The Studentized range upper quantiles q(k, df; 0.10) ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 1 8.929 13.437 16.358 18.488 20.150 21.504 22.642 23.621 24.477 25.237 25.918 26.536 27.100 27.618 28.097 28.542 28.958 29.347 29.713 2 4.129 5.733 6.772 7.538 8.139 8.633 9.049 9.409 9.725 10.006 10.259 10.488 10.698 10.891 11.070 11.237 11.392 11.538 11.676 3 3.328 4.467 5.199 5.738 6.162 6.511 6.806 7.062 7.287 7.487 7.667 7.831 7.982 8.120 8.248 8.368 8.479 8.584 8.683 4 3.015 3.976 4.586 5.035 5.388 5.679 5.926 6.139 6.327 6.494 6.645 6.783 6.909 7.025 7.132 7.233 7.326 7.414 7.497 5 2.850 3.717 4.264 4.664 4.979 5.238 5.458 5.648 5.816 5.965 6.100 6.223 6.336 6.439 6.536 6.626 6.710 6.788 6.863 6 2.748 3.558 4.065 4.435 4.726 4.966 5.168 5.344 5.499 5.637 5.762 5.875 5.979 6.075 6.164 6.247 6.325 6.398 6.466 7 2.679 3.451 3.931 4.280 4.555 4.780 4.971 5.137 5.283 5.413 5.530 5.637 5.735 5.826 5.910 5.988 6.061 6.130 6.195 8 2.630 3.374 3.834 4.169 4.431 4.646 4.829 4.987 5.126 5.250 5.362 5.464 5.558 5.644 5.724 5.799 5.869 5.935 5.997 9 2.592 3.316 3.761 4.084 4.337 4.545 4.721 4.873 5.007 5.126 5.234 5.333 5.423 5.506 5.583 5.655 5.722 5.786 5.845 10 2.563 3.270 3.704 4.018 4.264 4.465 4.636 4.783 4.913 5.029 5.134 5.229 5.316 5.397 5.472 5.542 5.607 5.668 5.726 ------------------------------------------------------------------------------------------------------------------------------------------ 11 2.540 3.234 3.658 3.965 4.205 4.401 4.567 4.711 4.838 4.951 5.053 5.145 5.231 5.309 5.382 5.450 5.514 5.573 5.630 12 2.521 3.204 3.621 3.921 4.156 4.349 4.511 4.652 4.776 4.886 4.986 5.076 5.160 5.236 5.308 5.374 5.436 5.495 5.550 13 2.504 3.179 3.589 3.885 4.116 4.304 4.464 4.602 4.724 4.832 4.930 5.019 5.100 5.175 5.245 5.310 5.371 5.429 5.483 14 2.491 3.158 3.563 3.854 4.081 4.267 4.424 4.560 4.679 4.786 4.882 4.969 5.050 5.124 5.192 5.256 5.316 5.372 5.426 15 2.479 3.140 3.540 3.828 4.052 4.235 4.390 4.524 4.641 4.746 4.841 4.927 5.006 5.079 5.146 5.209 5.268 5.324 5.376 16 2.469 3.124 3.520 3.804 4.026 4.207 4.360 4.492 4.608 4.712 4.805 4.890 4.968 5.040 5.106 5.169 5.227 5.282 5.333 17 2.460 3.110 3.503 3.784 4.003 4.182 4.334 4.464 4.579 4.681 4.774 4.857 4.934 5.005 5.071 5.133 5.190 5.244 5.295 18 2.452 3.098 3.487 3.766 3.984 4.161 4.310 4.440 4.553 4.654 4.746 4.829 4.905 4.975 5.040 5.101 5.158 5.211 5.262 19 2.445 3.087 3.474 3.751 3.966 4.142 4.290 4.418 4.530 4.630 4.721 4.803 4.878 4.948 5.012 5.072 5.129 5.182 5.232 20 2.439 3.077 3.462 3.736 3.950 4.124 4.271 4.398 4.510 4.609 4.699 4.780 4.855 4.923 4.987 5.047 5.103 5.155 5.205 ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 21 2.433 3.069 3.451 3.724 3.936 4.109 4.255 4.380 4.491 4.590 4.678 4.759 4.833 4.901 4.965 5.024 5.079 5.131 5.180 22 2.428 3.061 3.441 3.712 3.923 4.095 4.239 4.364 4.474 4.572 4.660 4.740 4.814 4.882 4.944 5.003 5.058 5.109 5.158 23 2.424 3.054 3.432 3.701 3.911 4.082 4.226 4.350 4.459 4.556 4.644 4.723 4.796 4.863 4.926 4.984 5.038 5.089 5.138 24 2.420 3.047 3.423 3.692 3.900 4.070 4.213 4.336 4.445 4.541 4.628 4.707 4.780 4.847 4.909 4.966 5.020 5.071 5.119 25 2.416 3.041 3.416 3.683 3.890 4.059 4.201 4.324 4.432 4.528 4.614 4.693 4.765 4.831 4.893 4.950 5.004 5.055 5.102 26 2.412 3.036 3.409 3.675 3.881 4.049 4.191 4.313 4.420 4.515 4.601 4.680 4.751 4.817 4.878 4.936 4.989 5.039 5.086 27 2.409 3.030 3.402 3.667 3.873 4.040 4.181 4.302 4.409 4.504 4.590 4.667 4.739 4.804 4.865 4.922 4.975 5.025 5.072 28 2.406 3.026 3.396 3.660 3.865 4.032 4.172 4.293 4.399 4.493 4.579 4.656 4.727 4.792 4.853 4.909 4.962 5.012 5.058 29 2.403 3.021 3.391 3.654 3.858 4.024 4.163 4.284 4.389 4.484 4.568 