Critical values q''(p, k, nu; 0.10) for Ryan's multiple range tests -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 16.358 16.358 16.358 18.488 18.488 18.488 18.488 20.150 20.150 20.150 20.150 20.150 21.504 21.504 21.504 21.504 21.504 21.504 22.642 22.642 22.642 22.642 22.642 22.642 22.642 2 6.000 6.000 6.772 6.744 7.481 7.481 7.538 7.414 8.217 8.345 8.345 8.345 8.029 8.893 9.030 9.030 9.030 9.030 8.599 9.521 9.666 9.666 9.666 9.666 9.666 3 4.453 4.467 5.199 4.863 5.459 5.459 5.738 5.219 5.851 6.071 6.071 6.162 5.534 6.199 6.432 6.514 6.514 6.514 5.820 6.513 6.758 6.845 6.862 6.862 6.862 4 3.891 3.976 4.586 4.196 4.716 4.716 5.035 4.455 4.998 5.225 5.225 5.388 4.681 5.245 5.482 5.597 5.597 5.679 4.883 5.465 5.711 5.831 5.891 5.891 5.926 5 3.605 3.717 4.264 3.861 4.336 4.336 4.664 4.076 4.567 4.790 4.790 4.979 4.261 4.767 4.997 5.123 5.123 5.238 4.425 4.944 5.181 5.311 5.387 5.387 5.458 6 3.433 3.558 4.065 3.661 4.107 4.107 4.435 3.851 4.309 4.526 4.526 4.726 4.013 4.483 4.706 4.834 4.834 4.966 4.156 4.635 4.864 4.996 5.079 5.079 5.168 7 3.319 3.451 3.931 3.529 3.955 3.955 4.280 3.702 4.138 4.349 4.349 4.555 3.850 4.294 4.511 4.640 4.640 4.780 3.980 4.431 4.653 4.785 4.871 4.871 4.971 8 3.238 3.374 3.834 3.435 3.846 3.846 4.169 3.597 4.016 4.223 4.223 4.431 3.735 4.161 4.372 4.501 4.501 4.646 3.855 4.287 4.503 4.634 4.722 4.722 4.829 9 3.177 3.316 3.761 3.365 3.764 3.764 4.084 3.519 3.925 4.128 4.128 4.337 3.650 4.061 4.269 4.396 4.396 4.545 3.763 4.180 4.390 4.521 4.610 4.610 4.721 10 3.129 3.270 3.704 3.311 3.701 3.704 4.018 3.459 3.854 4.054 4.054 4.264 3.584 3.984 4.188 4.315 4.315 4.465 3.693 4.097 4.303 4.433 4.522 4.522 4.636 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 11 3.092 3.234 3.658 3.267 3.650 3.658 3.965 3.411 3.798 3.995 3.995 4.205 3.532 3.923 4.123 4.250 4.250 4.401 3.636 4.031 4.234 4.362 4.452 4.452 4.567 12 3.061 3.204 3.621 3.232 3.609 3.621 3.921 3.371 3.752 3.947 3.947 4.156 3.489 3.873 4.071 4.196 4.196 4.349 3.590 3.977 4.177 4.305 4.394 4.394 4.511 13 3.035 3.179 3.589 3.203 3.574 3.589 3.885 3.339 3.714 3.907 3.907 4.116 3.454 3.831 4.027 4.152 4.152 4.304 3.552 3.933 4.130 4.257 4.346 4.346 4.464 14 3.013 3.158 3.563 3.178 3.545 3.563 3.854 3.312 3.682 3.873 3.873 4.081 3.424 3.796 3.990 4.114 4.114 4.267 3.520 3.895 4.090 4.216 4.305 4.305 4.424 15 2.995 3.140 3.540 3.157 3.520 3.540 3.828 3.288 3.654 3.844 3.844 4.052 3.398 3.766 3.958 4.082 4.082 4.235 3.493 3.863 4.056 4.181 4.270 4.270 4.390 16 2.979 3.124 3.520 3.139 3.499 3.520 3.804 3.268 3.630 3.819 3.819 4.026 3.376 3.740 3.931 4.053 4.053 4.207 3.470 3.835 4.027 4.151 4.240 4.240 4.360 17 2.965 3.110 3.503 3.123 3.480 3.503 3.784 3.250 3.609 3.797 3.797 4.003 3.357 3.718 3.907 4.029 4.029 4.182 3.449 3.811 4.001 4.125 4.213 4.213 4.334 18 2.952 3.098 3.487 3.109 3.463 