.463 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 3.404 3.418 3.429 3.439 3.448 3.456 3.463 3.469
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48 2.843 2.991 3.087 3.157 3.211 3.253 3.288 3.318 3.342 3.363 3.382 3.398 3.412 3.424 3.435 3.445 3.453 3.461 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 3.391 3.406 3.419 3.431 3.441 3.451 3.460 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 3.384 3.400 3.414 3.427 3.438 3.449 3.458 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 3.377 3.394 3.409 3.423 3.435 3.446 3.457 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 3.370 3.388 3.404 3.418 3.432 3.444 3.455 3.466
Inf 2.772 2.918 3.017 3.089 3.146 3.193 3.232 3.265 3.294 3.320 3.343 3.363 3.382 3.399 3.414 3.428 3.442 3.454 3.466
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Critical values q'(p, nu; 0.01) for Duncan's multiple range tests
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nu p-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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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 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 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 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 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 6.074 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 5.703 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 5.472 5.472 5.472 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 5.313 5.316 5.317 5.317 5.317 5.317 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 5.193 5.199 5.202 5.205 5.206 5.206 5.206 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 5.098 5.106 5.112 5.117 5.120 5.122 5.123 5.124
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11 4.392 4.579 4.697 4.780 4.841 4.887 4.923 4.952 4.975 4.994 5.009 5.021 5.031 5.039 5.045 5.050 5.054 5.057 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 4.957 4.969 4.978 4.986 4.993 4.998 5.002 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 4.904 4.917 4.927 4.936 4.944 4.950 4.955 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 4.859 4.872 4.884 4.894 4.902 4.909 4.916 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 4.820 4.834 4.846 4.857 4.866 4.874 4.881 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 4.785 4.800 4.813 4.825 4.835 4.843 4.851 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 4.755 4.771 4.785 4.797 4.807 4.816 4.824 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 4.729 4.745 4.759 4.771 4.782 4.792 4.801 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 4.705 4.722 4.736 4.749 4.760 4.771 4.780 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 4.684 4.701 4.716 4.729 4.741 4.751 4.761 4.769
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nu p-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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21 4.004 4.177 4.291 4.374 4.438 4.489 4.531 4.567 4.597 4.622 4.645 4.664 4.682 4.697 4.711 4.723 4.734 4.743 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 4.647 4.664 4.680 4.694 4.706 4.718 4.728 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 4.631 4.649 4.665 4.679 4.692 4.703 4.713 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 4.616 4.634 4.651 4.665 4.678 4.690 4.700 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 4.603 4.621 4.638 4.652 4.665 4.677 4.688 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 4.591 4.609 4.626 4.640 4.654 4.666 4.677 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 4.579 4.598 4.615 4.630 4.643 4.655 4.667 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 4.569 4.587 4.604 4.619 4.633 4.646 4.657 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 4.559 4.578 4.595 4.610 4.624 4.637 4.648 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 4.550 4.569 4.586 4.601 4.615 4.628 4.640 4.650
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31 3.881 4.047 4.159 4.241 4.305 4.357 4.400 4.436 4.468 4.495 4.519 4.541 4.560 4.577 4.593 4.607 4.620 4.632 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 4.533 4.552 4.570 4.585 4.600 4.613 4.625 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 4.525 4.545 4.562 4.578 4.592 4.606 4.618 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 4.518 4.538 4.555 4.571 4.586 4.599 4.611 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 4.511 4.531 4.549 4.565 4.579 4.593 4.605 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 4.505 4.525 4.543 4.559 4.573 4.587 4.599 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 4.499 4.519 4.537 4.553 4.568 4.581 4.594 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 4.493 4.513 4.531 4.548 4.562 4.576 4.589 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 4.488 4.508 4.526 4.542 4.557 4.571 4.584 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 4.483 4.503 4.521 4.537 4.552 4.566 4.579 4.591
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48 3.793 3.955 4.064 4.145 4.209 4.261 4.304 4.341 4.374 4.402 4.427 4.450 4.470 4.489 4.506 4.521 4.535 4.548 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 4.417 4.437 4.456 4.474 4.489 4.504 4.518 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 4.384 4.405 4.424 4.442 4.458 4.473 4.487 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 4.351 4.372 4.392 4.410 4.426 4.442 4.456 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 4.318 4.339 4.359 4.378 4.394 4.410 4.425 4.439
Inf 3.643 3.796 3.900 3.978 4.040 4.091 4.135 4.172 4.205 4.235 4.261 4.285 4.307 4.327 4.345 4.363 4.379 4.394 4.408
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