4.645 4.716 4.781 4.841 4.897 4.950 4.999 5.046 30 2.400 3.017 3.386 3.648 3.851 4.016 4.155 4.275 4.381 4.474 4.559 4.635 4.706 4.770 4.830 4.886 4.939 4.988 5.034 ------------------------------------------------------------------------------------------------------------------------------------------ 31 2.398 3.013 3.381 3.642 3.845 4.009 4.148 4.268 4.372 4.466 4.550 4.626 4.696 4.760 4.820 4.876 4.928 4.977 5.023 32 2.396 3.010 3.376 3.637 3.839 4.003 4.141 4.260 4.365 4.458 4.541 4.617 4.687 4.751 4.811 4.866 4.918 4.967 5.013 33 2.393 3.006 3.372 3.632 3.833 3.997 4.135 4.253 4.357 4.450 4.533 4.609 4.679 4.743 4.802 4.857 4.909 4.957 5.003 34 2.391 3.003 3.368 3.627 3.828 3.991 4.129 4.247 4.351 4.443 4.526 4.602 4.671 4.734 4.794 4.849 4.900 4.949 4.994 35 2.389 3.000 3.364 3.623 3.823 3.986 4.123 4.241 4.344 4.436 4.519 4.594 4.663 4.727 4.786 4.841 4.892 4.940 4.986 36 2.388 2.998 3.361 3.619 3.819 3.981 4.117 4.235 4.338 4.430 4.512 4.588 4.656 4.720 4.778 4.833 4.884 4.932 4.978 37 2.386 2.995 3.357 3.615 3.814 3.976 4.112 4.230 4.332 4.424 4.506 4.581 4.650 4.713 4.771 4.826 4.877 4.925 4.970 38 2.384 2.992 3.354 3.611 3.810 3.972 4.107 4.224 4.327 4.418 4.500 4.575 4.643 4.706 4.765 4.819 4.870 4.918 4.963 39 2.383 2.990 3.351 3.608 3.806 3.967 4.103 4.220 4.322 4.413 4.495 4.569 4.637 4.700 4.758 4.812 4.863 4.911 4.956 40 2.381 2.988 3.348 3.605 3.802 3.963 4.099 4.215 4.317 4.408 4.490 4.564 4.632 4.694 4.752 4.806 4.857 4.904 4.949 ------------------------------------------------------------------------------------------------------------------------------------------ 48 2.372 2.973 3.330 3.583 3.778 3.937 4.070 4.185 4.285 4.375 4.455 4.528 4.595 4.656 4.713 4.766 4.816 4.863 4.907 60 2.363 2.959 3.312 3.562 3.755 3.911 4.042 4.155 4.254 4.342 4.421 4.493 4.558 4.619 4.675 4.727 4.775 4.821 4.864 80 2.353 2.945 3.294 3.541 3.731 3.885 4.014 4.125 4.223 4.309 4.387 4.457 4.521 4.581 4.636 4.687 4.735 4.780 4.822 120 2.344 2.930 3.276 3.520 3.707 3.859 3.986 4.096 4.191 4.276 4.353 4.422 4.485 4.543 4.597 4.647 4.694 4.738 4.779 240 2.335 2.916 3.258 3.499 3.684 3.834 3.959 4.066 4.160 4.244 4.319 4.386 4.448 4.505 4.558 4.607 4.653 4.696 4.737 Inf 2.326 2.902 3.240 3.478 3.661 3.808 3.931 4.037 4.129 4.211 4.285 4.351 4.412 4.468 4.519 4.568 4.612 4.654 4.694  Pro Tukeyovu metodu (přednáška č.9) odpovídá značení:   );,(,1  dfkqrnrq  The Studentized range upper quantiles q(k, df; 0.05) ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 1 17.969 26.976 32.819 37.082 40.408 43.119 45.397 47.357 49.071 50.592 51.957 53.194 54.323 55.361 56.320 57.212 58.044 58.824 59.558 2 6.085 8.331 9.798 10.881 11.734 12.435 13.027 13.539 13.988 14.389 14.749 15.076 15.375 15.650 15.905 16.143 16.365 16.573 16.769 3 4.501 5.910 6.825 7.502 8.037 8.478 8.852 9.177 9.462 9.717 9.946 10.155 10.346 10.522 10.686 10.838 10.980 11.114 11.240 4 3.926 5.040 5.757 6.287 6.706 7.053 7.347 7.602 7.826 8.027 8.208 8.373 8.524 8.664 8.793 8.914 9.027 9.133 9.233 5 3.635 4.602 5.218 5.673 6.033 6.330 6.582 6.801 6.995 7.167 7.323 7.466 7.596 7.716 7.828 7.932 8.030 8.122 8.208 6 3.460 4.339 4.896 5.305 5.628 5.895 6.122 6.319 6.493 6.649 6.789 6.917 7.034 7.143 7.244 7.338 7.426 7.508 7.586 7 3.344 4.165 4.681 5.060 5.359 5.606 5.815 5.997 6.158 6.302 6.431 6.550 6.658 6.759 6.852 6.939 7.020 7.097 7.169 8 3.261 4.041 4.529 4.886 5.167 5.399 5.596 5.767 5.918 6.053 6.175 6.287 6.389 6.483 6.571 6.653 6.729 6.801 6.869 9 3.199 3.948 4.415 4.755 5.024 5.244 5.432 5.595 5.738 5.867 5.983 6.089 6.186 6.276 6.359 6.437 6.510 6.579 6.643 10 3.151 3.877 4.327 4.654 4.912 5.124 5.304 5.460 5.598 5.722 5.833 5.935 