SOURCEBOOK

Intro | Statistical Tables

Tukey's HSD

Values of Tukey's HSD Statistic

Tabled Values are HSD Statistics for the Given Probabilities and Degrees of Freedom

dfEFFECT = 1       dfEFFECT = 2       dfEFFECT = 3       dfEFFECT = 4    
dfERROR p = .05 p = .01   dfERROR p = .05 p = .01   dfERROR p = .05 p = .01   dfERROR p = .05 p = .01
2 4.303 9.925   2 5.891 13.449   2 6.928 15.764   2 7.694 17.478
3 3.182 5.841   3 4.179 7.508   3 4.826 8.605   3 5.304 9.422
4 2.776 4.604   4 3.564 5.742   4 4.071 6.486   4 4.446 7.042
5 2.571 4.032   5 3.254 4.933   5 3.690 5.518   5 4.012 5.955
6 2.447 3.707   6 3.068 4.476   6 3.462 4.973   6 3.751 5.343
7 2.365 3.499   7 2.945 4.186   7 3.310 4.626   7 3.578 4.953
8 2.306 3.355   8 2.857 3.985   8 3.202 4.387   8 3.455 4.684
9 2.262 3.250   9 2.792 3.838   9 3.122 4.212   9 3.363 4.488
10 2.228 3.169   10 2.741 3.727   10 3.059 4.079   10 3.291 4.339
11 2.201 3.106   11 2.701 3.639   11 3.010 3.974   11 3.234 4.222
12 2.179 3.055   12 2.668 3.568   12 2.969 3.890   12 3.187 4.127
13 2.160 3.012   13 2.640 3.510   13 2.935 3.821   13 3.149 4.049
14 2.145 2.977   14 2.617 3.461   14 2.907 3.763   14 3.116 3.984
15 2.131 2.947   15 2.597 3.420   15 2.882 3.714   15 3.088 3.929
16 2.120 2.921   16 2.580 3.384   16 2.861 3.671   16 3.064 3.881
17 2.110 2.898   17 2.565 3.353   17 2.843 3.634   17 3.042 3.840
18 2.101 2.878   18 2.552 3.326   18 2.826 3.602   18 3.024 3.803
19 2.093 2.861   19 2.540 3.302   19 2.812 3.574   19 3.007 3.771
20 2.086 2.845   20 2.530 3.280   20 2.799 3.548   20 2.992 3.743
21 2.080 2.831   21 2.521 3.261   21 2.787 3.526   21 2.979 3.717
22 2.074 2.819   22 2.512 3.244   22 2.777 3.505   22 2.967 3.694
23 2.069 2.807   23 2.504 3.228   23 2.767 3.487   23 2.956 3.674
24 2.064 2.797   24 2.497 3.214   24 2.759 3.470   24 2.946 3.655
25 2.060 2.787   25 2.491 3.201   25 2.751 3.454   25 2.937 3.637
26 2.056 2.779   26 2.485 3.189   26 2.743 3.440   26 2.928 3.621
27 2.052 2.771   27 2.479 3.178   27 2.737 3.427   27 2.921 3.607
28 2.048 2.763   28 2.474 3.168   28 2.730 3.415   28 2.913 3.593
29 2.045 2.756   29 2.470 3.159   29 2.725 3.404   29 2.907 3.581
30 2.042 2.750   30 2.465 3.150   30 2.719 3.394   30 2.901 3.569
35 2.030 2.724   35 2.447 3.114   35 2.697 3.351   35 2.875 3.522
40 2.021 2.704   40 2.434 3.088   40 2.680 3.320   40 2.856 3.487
45 2.014 2.690   45 2.424 3.068   45 2.668 3.296   45 2.841 3.460
50 2.009 2.678   50 2.415 3.052   50 2.658 3.277   50 2.830 3.438
55 2.004 2.668   55 2.409 3.039   55 2.649 3.262   55 2.820 3.421
60 2.000 2.660   60 2.403 3.028   60 2.643 3.249   60 2.812 3.407
70 1.994 2.648   70 2.395 3.011   70 2.632 3.229   70 2.800 3.384
80 1.990 2.639   80 2.388 2.999   80 2.624 3.214   80 2.791 3.368
90 1.987 2.632   90 2.383 2.989   90 2.618 3.203   90 2.784 3.355
100 1.984 2.626   100 2.379 2.981   100 2.613 3.193   100 2.778 3.345
120 1.980 2.617   120 2.373 2.970   120 2.605 3.180   120 2.770 3.329
240 1.970 2.596   240 2.358 2.941   240 2.587 3.146   240 2.749 3.292
∞ 1.960 2.576   ∞ 2.344 2.914   ∞ 2.569 3.113   ∞ 2.728 3.255