3.487 3.766 3.235 3.591 3.777 3.777 3.984 3.340 3.698 3.885 4.007 4.007 4.161 3.431 3.789 3.978 4.102 4.190 4.190 4.310 19 2.941 3.087 3.474 3.096 3.448 3.474 3.751 3.221 3.574 3.760 3.760 3.966 3.325 3.680 3.867 3.988 3.988 4.142 3.415 3.771 3.958 4.081 4.169 4.169 4.290 20 2.932 3.077 3.462 3.085 3.435 3.462 3.736 3.208 3.560 3.744 3.744 3.950 3.312 3.664 3.850 3.971 3.971 4.124 3.401 3.754 3.940 4.062 4.150 4.150 4.271 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 21 2.923 3.069 3.451 3.075 3.423 3.451 3.724 3.197 3.547 3.730 3.730 3.936 3.300 3.650 3.835 3.955 3.955 4.109 3.388 3.738 3.924 4.046 4.134 4.134 4.255 22 2.915 3.061 3.441 3.066 3.413 3.441 3.712 3.187 3.535 3.718 3.718 3.923 3.289 3.637 3.821 3.941 3.941 4.095 3.376 3.725 3.909 4.031 4.118 4.118 4.239 23 2.907 3.054 3.432 3.057 3.403 3.432 3.701 3.178 3.524 3.706 3.706 3.911 3.279 3.625 3.808 3.928 3.928 4.082 3.366 3.712 3.896 4.017 4.105 4.105 4.226 24 2.901 3.047 3.423 3.050 3.394 3.423 3.692 3.170 3.514 3.696 3.696 3.900 3.270 3.615 3.797 3.917 3.917 4.070 3.356 3.701 3.884 4.004 4.092 4.092 4.213 25 2.895 3.041 3.416 3.043 3.386 3.416 3.683 3.162 3.505 3.686 3.686 3.890 3.262 3.605 3.787 3.906 3.906 4.059 3.347 3.690 3.873 3.993 4.080 4.080 4.201 26 2.889 3.036 3.409 3.037 3.378 3.409 3.675 3.155 3.497 3.677 3.677 3.881 3.254 3.596 3.777 3.896 3.896 4.049 3.339 3.681 3.863 3.982 4.070 4.070 4.191 27 2.884 3.030 3.402 3.031 3.371 3.402 3.667 3.149 3.489 3.669 3.669 3.873 3.247 3.588 3.768 3.887 3.887 4.040 3.332 3.672 3.853 3.973 4.060 4.060 4.181 28 2.879 3.026 3.396 3.025 3.365 3.396 3.660 3.143 3.482 3.662 3.662 3.865 3.241 3.580 3.760 3.879 3.879 4.032 3.325 3.664 3.845 3.964 4.051 4.051 4.172 29 2.875 3.021 3.391 3.020 3.359 3.391 3.654 3.137 3.476 3.655 3.655 3.858 3.235 3.573 3.753 3.871 3.871 4.024 3.318 3.656 3.836 3.955 4.042 4.042 4.163 30 2.871 3.017 3.386 3.016 3.353 3.386 3.648 3.132 3.470 3.648 3.648 3.851 3.229 3.566 3.746 3.864 3.864 4.016 3.312 3.649 3.829 3.948 4.034 4.034 4.155 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 31 2.867 3.013 3.381 3.011 3.348 3.381 3.642 3.127 3.464 3.642 3.642 3.845 3.224 3.560 3.739 3.857 3.857 4.009 3.307 3.643 3.822 3.940 4.027 4.027 4.148 32 2.863 3.010 3.376 3.007 3.343 3.376 3.637 3.123 3.459 3.636 3.637 3.839 3.219 3.554 3.733 3.851 3.851 4.003 3.302 3.637 3.815 3.934 4.020 4.020 4.141 33 2.860 3.006 3.372 3.004 3.339 3.372 3.632 3.119 3.454 3.631 3.632 3.833 3.215 3.549 3.727 3.845 3.845 3.997 3.297 3.631 3.809 3.927 4.014 4.014 4.135 34 2.857 3.003 3.368 3.000 3.335 3.368 3.627 3.115 3.449 3.626 3.627 3.828 3.210 3.544 3.722 3.839 3.839 3.991 3.292 3.625 3.803 3.921 4.008 4.008 4.129 35 2.854 3.000 3.364 2.997 3.331 3.364 3.623 3.111 3.444 3.621 3.623 3.823 3.206 3.539 3.717 3.834 3.834 3.986 3.288 3.620 3.798 3.916 4.002 4.002 4.123 