6.028 6.114 6.194 6.269 6.339 6.405 6.467 ------------------------------------------------------------------------------------------------------------------------------------------ 11 3.113 3.820 4.256 4.574 4.823 5.028 5.202 5.353 5.486 5.605 5.713 5.811 5.901 5.984 6.062 6.134 6.202 6.265 6.325 12 3.081 3.773 4.199 4.508 4.750 4.950 5.119 5.265 5.395 5.510 5.615 5.710 5.797 5.878 5.953 6.023 6.089 6.151 6.209 13 3.055 3.734 4.151 4.453 4.690 4.884 5.049 5.192 5.318 5.431 5.533 5.625 5.711 5.789 5.862 5.931 5.995 6.055 6.112 14 3.033 3.701 4.111 4.407 4.639 4.829 4.990 5.130 5.253 5.364 5.463 5.554 5.637 5.714 5.785 5.852 5.915 5.973 6.029 15 3.014 3.673 4.076 4.367 4.595 4.782 4.940 5.077 5.198 5.306 5.403 5.492 5.574 5.649 5.719 5.785 5.846 5.904 5.958 16 2.998 3.649 4.046 4.333 4.557 4.741 4.896 5.031 5.150 5.256 5.352 5.439 5.519 5.593 5.662 5.726 5.786 5.843 5.896 17 2.984 3.628 4.020 4.303 4.524 4.705 4.858 4.991 5.108 5.212 5.306 5.392 5.471 5.544 5.612 5.675 5.734 5.790 5.842 18 2.971 3.609 3.997 4.276 4.494 4.673 4.824 4.955 5.071 5.173 5.266 5.351 5.429 5.501 5.567 5.629 5.688 5.743 5.794 19 2.960 3.593 3.977 4.253 4.468 4.645 4.794 4.924 5.037 5.139 5.231 5.314 5.391 5.462 5.528 5.589 5.647 5.701 5.752 20 2.950 3.578 3.958 4.232 4.445 4.620 4.768 4.895 5.008 5.108 5.199 5.282 5.357 5.427 5.492 5.553 5.610 5.663 5.714 ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 21 2.941 3.565 3.942 4.213 4.424 4.597 4.743 4.870 4.981 5.081 5.170 5.252 5.327 5.396 5.460 5.520 5.576 5.629 5.679 22 2.933 3.553 3.927 4.196 4.405 4.577 4.722 4.847 4.957 5.056 5.144 5.225 5.299 5.368 5.431 5.491 5.546 5.599 5.648 23 2.926 3.542 3.914 4.180 4.388 4.558 4.702 4.826 4.935 5.033 5.121 5.201 5.274 5.342 5.405 5.464 5.519 5.571 5.620 24 2.919 3.532 3.901 4.166 4.373 4.541 4.684 4.807 4.915 5.012 5.099 5.179 5.251 5.319 5.381 5.439 5.494 5.545 5.594 25 2.913 3.523 3.890 4.153 4.358 4.526 4.667 4.789 4.897 4.993 5.079 5.158 5.230 5.297 5.359 5.417 5.471 5.522 5.570 26 2.907 3.514 3.880 4.141 4.345 4.511 4.652 4.773 4.880 4.975 5.061 5.139 5.211 5.277 5.339 5.396 5.450 5.500 5.548 27 2.902 3.506 3.870 4.130 4.333 4.498 4.638 4.758 4.864 4.959 5.044 5.122 5.193 5.259 5.320 5.377 5.430 5.480 5.528 28 2.897 3.499 3.861 4.120 4.322 4.486 4.625 4.745 4.850 4.944 5.029 5.106 5.177 5.242 5.302 5.359 5.412 5.462 5.509 29 2.892 3.493 3.853 4.111 4.311 4.475 4.613 4.732 4.837 4.930 5.014 5.091 5.161 5.226 5.286 5.342 5.395 5.445 5.491 30 2.888 3.486 3.845 4.102 4.301 4.464 4.601 4.720 4.824 4.917 5.001 5.077 5.147 5.211 5.271 5.327 5.379 5.429 5.475 ------------------------------------------------------------------------------------------------------------------------------------------ 31 2.884 3.481 3.838 4.094 4.292 4.454 4.591 4.709 4.812 4.905 4.988 5.064 5.134 5.198 5.257 5.313 5.365 5.414 5.460 32 2.881 3.475 3.832 4.086 4.284 4.445 4.581 4.698 4.802 4.894 4.976 5.052 5.121 5.185 5.244 5.299 5.351 5.400 5.445 33 2.877 3.470 3.825 4.079 4.276 4.436 4.572 4.689 4.791 4.883 4.965 5.040 5.109 5.173 5.232 5.287 5.338 5.386 5.432 34 2.874 3.465 3.820 4.072 4.268 4.428 4.563 4.680 4.782 4.873 4.955 5.030 5.098 5.161 5.220 5.275 5.326 5.374 5.420 35 2.871 3.461 3.814 4.066 4.261 4.421 4.555 4.671 4.773 4.863 4.945 5.020 5.088 5.151 5.209 5.264 5.315 5.362 5.408 36 2.868 3.457 3.809 4.060 4.255 4.414 4.547 4.663 4.764 4.855 4.936 5.010 5.078 5.141 5.199 5.253 5.304 5.352 5.397 37 2.865 3.453 3.804 4.054 4.249 4.407 4.540 4.655 4.756 4.846 4.927 5.001 5.069 5.131 5.189 5.243 5.294 5.341 5.386 38 2.863 3.449 3.799 4.049 4.243 4.400 4.533 4.648 4.749 4.838 4.919 4.993 5.060 5.122 5.180 5.234 5.284 5.331 5.376 39 2.861 3.445 