36 2.851 2.998 3.361 2.993 3.327 3.361 3.619 3.108 3.440 3.617 3.619 3.819 3.203 3.535 3.712 3.829 3.829 3.981 3.284 3.615 3.793 3.910 3.996 3.996 4.117 37 2.848 2.995 3.357 2.990 3.323 3.357 3.615 3.104 3.436 3.613 3.615 3.814 3.199 3.531 3.707 3.824 3.824 3.976 3.280 3.611 3.788 3.905 3.991 3.991 4.112 38 2.846 2.992 3.354 2.988 3.320 3.354 3.611 3.101 3.433 3.609 3.611 3.810 3.196 3.527 3.703 3.820 3.820 3.972 3.277 3.607 3.783 3.901 3.987 3.987 4.107 39 2.843 2.990 3.351 2.985 3.317 3.351 3.608 3.098 3.429 3.605 3.608 3.806 3.193 3.523 3.699 3.816 3.816 3.967 3.273 3.603 3.779 3.896 3.982 3.982 4.103 40 2.841 2.988 3.348 2.982 3.314 3.348 3.605 3.095 3.426 3.602 3.605 3.802 3.189 3.519 3.695 3.812 3.812 3.963 3.270 3.599 3.775 3.892 3.978 3.978 4.099 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 48 2.827 2.973 3.330 2.966 3.294 3.330 3.583 3.077 3.404 3.579 3.583 3.778 3.170 3.496 3.670 3.786 3.786 3.937 3.249 3.574 3.748 3.864 3.950 3.950 4.070 60 2.812 2.959 3.312 2.950 3.275 3.312 3.562 3.059 3.383 3.556 3.562 3.755 3.151 3.473 3.645 3.760 3.760 3.911 3.228 3.550 3.722 3.837 3.922 3.922 4.042 80 2.798 2.945 3.294 2.933 3.256 3.294 3.541 3.042 3.362 3.533 3.541 3.731 3.131 3.450 3.621 3.735 3.735 3.885 3.208 3.525 3.696 3.810 3.894 3.894 4.014 120 2.784 2.930 3.276 2.918 3.237 3.276 3.520 3.024 3.341 3.511 3.520 3.707 3.113 3.428 3.597 3.710 3.710 3.859 3.188 3.501 3.670 3.783 3.867 3.867 3.986 240 2.770 2.916 3.258 2.902 3.218 3.258 3.499 3.007 3.320 3.488 3.499 3.684 3.094 3.405 3.573 3.685 3.685 3.834 3.168 3.478 3.645 3.757 3.840 3.840 3.959 Inf 2.756 2.902 3.240 2.886 3.199 3.240 3.478 2.990 3.300 3.466 3.478 3.661 3.075 3.383 3.549 3.660 3.661 3.808 3.148 3.454 3.619 3.730 3.813 3.813 3.931 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Critical values q''(p, k, nu; 0.05) for Ryan's multiple range tests -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 32.819 32.819 32.819 37.082 37.082 37.082 37.082 40.408 40.408 40.408 40.408 40.408 43.119 43.119 43.119 43.119 43.119 43.119 45.397 45.397 45.397 45.397 45.397 45.397 45.397 2 8.718 8.718 9.798 9.772 10.811 10.811 10.881 10.723 11.859 12.036 12.036 12.036 11.597 12.821 13.011 13.011 13.011 13.011 12.409 13.716 13.918 13.918 13.918 13.918 13.918 3 5.878 5.910 6.825 6.385 7.138 7.138 7.502 6.826 7.625 7.910 7.910 8.037 7.218 8.059 8.360 8.471 8.471 8.478 7.573 8.452 8.767 8.884 8.912 8.912 8.912 4 4.923 5.040 5.757 5.274 5.893 5.893 6.287 5.573 6.220 6.497 6.497 6.706 5.834 6.507 6.795 6.940 6.940 7.053 6.068 6.763 7.062 7.213 7.292 7.292 7.347 5 4.458 4.602 5.218 4.739 5.284 5.284 5.673 4.975 5.540 5.801 5.801 6.033 5.180 5.762 6.032 6.183 6.183 6.330 5.362 5.958 6.237 6.393 6.487 6.487 6.582 6 4.184 4.339 4.896 4.427 4.926 4.926 5.305 4.630 5.142 5.390 5.390 5.628 4.804 5.329 5.584 5.735 5.735 5.895 4.957 5.494 5.755 5.910 6.009 6.009 6.122 7 4.006 4.165 4.681 4.224 4.691 4.691 5.060 4.406 4.883 5.121 5.121 5.359 4.561 5.048 5.291 5.439 5.439 5.606 4.697 5.193 5.441 5.592 5.693 5.693 5.815 8 3.880 4.041 4.529 4.082 4.525 4.529 4.886 4.249 4.701 4.930 4.930 5.167 4.392 4.851 5.085 5.230 5.230 5.399 4.516 4.982 5.220 5.368 5.469 5.469 5.596 9 3.786 3.948 4.415 3.977 4.403 4.415 4.755 4.134 4.567 4.789 4.789 5.024 4.267 4.706 4.932 5.074 5.074 5.244 4.383 4.827 5.057 5.202 5.303 5.303 5.432 10 3.714 3.877 4.327 3.896 4.308 4.327 4.654 4.045 4.463 4.679 4.679 4.912 4.171 4.594 4.814 4.954 4.954 5.124 4.281 4.708 4.931 5.074 5.174 5.174 5.304 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 11 3.657 3.820 4.256 3.832 4.233 4.256 4.574 3.975 4.381 4.593 4.593 4.823 4.096 4.506 4.721 4.858 4.858 5.028 4.200 4.615 4.832 4.972 5.071 5.071 5.202 12 3.611 3.773 4.199 3.780 4.172 4.199 4.508 3.918 4.314 4.522 4.522 4.750 4.034 4.434 4.645 4.781 4.781 4.950 4.135 4.538 4.751 4.889 4.987 4.987 5.119 13 3.572 3.734 4.151 3.737 4.122 4.151 4.453 3.871 4.259 4.463 4.463 4.690 3.984 4.375 4.582 4.716 4.716 4.884 4.082 4.475 4.684 4.820 4.917 4.917 5.049 14 3.540 3.701 4.111 3.700 4.079 4.111 4.407 3.831 4.213 4.414 4.414 4.639 3.941 4.325 4.529 4.661 4.661 4.829 4.037 4.423 4.628 4.762 4.859 4.859 4.990 15 3.512 3.673 4.076 3.670 4.043 4.076 4.367 3.798 4.173 4.372 4.372 4.595 3.905 4.283 4.484 4.615 4.615 4.782 3.998 4.378 4.580 4.713 4.809 4.809 4.940 16 3.488 3.649 4.046 3.643 4.011 4.046 4.333 3.768 4.139 4.335 4.335 4.557 3.874 4.246 4.444 4.575 4.575 4.741 3.965 4.339 4.539 4.670 4.765 4.765 4.896 17 3.467 3.628 4.020 3.620 3.984 4.020 4.303 3.743 4.109 4.304 4.304 4.524 3.847 4.214 4.410 4.539 4.539 4.705 3.936 4.305 4.502 4.633 4.727 4.727 4.858 18 3.449 3.609 3.997 3.599 3.960 3.997 4.276 3.721 4.083 4.276 4.276 4.494 3.823 4.186 4.380 4.509 4.509 4.673 3.911 4.275 4.471 4.600 4.694 4.694 4.824 19 3.433 3.593 3.977 3.581 3.938 3.977 4.253 3.701 4.060 4.251 4.253 4.468 3.802 4.161 4.354 4.481 4.481 4.645 3.889 4.249 4.443 4.571 4.664 4.664 4.794 20 3.418 3.578 3.958 3.565 3.919 3.958 4.232 3.684 4.039 4.229 4.232 4.445 3.783 4.139 4.330 4.457 4.457 4.620 3.869 4.226 4.418 4.545 4.638 4.638 4.768 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 21 3.405 3.565 3.942 3.550 3.902 3.942 4.213 3.668 4.020 4.209 4.213 4.424 3.766 4.119 4.309 4.435 4.435 4.597 3.851 4.205 4.395 4.521 4.614 4.614 4.743 22 3.393 3.553 3.927 3.537 3.887 3.927 4.196 3.654 4.004 4.191 4.196 4.405 3.751 4.101 4.290 4.415 4.415 4.577 3.835 4.186 4.375 4.500 4.593 4.593 4.722 23 3.383 3.542 3.914 3.526 3.873 3.914 4.180 3.641 3.988 4.175 4.180 4.388 3.737 4.085 4.272 4.397 4.397 4.558 3.820 4.168 4.356 4.481 4.573 4.573 4.702 24 3.373 3.532 3.901 3.515 3.860 3.901 4.166 3.629 3.974 4.160 4.166 4.373 