3.795 4.044 4.237 4.394 4.527 4.641 4.741 4.831 4.911 4.985 5.052 5.114 5.171 5.225 5.275 5.322 5.367 40 2.858 3.442 3.791 4.039 4.232 4.388 4.521 4.634 4.735 4.824 4.904 4.977 5.044 5.106 5.163 5.216 5.266 5.313 5.358 ------------------------------------------------------------------------------------------------------------------------------------------ 48 2.843 3.420 3.764 4.008 4.197 4.351 4.481 4.592 4.690 4.777 4.856 4.927 4.993 5.053 5.109 5.161 5.210 5.256 5.299 60 2.829 3.399 3.737 3.977 4.163 4.314 4.441 4.550 4.646 4.732 4.808 4.878 4.942 5.001 5.056 5.107 5.154 5.199 5.241 80 2.814 3.377 3.711 3.947 4.129 4.277 4.402 4.509 4.603 4.686 4.761 4.829 4.892 4.949 5.003 5.052 5.099 5.142 5.183 120 2.800 3.356 3.685 3.917 4.096 4.241 4.363 4.468 4.560 4.641 4.714 4.781 4.842 4.898 4.950 4.998 5.043 5.086 5.126 240 2.786 3.335 3.659 3.887 4.063 4.205 4.324 4.427 4.517 4.596 4.668 4.733 4.792 4.847 4.897 4.944 4.988 5.030 5.069 Inf 2.772 3.314 3.633 3.858 4.030 4.170 4.286 4.387 4.474 4.552 4.622 4.685 4.743 4.796 4.845 4.891 4.934 4.974 5.012  Pro Tukeyovu metodu (přednáška č.9) odpovídá značení:   );,(,1  dfkqrnrq  The Studentized range upper quantiles q(k, df; 0.01) ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 1 90.024 135.04 164.25 185.57 202.21 215.77 227.17 236.97 245.54 253.15 259.98 266.16 271.81 277.00 281.80 286.26 290.43 294.33 297.99 2 14.036 19.019 22.294 24.717 26.629 28.201 29.530 30.679 31.689 32.589 33.398 34.134 34.806 35.426 36.000 36.534 37.034 37.502 37.943 3 8.260 10.619 12.170 13.324 14.241 14.998 15.641 16.199 16.691 17.130 17.526 17.887 18.217 18.522 18.805 19.068 19.315 19.546 19.765 4 6.511 8.120 9.173 9.958 10.583 11.101 11.542 11.925 12.264 12.567 12.840 13.090 13.318 13.530 13.726 13.909 14.081 14.242 14.394 5 5.702 6.976 7.804 8.421 8.913 9.321 9.669 9.971 10.239 10.479 10.696 10.894 11.076 11.244 11.400 11.545 11.682 11.811 11.932 6 5.243 6.331 7.033 7.556 7.972 8.318 8.612 8.869 9.097 9.300 9.485 9.653 9.808 9.951 10.084 10.208 10.325 10.434 10.538 7 4.949 5.919 6.542 7.005 7.373 7.678 7.939 8.166 8.367 8.548 8.711 8.860 8.997 9.124 9.242 9.353 9.456 9.553 9.645 8 4.745 5.635 6.204 6.625 6.959 7.237 7.474 7.680 7.863 8.027 8.176 8.311 8.436 8.552 8.659 8.760 8.854 8.943 9.027 9 4.596 5.428 5.957 6.347 6.657 6.915 7.134 7.325 7.494 7.646 7.784 7.910 8.025 8.132 8.232 8.325 8.412 8.495 8.573 10 4.482 5.270 5.769 6.136 6.428 6.669 6.875 7.054 7.213 7.356 7.485 7.603 7.712 7.812 7.906 7.993 8.075 8.153 8.226 ------------------------------------------------------------------------------------------------------------------------------------------ 11 4.392 5.146 5.621 5.970 6.247 6.476 6.671 6.841 6.992 7.127 7.250 7.362 7.464 7.560 7.648 7.731 7.809 7.883 7.952 12 4.320 5.046 5.502 5.836 6.101 6.320 6.507 6.670 6.814 6.943 7.060 7.166 7.265 7.356 7.441 7.520 7.594 7.664 7.730 13 4.260 4.964 5.404 5.726 5.981 6.192 6.372 6.528 6.666 6.791 6.903 7.006 7.100 7.188 7.269 7.345 7.417 7.484 7.548 14 4.210 4.895 5.322 5.634 5.881 6.085 6.258 6.409 6.543 6.663 6.772 6.871 6.962 7.047 7.125 7.199 7.268 7.333 7.394 15 4.167 4.836 5.252 5.556 5.796 5.994 6.162 6.309 6.438 6.555 6.660 6.756 6.845 6.927 7.003 7.074 7.141 7.204 7.264 16 4.131 4.786 5.192 5.489 5.722 5.915 6.079 6.222 6.348 6.461 6.564 6.658 6.744 6.823 6.897 6.967 7.032 7.093 7.151 17 4.099 4.742 5.140 5.430 5.659 5.847 6.007 6.147 6.270 6.380 6.480 6.572 6.656 6.733 6.806 6.873 6.937 6.997 7.053 18 4.071 4.703 5.094 5.379 5.603 5.787 5.944 6.081 6.201 6.309 6.407 6.496 6.579 6.655 6.725 6.791 6.854 6.912 6.967 19 4.046 4.669 5.054 5.334 5.553 5.735 5.889 6.022 6.141 6.246 6.342 6.430 6.510 6.585 6.654 