3.725 4.070 4.256 4.380 4.380 4.541 3.807 4.153 4.339 4.464 4.555 4.555 4.684 25 3.364 3.523 3.890 3.505 3.848 3.890 4.153 3.618 3.962 4.146 4.153 4.358 3.713 4.057 4.242 4.365 4.365 4.526 3.795 4.138 4.324 4.448 4.539 4.539 4.667 26 3.356 3.514 3.880 3.496 3.837 3.880 4.141 3.608 3.950 4.134 4.141 4.345 3.703 4.044 4.228 4.351 4.351 4.511 3.784 4.125 4.310 4.433 4.524 4.524 4.652 27 3.348 3.506 3.870 3.487 3.828 3.870 4.130 3.599 3.939 4.122 4.130 4.333 3.693 4.033 4.216 4.338 4.338 4.498 3.773 4.113 4.297 4.420 4.510 4.510 4.638 28 3.341 3.499 3.861 3.480 3.818 3.861 4.120 3.591 3.929 4.112 4.120 4.322 3.684 4.022 4.205 4.327 4.327 4.486 3.764 4.102 4.285 4.407 4.497 4.497 4.625 29 3.335 3.493 3.853 3.472 3.810 3.853 4.111 3.583 3.920 4.102 4.111 4.311 3.676 4.012 4.194 4.316 4.316 4.475 3.755 4.091 4.274 4.396 4.485 4.485 4.613 30 3.329 3.486 3.845 3.466 3.802 3.845 4.102 3.576 3.912 4.092 4.102 4.301 3.668 4.003 4.184 4.305 4.305 4.464 3.747 4.082 4.263 4.385 4.474 4.474 4.601 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 31 3.323 3.481 3.838 3.459 3.795 3.838 4.094 3.569 3.904 4.084 4.094 4.292 3.661 3.995 4.175 4.296 4.296 4.454 3.739 4.073 4.254 4.375 4.464 4.464 4.591 32 3.318 3.475 3.832 3.454 3.788 3.832 4.086 3.563 3.896 4.076 4.086 4.284 3.654 3.987 4.167 4.287 4.287 4.445 3.732 4.064 4.245 4.365 4.454 4.454 4.581 33 3.313 3.470 3.825 3.448 3.781 3.825 4.079 3.557 3.889 4.068 4.079 4.276 3.648 3.979 4.159 4.279 4.279 4.436 3.725 4.057 4.236 4.356 4.445 4.445 4.572 34 3.309 3.465 3.820 3.443 3.775 3.820 4.072 3.551 3.883 4.061 4.072 4.268 3.642 3.972 4.151 4.271 4.271 4.428 3.719 4.049 4.228 4.348 4.437 4.437 4.563 35 3.304 3.461 3.814 3.438 3.769 3.814 4.066 3.546 3.876 4.055 4.066 4.261 3.636 3.966 4.144 4.263 4.263 4.421 3.713 4.042 4.221 4.340 4.429 4.429 4.555 36 3.300 3.457 3.809 3.434 3.764 3.809 4.060 3.541 3.871 4.048 4.060 4.255 3.631 3.959 4.137 4.257 4.257 4.414 3.708 4.036 4.214 4.333 4.422 4.422 4.547 37 3.296 3.453 3.804 3.429 3.759 3.804 4.054 3.536 3.865 4.042 4.054 4.249 3.626 3.954 4.131 4.250 4.250 4.407 3.702 4.029 4.207 4.326 4.414 4.414 4.540 38 3.293 3.449 3.799 3.425 3.754 3.799 4.049 3.532 3.860 4.037 4.049 4.243 3.621 3.948 4.125 4.244 4.244 4.400 3.697 4.024 4.201 4.320 4.408 4.408 4.533 39 3.289 3.445 3.795 3.422 3.750 3.795 4.044 3.528 3.855 4.032 4.044 4.237 3.617 3.943 4.120 4.238 4.238 4.394 3.693 4.018 4.195 4.313 4.401 4.401 4.527 40 3.286 3.442 3.791 3.418 3.745 3.791 4.039 3.524 3.850 4.027 4.039 4.232 3.612 3.938 4.114 4.232 4.232 4.388 3.688 4.013 4.189 4.308 4.395 4.395 4.521 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 48 3.265 3.420 3.764 3.395 3.718 3.764 4.008 3.499 3.820 3.994 4.008 4.197 3.585 3.906 4.080 4.196 4.197 4.351 3.660 3.979 4.153 4.270 4.356 4.356 4.481 60 3.244 3.399 3.737 3.371 3.690 3.737 3.977 3.474 3.791 3.962 3.977 4.163 3.559 3.874 4.046 4.161 4.163 4.314 3.632 3.946 4.117 4.232 4.318 4.318 4.441 80 3.223 3.377 3.711 3.349 3.663 3.711 3.947 3.449 3.761 3.931 3.947 4.129 3.532 3.843 4.012 4.126 4.129 4.277 3.604 3.913 4.081 4.195 4.280 4.280 4.402 120 3.203 3.356 3.685 3.326 3.636 3.685 3.917 3.425 3.733 3.900 3.917 4.096 3.506 3.812 3.979 4.091 4.096 4.241 3.576 3.881 4.046 4.159 4.242 4.242 4.363 240 3.183 3.335 3.659 3.304 3.610 3.659 3.887 3.401 3.704 3.869 3.887 4.063 3.481 3.782 3.946 4.057 4.063 4.205 3.549 3.849 4.012 4.122 4.205 4.205 4.324 Inf 3.163 3.314 3.633 3.282 3.584 3.633 3.858 3.377 3.676 3.838 3.858 4.030 3.456 3.752 3.914 4.023 4.030 4.170 3.523 3.817 3.978 4.087 4.168 4.170 4.286 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Critical values q''(p, k, nu; 0.01) for Ryan's multiple range tests -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1 164.26 164.26 164.26 185.58 185.58 185.58 185.58 202.21 202.21 202.21 202.21 202.21 215.77 215.77 215.77 215.77 215.77 215.77 227.17 227.17 227.17 227.17 227.17 227.17 227.17 2 19.900 19.900 22.294 22.260 24.578 24.578 24.717 24.393 26.931 27.320 27.320 27.320 26.353 29.094 29.514 29.514 29.514 29.514 28.178 31.107 31.556 31.556 31.556 31.556 31.556 3 10.531 10.619 12.170 11.376 12.670 12.670 13.324 12.113 13.488 13.991 13.991 14.241 12.771 14.218 14.749 14.955 14.955 14.998 13.368 14.881 15.437 15.653 15.715 15.715 15.715 4 7.911 8.120 9.173 8.410 9.337 9.337 9.958 8.837 9.807 10.236 10.236 10.583 9.212 10.220 10.667 10.901 10.901 11.101 9.548 10.590 11.053 11.296 11.431 11.431 11.542 5 6.747 6.976 7.804 7.109 7.857 7.857 8.421 7.415 8.191 8.563 8.563 8.913 7.682 8.481 8.866 9.089 9.089 9.321 7.919 8.740 9.135 9.365 9.510 9.510 9.669 6 6.102 6.331 7.033 6.394 7.038 7.038 7.556 6.639 7.303 7.636 7.636 7.972 6.851 7.531 7.873 8.082 8.082 8.318 7.038 7.733 8.083 8.297 8.440 8.440 8.612 7 5.696 5.919 6.542 5.946 6.523 6.542 7.005 6.155 6.746 7.051 7.051 7.373 6.335 6.939 7.250 7.446 7.446 7.678 6.493 7.108 7.426 7.626 7.763 7.763 7.939 8 5.418 5.635 6.204 5.641 6.171 6.204 6.625 5.826 6.367 6.651 6.651 6.959 5.985 6.536 6.825 7.011 7.011 7.237 6.125 6.683 6.978 7.167 7.299 7.299 7.474 9 5.216 5.428 5.957 5.420 5.916 5.957 6.347 5.589 6.093 6.361 6.361 6.657 5.733 6.245 6.517 6.694 6.694 6.915 5.859 6.378 6.654 6.834 6.962 6.962 7.134 10 5.063 5.270 5.769 5.253 5.722 5.769 6.136 5.410 5.886 6.141 6.141 6.428 5.543 6.026 6.285 6.454 6.454 6.669 5.660 6.147 6.410 6.582 6.706 6.706 6.875 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 11 4.943 5.146 5.621 5.122 5.571 5.621 5.970 5.270 5.724 5.969 5.970 6.247 5.395 5.854 6.103 6.266 6.266 6.476 5.505 5.968 6.219 6.385 6.506 6.506 6.671 12 4.847 5.046 5.502 5.017 5.449 5.502 5.836 5.158 5.594 5.831 5.836 6.101 5.277 5.717 5.957 6.115 6.115 