6.719 6.780 6.837 6.891 20 4.024 4.639 5.018 5.293 5.510 5.688 5.839 5.970 6.086 6.190 6.285 6.370 6.449 6.523 6.591 6.654 6.714 6.770 6.823 ------------------------------------------------------------------------------------------------------------------------------------------ df k-> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ------------------------------------------------------------------------------------------------------------------------------------------ 21 4.004 4.612 4.986 5.257 5.470 5.646 5.794 5.924 6.038 6.140 6.233 6.317 6.395 6.467 6.534 6.596 6.655 6.710 6.762 22 3.986 4.588 4.957 5.225 5.435 5.608 5.754 5.882 5.994 6.095 6.186 6.269 6.346 6.417 6.482 6.544 6.602 6.656 6.707 23 3.970 4.566 4.931 5.195 5.403 5.573 5.718 5.844 5.955 6.054 6.144 6.226 6.301 6.371 6.436 6.497 6.553 6.607 6.658 24 3.955 4.546 4.907 5.168 5.373 5.542 5.685 5.809 5.919 6.017 6.105 6.186 6.261 6.330 6.394 6.453 6.510 6.562 6.612 25 3.942 4.527 4.885 5.144 5.347 5.513 5.655 5.778 5.886 5.983 6.070 6.150 6.224 6.292 6.355 6.414 6.469 6.522 6.571 26 3.930 4.510 4.865 5.121 5.322 5.487 5.627 5.749 5.856 5.951 6.038 6.117 6.190 6.257 6.319 6.378 6.432 6.484 6.533 27 3.918 4.495 4.847 5.101 5.300 5.463 5.602 5.722 5.828 5.923 6.008 6.087 6.158 6.225 6.287 6.344 6.399 6.450 6.498 28 3.908 4.481 4.830 5.082 5.279 5.441 5.578 5.697 5.802 5.896 5.981 6.058 6.129 6.195 6.256 6.314 6.367 6.418 6.465 29 3.898 4.467 4.814 5.064 5.260 5.420 5.556 5.674 5.778 5.871 5.955 6.032 6.103 6.168 6.228 6.285 6.338 6.388 6.435 30 3.889 4.455 4.799 5.048 5.242 5.401 5.536 5.653 5.756 5.848 5.932 6.008 6.078 6.142 6.202 6.258 6.311 6.361 6.407 ------------------------------------------------------------------------------------------------------------------------------------------ 31 3.881 4.443 4.786 5.032 5.225 5.383 5.517 5.633 5.736 5.827 5.910 5.985 6.055 6.119 6.178 6.234 6.286 6.335 6.381 32 3.873 4.433 4.773 5.018 5.210 5.367 5.500 5.615 5.716 5.807 5.889 5.964 6.033 6.096 6.155 6.211 6.262 6.311 6.357 33 3.865 4.423 4.761 5.005 5.195 5.351 5.483 5.598 5.698 5.789 5.870 5.944 6.013 6.076 6.134 6.189 6.240 6.289 6.334 34 3.859 4.413 4.750 4.992 5.181 5.336 5.468 5.581 5.682 5.771 5.852 5.926 5.994 6.056 6.114 6.169 6.220 6.268 6.313 35 3.852 4.404 4.739 4.980 5.169 5.323 5.453 5.566 5.666 5.755 5.835 5.908 5.976 6.038 6.096 6.150 6.200 6.248 6.293 36 3.846 4.396 4.729 4.969 5.156 5.310 5.439 5.552 5.651 5.739 5.819 5.892 5.959 6.021 6.078 6.132 6.182 6.229 6.274 37 3.840 4.388 4.720 4.959 5.145 5.298 5.427 5.538 5.637 5.725 5.804 5.876 5.943 6.004 6.061 6.115 6.165 6.212 6.256 38 3.835 4.381 4.711 4.949 5.134 5.286 5.414 5.526 5.623 5.711 5.790 5.862 5.928 5.989 6.046 6.099 6.148 6.195 6.239 39 3.830 4.374 4.703 4.940 5.124 5.275 5.403 5.513 5.611 5.698 5.776 5.848 5.914 5.974 6.031 6.084 6.133 6.179 6.223 40 3.825 4.367 4.695 4.931 5.114 5.265 5.392 5.502 5.599 5.685 5.764 5.835 5.900 5.961 6.017 6.069 6.118 6.165 6.208 ------------------------------------------------------------------------------------------------------------------------------------------ 48 3.793 4.324 4.644 4.874 5.052 5.198 5.322 5.428 5.522 5.606 5.681 5.750 5.814 5.872 5.926 5.977 6.024 6.069 6.111 60 3.762 4.282 4.594 4.818 4.991 5.133 5.253 5.356 5.447 5.528 5.601 5.667 5.728 5.784 5.837 5.886 5.931 5.974 6.015 80 3.732 4.241 4.545 4.763 4.931 5.069 5.185 5.284 5.372 5.451 5.521 5.585 5.644 5.698 5.749 5.796 5.840 5.881 5.920 120 3.702 4.200 4.497 4.709 4.872 5.005 5.118 5.214 5.299 5.375 5.443 5.505 5.561 5.614 5.662 5.708 5.750 5.790 5.827 240 3.672 4.160 4.450 4.655 4.814 4.943 5.052 5.145 5.227 5.300 5.366 5.426 5.480 5.530 5.577 5.621 