6.320 5.380 5.824 6.066 6.227 6.344 6.344 6.507 13 4.768 4.964 5.404 4.932 5.349 5.404 5.726 5.066 5.488 5.717 5.726 5.981 5.180 5.605 5.837 5.991 5.991 6.192 5.279 5.707 5.941 6.097 6.212 6.212 6.372 14 4.701 4.895 5.322 4.860 5.266 5.322 5.634 4.989 5.399 5.622 5.634 5.881 5.099 5.511 5.737 5.888 5.888 6.085 5.194 5.609 5.836 5.989 6.101 6.101 6.258 15 4.645 4.836 5.252 4.799 5.195 5.252 5.556 4.924 5.323 5.542 5.556 5.796 5.030 5.432 5.652 5.800 5.800 5.994 5.122 5.526 5.748 5.897 6.007 6.007 6.162 16 4.597 4.786 5.192 4.747 5.135 5.192 5.489 4.869 5.259 5.473 5.489 5.722 4.972 5.364 5.580 5.724 5.724 5.915 5.061 5.455 5.672 5.818 5.926 5.926 6.079 17 4.556 4.742 5.140 4.702 5.082 5.140 5.430 4.821 5.203 5.413 5.430 5.659 4.921 5.305 5.517 5.659 5.659 5.847 5.008 5.394 5.606 5.750 5.856 5.856 6.007 18 4.519 4.703 5.094 4.662 5.036 5.094 5.379 4.778 5.154 5.361 5.379 5.603 4.877 5.254 5.461 5.602 5.603 5.787 4.962 5.340 5.549 5.690 5.795 5.795 5.944 19 4.487 4.669 5.054 4.627 4.995 5.054 5.334 4.741 5.111 5.314 5.334 5.553 4.838 5.208 5.413 5.551 5.553 5.735 4.921 5.293 5.498 5.637 5.741 5.741 5.889 20 4.458 4.639 5.018 4.596 4.959 5.018 5.293 4.708 5.072 5.273 5.293 5.510 4.803 5.168 5.370 5.506 5.510 5.688 4.884 5.251 5.453 5.590 5.693 5.693 5.839 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- k-> 4 4 4 5 5 5 5 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 nu p-> 2 3 4 2 3 4 5 2 3 4 5 6 2 3 4 5 6 7 2 3 4 5 6 7 8 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 21 4.432 4.612 4.986 4.568 4.927 4.986 5.257 4.679 5.038 5.236 5.257 5.470 4.772 5.132 5.331 5.466 5.470 5.646 4.852 5.213 5.413 5.548 5.649 5.649 5.794 22 4.409 4.588 4.957 4.543 4.898 4.957 5.225 4.652 5.007 5.203 5.225 5.435 4.744 5.099 5.296 5.430 5.435 5.608 4.823 5.179 5.376 5.511 5.611 5.611 5.754 23 4.388 4.566 4.931 4.521 4.871 4.931 5.195 4.628 4.979 5.173 5.195 5.403 4.718 5.070 5.265 5.397 5.403 5.573 4.796 5.149 5.344 5.476 5.575 5.575 5.718 24 4.369 4.546 4.907 4.500 4.847 4.907 5.168 4.606 4.954 5.146 5.168 5.373 4.695 5.043 5.236 5.367 5.373 5.542 4.772 5.121 5.314 5.445 5.544 5.544 5.685 25 4.352 4.527 4.885 4.481 4.826 4.885 5.144 4.586 4.931 5.121 5.144 5.347 4.674 5.019 5.210 5.340 5.347 5.513 4.751 5.095 5.287 5.417 5.514 5.514 5.655 26 4.336 4.510 4.865 4.464 4.805 4.865 5.121 4.568 4.909 5.098 5.121 5.322 4.655 4.997 5.186 5.315 5.322 5.487 4.730 5.072 5.262 5.391 5.488 5.488 5.627 27 4.321 4.495 4.847 4.448 4.787 4.847 5.101 4.551 4.890 5.077 5.101 5.300 4.638 4.976 5.164 5.292 5.300 5.463 4.712 5.051 5.239 5.367 5.463 5.463 5.602 28 4.308 4.481 4.830 4.434 4.770 4.830 5.082 4.536 4.872 5.058 5.082 5.279 4.621 4.957 5.144 5.271 5.279 5.441 4.695 5.031 5.218 5.345 5.440 5.441 5.578 29 4.295 4.467 4.814 4.420 4.754 4.814 5.064 4.521 4.855 5.040 5.064 5.260 4.606 4.940 5.125 