5.661 5.699 5.735 Inf 3.643 4.120 4.403 4.603 4.757 4.882 4.987 5.078 5.157 5.227 5.290 5.348 5.400 5.448 5.493 5.535 5.574 5.611 5.645 ------------------------------------------------------------------------------------------------------------------------------------------  Pro Tukeyovu metodu (přednáška č.9) odpovídá značení:   );,(,1  dfkqrnrq   Zdroj: http://cse.niaes.affrc.go.jp/miwa/probcalc/s-range/srng_tbl.html Kritické hodnoty Dn(α) Kolmogorovova-Smirnovova testu n= 4,…,40, α=0,01, α=0,05, α=0,10, α=0,15 a α=0,20. alfa n 0,20 0,15 0,10 0,05 0,01 4 0,4927 0,5221 0,5652 0,6239 0,7342 5 0,4470 0,4754 0,5095 0,5633 0,6685 6 0,4104 0,4334 0,4680 0,5193 0,6166 7 0,3815 0,4043 0,4361 0,4834 0,5758 8 0,3583 0,3801 0,4096 0,4543 0,5418 9 0,3391 0,3591 0,3875 0,4300 0,5133 10 0,3226 0,3416 0,3687 0,4093 0,4889 11 0,3083 0,3266 0,3524 0,3912 0,4677 12 0,2958 0,3134 0,3382 0,3754 0,4491 13 0,2847 0,3016 0,3255 0,3614 0,4325 14 0,2748 0,2911 0,3142 0,3489 0,4176 15 0,2659 0,2816 0,3040 0,3376 0,4042 16 0,2578 0,2731 0,2947 0,3273 0,3920 17 0,2504 0,2652 0,2863 0,3180 0,3809 18 0,2436 0,2580 0,2785 0,3094 0,3706 19 0,2374 0,2514 0,2714 0,3014 0,3612 20 0,2316 0,2452 0,2647 0,2941 0,3524 21 0,2263 0,2403 0,2587 0,2873 0,3443 22 0,2213 0,2350 0,2529 0,2809 0,3367 23 0,2166 0,2300 0,2475 0,2749 0,3296 24 0,2122 0,2253 0,2425 0,2693 0,3229 25 0,2080 0,2209 0,2377 0,2641 0,3166 26 0,2041 0,2167 0,2333 0,2591 0,3106 27 0,2004 0,2128 0,2290 0,2544 0,3050 28 0,1969 0,2090 0,2250 0,2500 0,2997 29 0,1936 0,2055 0,2212 0,2457 0,2947 30 0,1904 0,2022 0,2176 0,2417 0,2899 31 0,1874 0,1990 0,2142 0,2379 0,2853 32 0,1845 0,1959 0,2109 0,2343 0,2809 33 0,1818 0,1930 0,2078 0,2308 0,2768 34 0,1792 0,1902 0,2048 0,2275 0,2728 35 0,1767 0,1875 0,2019 0,2243 0,2690 36 0,1743 0,1850 0,1991 0,2212 0,2653 37 0,1719 0,1825 0,1965 0,2183 0,2618 38 0,1697 0,1802 0,1940 0,2155 0,2584 39 0,1676 0,1779 0,1915 0,2127 0,2552 40 0,1655 0,1757 0,1892 0,2101 0,2521 Pro n>40 lze Dn(α) aproximovat pomocí  2 ln n2 1 Zdroj: kstest v MATLABu. Modifikované kritické hodnoty Dn * (α) Kolmogorovova-Smirnovova testu n= 4,…,40, α=0,01, α=0,05, α=0,10, α=0,15 a α=0,20. alfa n 0,20 0,15 0,10 0,05 0,01 4 0,3028 0,3213 0,3453 0,3754 0,4131 5 0,2893 0,3026 0,3189 0,3431 0,3966 6 0,2688 0,2810 0,2973 0,3236 0,3703 7 0,2523 0,2643 0,2802 0,3041 0,3506 8 0,2387 0,2502 0,2651 0,2880 0,3326 9 0,2271 0,2379 0,2520 0,2740 0,3171 10 0,2171 0,2274 0,2410 0,2620 0,3034 11 0,2082 0,2181 0,2312 0,2515 0,2915 12 0,2002 0,2098 0,2224 0,2418 0,2808 13 0,1932 0,2025 0,2145 0,2333 0,2706 14 0,1868 0,1958 0,2075 0,2257 0,2619 15 0,1811 0,1898 0,2012 0,2189 0,2539 16 0,1759 0,1843 0,1953 0,2126 0,2472 17 0,1711 0,1792 0,1900 0,2068 0,2403 18 0,1666 0,1746 0,1850 0,2013 0,2341 19 0,1625 0,1703 0,1806 0,1965 0,2285 20 0,1587 0,1663 0,1763 0,1920 0,2232 21 0,1551 0,1626 0,1723 0,1877 0,2183 22 0,1518 0,1591 0,1687 0,1837 0,2137 23 0,1487 0,1558 0,1652 0,1799 0,2093 24 0,1458 0,1528 0,1619 0,1764 0,2052 25 0,1430 0,1499 0,1589 0,1730 0,2014 26 0,1404 0,1471 0,1560 0,1699 0,1977 27 0,1379 0,1445 0,1532 0,1669 0,1943 28 0,1356 0,1421 0,1506 0,1641 0,1910 29 0,1334 0,1398 0,1482 0,1614 0,1879 30 0,1312 0,1375 0,1458 0,1588 0,1849 31 0,1292 0,1354 0,1436 0,1564 0,1821 32 0,1273 0,1334 0,1414 0,1541 0,1794 33 0,1255 0,1315 0,1394 0,1518 0,1768 34 0,1237 0,1296 0,1374 0,1497 0,1743 35 0,1220 0,1279 0,1356 0,1476 0,1720 36 0,1204 0,1262 0,1338 0,1457 0,1697 37 0,1188 0,1245 0,1320 0,1438 0,1675 38 0,1173 0,1230 0,1304 0,1420 0,1654 39 0,1159 0,1214 0,1288 0,1402 0,1634 40 0,1145 0,1200 0,1272 0,1385 0,1614 >40 0,741 fN 0,775 fN 0,819 fN 0,895 fN 1,035 fN Pro n>40 lze Dn * (α) aproximovat pomocí posledního řádku tabulky, kde 01,0 83,0    n n fN . Zdroj: http://www.utdallas.edu/~herve/Abdi-Lillie2007-pretty.pdf +lillietest v MATLABu. Koeficienty  n ia pro Shapiro – Wilkův test: n 2 3 4 5 6 7 8 9 10 i  1 0.7071 0.7071 0.6872 0.6646 0.6431 0.6233 0.6052 0.5888 0.5739 2 0.0000 0.1677 0.2413 0.2806 0.3031 0.3164 0.3244 0.3291 3 0.0000 0.0875 0.1401 0.1743 0.1976 0.2141 4 0.0000 0.0561 0.0947 0.1224 5 0.0000 0.0399 n 11 12 13 14 15 16 17 18 19 20 i  1 0.5601 0.5475 0.5359 0.5251 0.5150 0.5056 0.4963 0.4886 0.4808 0.4734 2 0.3315 0.3325 0.3325 0.3318 0.3306 0.3290 0.3273 0.3253 0.3232 0.3211 3 0.2260 0.2347 0.2412 0.2460 0.2495 0.2521 0.2540 0.2553 0.2561 0.2565 4 0.1429 0.1586 0.1707 0.1802 0.1878 0.1939 0.1988 0.2027 0.2059 0.2085 5 0.0695 0.0922 0.1099 0.1240 0.1353 0.1447 0.1524 0.1587 0.1641 0.1686 6 0.0000 0.0303 0.0539 0.0727 0.0880 0.1005 0.1109 0.1197 0.1271 0.1334 7 0.0000 0.0240 0.0433 0.0593 0.0725 0.0837 0.0932 0.1013 8 0.0000 0.0196 0.0359 0.0496 0.0612 0.0711 9 0.0000 0.0163 0.0303 0.0422 10 0.0000 0.0140 n 21 22 23 24 25 26 27 28 29 30 i  1 0.4643 0.4590 0.4542 0.4493 0.4450 0.4407 0.4366 0.4328 0.4291 0.4254 2 0.3185 0.3156 0.3126 0.3098 0.3069 0.3043 0.3018 0.2992 0.2968 0.2944 3 0.2578 0.2571 0.2563 0.2554 0.2543 0.2533 0.2522 0.2510 0.2499 0.2487 4 0.2119 0.2131 0.2139 0.2145 0.2148 0.2151 0.2152 0.2151 0.2150 0.2148 5 0.1736 0.1764 0.1787 0.1807 0.1822 0.1836 0.1848 0.1857 0.1064 0.1870 6 0.1399 0.1443 0.1480 0.1512 0.1539 0.1563 0.1584 0.1601 0.1616 0.1630 7 0.1092 0.1150 0.1201 0.1245 0.1283 0.1316 0.1346 0.1372 0.1395 0.1415 8 0.0804 0.0878 0.0941 0.0997 0.1046 0.1089 0.1128 0.1162 0.1192 0.1219 9 0.0530 0.0618 0.0696 0.0764 0.0823 0.0876 0.0923 0.0965 0.1002 0.1036 10 0.0263 0.0368 0.0459 0.0539 0.0610 0.0672 0.0728 0.0778 0.0822 0.0862 11 0.0000 0.0122 0.0228 0.0321 0.0403 0.0476 0.0540 0.0598 0.0650 0.0697 12 0.0000 0.0107 0.0200 0.0284 0.0358 0.0424 0.0483 0.0537 13 0.0000 0.0094 0.0178 0.0253 0.0320 0.0381 14 0.0000 0.0084 0.0159 0.0227 15 0.0000 0.0076 Zdroj: http://www.kmt.zcu.cz/person/Kohout/info_soubory/letnisem/ruzne/SWkoeficienty.pdf http://www.santemaghreb.com/algerie/stat/stat_10.htm#28 Kritické hodnoty pro Shapiro – Wilkův test: Zdroj: http://www.kmt.zcu.cz/person/Kohout/info_soubory/letnisem/ruzne/SWkrithodnoty.pdf Kritické hodnoty znaménkového testu pro n = 6, 7, .., 20, α = 0,05 a α = 0,01 n α = 0,05 α = 0,01 k1 k2 k1 k2 6 0 6 - - 7 0 7 - - 8 0 8 0 8 9 1 8 0 9 10 1 9 0 10 11 1 10 0 11 12 2 10 1 11 13 2 11 1 12 14 2 12 1 13 15 3 12 2 13 16 3 13 2 14 17 4 13 2 15 18 4 14 3 15 19 4 15 3 16 20 5 15 3 17 Zdroj: Anděl, J.: Matematická statistika. (Tabulka XVIII.8). Kritické hodnoty jednovýběrového Wilcoxonova testu pro n = 6, 7, .., 30, α = 0,05 a α = 0,01 n α = 0,05 α = 0,01 krit. hodnota krit. hodnota 6 0 - 7 2 - 8 3 0 9 5 1 10 8 3 11 10 5 12 13 7 13 17 9 14 21 12 15 25 15 16 29 19 17 34 23 18 40 27 19 46 32 20 52 37 21 58 42 22 65 48 23 73 54 24 81 61 25 89 68 26 98 75 27 107 83 28 116 91 29 126 100 30 137 109 Zdroj: Anděl, J.: Matematická statistika. (Tabulka XVIII.9). Kritické hodnoty dvouvýběrového Wilcoxonova testu pro m = 1, 2, .., 30, n = 1, 2, …, 30, α = 0,05 n m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 - 2 - - 3 - - - 4 - - - 0 5 - - 0 1 2 6 - - 1 2 3 5 7 - - 1 3 5 6 8 8 - 0 2 4 6 8 10 13 9 - 0 2 4 7 10 12 15 17 10 - 0 3 5 8 11 14 17 20 23 11 -- 0 3 6 9 13 16 19 23 26 30 12 - 1 4 7 11 14 18 22 26 29 33 37 13 - 1 4 8 12 16 20 24 28 33 37 41 45 14 - 1 5 9 13 17 22 26 31 36 40 45 50 55 15 - 1 5 10 14 19 24 29 34 39 44 49 54 59 64 16 - 1 6 11 15 21 26 31 37 42 47 53 59 64 70 75 17 - 2 6 11 17 22 28 34 39 45 51 57 63 69 75 81 