5.251 5.260 5.420 4.679 5.013 5.198 5.325 5.419 5.420 5.556 30 4.283 4.455 4.799 4.407 4.740 4.799 5.048 4.508 4.840 5.023 5.048 5.242 4.592 4.924 5.107 5.233 5.242 5.401 4.665 4.996 5.180 5.306 5.400 5.401 5.536 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 31 4.273 4.443 4.786 4.396 4.726 4.786 5.032 4.495 4.825 5.008 5.032 5.225 4.579 4.909 5.091 5.216 5.225 5.383 4.651 4.980 5.163 5.288 5.382 5.383 5.517 32 4.262 4.433 4.773 4.385 4.713 4.773 5.018 4.484 4.812 4.993 5.018 5.210 4.567 4.894 5.076 5.200 5.210 5.367 4.638 4.966 5.147 5.271 5.365 5.367 5.500 33 4.253 4.423 4.761 4.375 4.701 4.761 5.005 4.473 4.799 4.980 5.005 5.195 4.556 4.881 5.062 5.185 5.195 5.351 4.627 4.952 5.133 5.256 5.349 5.351 5.483 34 4.244 4.413 4.750 4.365 4.690 4.750 4.992 4.463 4.787 4.967 4.992 5.181 4.545 4.869 5.049 5.171 5.181 5.336 4.615 4.939 5.119 5.242 5.334 5.336 5.468 35 4.236 4.404 4.739 4.356 4.680 4.739 4.980 4.453 4.776 4.955 4.980 5.169 4.535 4.857 5.036 5.158 5.169 5.323 4.605 4.927 5.106 5.228 5.320 5.323 5.453 36 4.228 4.396 4.729 4.348 4.670 4.729 4.969 4.444 4.766 4.944 4.969 5.156 4.525 4.846 5.024 5.146 5.156 5.310 4.595 4.916 5.094 5.215 5.307 5.310 5.439 37 4.220 4.388 4.720 4.340 4.661 4.720 4.959 4.436 4.756 4.933 4.959 5.145 4.517 4.836 5.013 5.134 5.145 5.298 4.586 4.905 5.082 5.203 5.294 5.298 5.427 38 4.213 4.381 4.711 4.332 4.652 4.711 4.949 4.428 4.747 4.923 4.949 5.134 4.508 4.826 5.003 5.123 5.134 5.286 4.577 4.895 5.071 5.192 5.283 5.286 5.414 39 4.207 4.374 4.703 4.325 4.644 4.703 4.940 4.420 4.738 4.914 4.940 5.124 4.500 4.817 4.993 5.113 5.124 5.275 4.569 4.885 5.061 5.181 5.272 5.275 5.403 40 4.201 4.367 4.695 4.318 4.636 4.695 4.931 4.413 4.730 4.905 4.931 5.114 4.493 4.808 4.984 5.103 5.114 5.265 4.561 4.876 5.051 5.171 5.261 5.265 5.392 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 48 4.160 4.324 4.644 4.275 4.585 4.644 4.874 4.367 4.676 4.847 4.874 5.052 4.445 4.752 4.923 5.040 5.052 5.198 4.511 4.818 4.989 5.105 5.193 5.198 5.322 60 4.121 4.282 4.594 4.232 4.535 4.594 4.818 4.322 4.624 4.791 4.818 4.991 4.397 4.697 4.864 4.978 4.991 5.133 4.462 4.761 4.927 5.041 5.127 5.133 5.253 80 4.082 4.241 4.545 4.190 4.487 4.545 4.763 4.278 4.572 4.735 4.763 4.931 4.351 4.644 4.806 4.918 4.931 5.069 4.413 4.705 4.867 4.978 5.062 5.069 5.185 120 4.043 4.200 4.497 4.149 4.439 4.497 4.709 4.234 4.522 4.681 4.709 4.872 4.305 4.591 4.749 4.858 4.872 5.005 4.366 4.650 4.808 4.916 4.998 5.005 5.118 240 4.006 4.160 4.450 4.109 4.392 4.450 4.655 4.191 4.472 4.627 4.655 4.814 4.260 4.539 4.693 4.799 4.814 4.943 4.320 4.596 4.750 4.855 4.935 4.943 5.052 Inf 3.969 4.120 4.403 4.069 4.345 4.403 4.603 4.150 4.423 4.575 4.603 4.757 4.217 4.488 4.639 4.742 4.757 4.882 4.274 4.543 4.693 4.796 4.873 4.882 4.987 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