87 18 - 2 7 12 18 24 30 36 42 48 55 61 67 74 80 86 93 99 19 - 2 7 13 19 25 32 38 45 52 58 65 72 78 85 92 99 106 113 20 - 2 8 14 20 27 34 41 48 55 62 69 76 83 90 98 105 112 119 127 21 - 2 8 15 22 29 36 43 50 58 65 73 80 88 96 103 111 119 126 134 22 - 3 9 16 23 30 38 45 53 61 69 77 85 93 101 109 117 125 133 141 23 - 3 9 17 24 32 40 48 56 64 73 81 89 98 106 115 123 132 140 149 24 - 3 10 17 25 33 42 50 59 67 76 85 94 102 111 120 129 138 147 156 25 - 3 10 18 27 35 44 53 62 71 80 89 98 107 117 126 135 145 154 161 26 - 4 11 19 28 37 46 55 64 74 83 93 102 112 122 132 141 151 161 171 27 - 4 11 20 29 38 48 57 67 77 87 97 107 117 127 137 147 158 168 178 28 - 4 12 21 30 40 50 60 70 80 90 101 111 122 132 143 154 164 175 186 29 - 4 13 22 32 42 52 62 73 83 94 105 116 127 138 149 160 171 182 193 30 - 5 13 23 33 43 54 65 76 87 98 109 120 131 143 154 166 177 189 200 Zdroj: Anděl, J.: Matematická statistika. (Tabulka XVIII.10a). Kritické hodnoty Neményiho metody, r = 3, 4, .., 10, n = 1, 2, …, 25, α = 0,05 r n 3 4 5 6 7 8 9 10 1 3,3 4,7 6,1 7,5 9,0 10,5 12,0 13,5 2 8,8 12,6 16,5 20,5 24,7 28,9 33,1 37,4 3 15,7 22,7 29,9 37,3 44,8 52,5 60,3 68,2 4 23,9 34,6 45,6 57,0 68,6 80,4 92,4 104,6 5 33,1 48,1 63,5 79,3 95,5 112,0 128,8 145,8 6 43,3 62,9 83,2 104,0 125,3 147,0 169,1 191,4 7 54,4 79,1 104,6 130,8 157,6 184,9 212,8 240,9 8 66,3 96,4 127,6 159,6 192,4 225,7 259,7 294,1 9 75,9 114,8 152,0 190,2 229,3 269,1 309,6 350,6 10 92,3 134,3 177,8 222,6 268,4 315,0 362,4 410,5 11 106,3 154,8 205,0 256,6 309,4 363,2 417,9 473,3 12 120,9 176,2 233,4 292,2 352,4 413,6 476,0 539,1 13 136,2 198,5 263,0 329,3 397,1 466,2 536,5 607,7 14 152,1 221,7 293,8 367,8 443,6 520,8 599,4 679,0 15 168,6 245,7 325,7 407,8 491,9 577,4 664,6 752,8 16 185,6 270,6 358,6 449,1 541,7 635,9 732,0 829,2 17 203,1 296,2 392,6 491,7 593,1 696,3 801,5 907,9 18 221,2 322,6 427,6 535,5 646,1 758,5 873,1 989,0 19 239,8 349,7 463,6 580,6 700,5 822,4 946,7 1072,4 20 258,8 377,6 500,5 626,9 756,4 888,1 1022,3 1158,1 21 278,4 406,1 538,4 674,4 813,7 955,4 1099,8 1245,9 22 298,4 435,3 577,2 723,0 872,3 1024,3 1179,1 1335,7 23 318,9 465,2 616,9 772,7 932,4 1094,8 1260,3 1427,7 24 339,8 495,8 657,4 823,5 993,7 1166,8 1343,2 1521,7 25 361,1 527,0 698,8 875,4 1056,3 1240,4 1427,9 1611,6 Zdroj: Blatná, Dagmar: Neparametrické metody. Tabulka T21/1. Kritické hodnoty pro Spearmanův koeficient pořadové korelace, n=5,..30, , α = 0,05 a , α = 0,01 alfa n 0,05 0,01 5 0,900 1,000 6 0,829 0,943 7 0,714 0,893 8 0,643 0,833 9 0,600 0,783 10 0,564 0,745 11 0,536 0,709 12 0,503 0,671 13 0,484 0,648 14 0,464 0,622 15 0,443 0,604 16 0,429 0,582 17 0,414 0,566 18 0,401 0,550 19 0,391 0,535 20 0,380 0,520 21 0,370 0,508 22 0,361 0,496 23 0,353 0,486 24 0,344 0,476 25 0,337 0,466 26 0,331 0,457 27 0,324 0,448 28 0,317 0,440 29 0,312 0,433 30 0,306 0,425 Adapted from Zar, J. H. (1972). Significance testing of the Spearman rank correlation. Journal of the American Statistical Association. 67, 578 – 580. Zdroj: http://www.ace.upm.edu.my/~bas/5950/Spearman%20Rho%20Table.pdf Pro n > 20 lze použít testovou statistiku 2 S S 0 r1 2nr T    , která se v případě platnosti nulové hypotézy asymptoticky řídí rozložením t(n-2). Pro n > 30 lze použít testovou statistiku 1nrs  . Platí-li H0, pak 1nrs  ≈ N(0, 1). alfa n 0,05 0,01 5 1,000 * 6 0,886 1,000 7 0,786 0,929 8 0,738 0,881 9 0,700 0,833 10 0,648 0,794 11 0,618 0,755 12 0,587 0,727 13 0,560 0,703 14 0,538 0,675 15 0,521 0,654 16 0,503 0,635 17 0,485 0,615 18 0,472 0,600 19 0,460 0,584 20 0,447 0,570 21 0,435 0,556 22 0,425 0,544 23 0,415 0,532 24 0,406 0,521 25 0,398 0,511 26 0,390 0,501 27 0,382 0,491 28 0,375 0,483 29 0,368 0,475 30 0,362 0,467