Values of Tukey's HSD Statistic

Tabled Values are HSD Statistics for the Given Probabilities and dfEFFECT = 1

dfERROR .90 .80 .70 .60 .50 .40 .30 .20 .10 .05 .04 .03 .02 .01 .001
2 .142 .289 .445 .617 .816 1.06 1.386 1.886 2.920 4.303 4.849 5.643 6.965 9.925 31.599
3 .137 .277 .424 .584 .765 .978 1.250 1.638 2.353 3.182 3.482 3.896 4.541 5.841 12.924
4 .134 .271 .414 .569 .741 .941 1.190 1.533 2.132 2.776 2.999 3.298 3.747 4.604 8.610
5 .132 .267 .408 .559 .727 .920 1.156 1.476 2.015 2.571 2.757 3.003 3.365 4.032 6.869
6 .131 .265 .404 .553 .718 .906 1.134 1.440 1.943 2.447 2.612 2.829 3.143 3.707 5.959
7 .130 .263 .402 .549 .711 .896 1.119 1.415 1.895 2.365 2.517 2.715 2.998 3.499 5.408
8 .130 .262 .399 .546 .706 .889 1.108 1.397 1.860 2.306 2.449 2.634 2.896 3.355 5.041
9 .129 .261 .398 .543 .703 .883 1.100 1.383 1.833 2.262 2.398 2.574 2.821 3.250 4.781
10 .129 .260 .397 .542 .700 .879 1.093 1.372 1.812 2.228 2.359 2.527 2.764 3.169 4.587
11 .129 .260 .396 .540 .697 .876 1.088 1.363 1.796 2.201 2.328 2.491 2.718 3.106 4.437
12 .128 .259 .395 .539 .695 .873 1.083 1.356 1.782 2.179 2.303 2.461 2.681 3.055 4.318
13 .128 .259 .394 .538 .694 .870 1.079 1.350 1.771 2.160 2.282 2.436 2.650 3.012 4.221
14 .128 .258 .393 .537 .692 .868 1.076 1.345 1.761 2.145 2.264 2.415 2.624 2.977 4.140
15 .128 .258 .393 .536 .691 .866 1.074 1.341 1.753 2.131 2.249 2.397 2.602 2.947 4.073
16 .128 .258 .392 .535 .690 .865 1.071 1.337 1.746 2.120 2.235 2.382 2.583 2.921 4.015
17 .128 .257 .392 .534 .689 .863 1.069 1.333 1.740 2.110 2.224 2.368 2.567 2.898 3.965
18 .127 .257 .392 .534 .688 .862 1.067 1.330 1.734 2.101 2.214 2.356 2.552 2.878 3.922
19 .127 .257 .391 .533 .688 .861 1.066 1.328 1.729 2.093 2.205 2.346 2.539 2.861 3.883
20 .127 .257 .391 .533 .687 .860 1.064 1.325 1.725 2.086 2.197 2.336 2.528 2.845 3.850
21 .127 .257 .391 .532 .686 .859 1.063 1.323 1.721 2.080 2.189 2.328 2.518 2.831 3.819
22 .127 .256 .390 .532 .686 .858 1.061 1.321 1.717 2.074 2.183 2.320 2.508 2.819 3.792
23 .127 .256 .390 .532 .685 .858 1.060 1.319 1.714 2.069 2.177 2.313 2.500 2.807 3.768
24 .127 .256 .390 .531 .685 .857 1.059 1.318 1.711 2.064 2.172 2.307 2.492 2.797 3.745
25 .127 .256 .390 .531 .684 .856 1.058 1.316 1.708 2.060 2.167 2.301 2.485 2.787 3.725
26 .127 .256 .390 .531 .684 .856 1.058 1.315 1.706 2.056 2.162 2.296 2.479 2.779 3.707
27 .127 .256 .389 .531 .684 .855 1.057 1.314 1.703 2.052 2.158 2.291 2.473 2.771 3.690
28 .127 .256 .389 .530 .683 .855 1.056 1.313 1.701 2.048 2.154 2.286 2.467 2.763 3.674
29 .127 .256 .389 .530 .683 .854 1.055 1.311 1.699 2.045 2.150 2.282 2.462 2.756 3.659
30 .127 .256 .389 .530 .683 .854 1.055 1.310 1.697 2.042 2.147 2.278 2.457 2.750 3.646
35 .127 .255 .388 .529 .682 .852 1.052 1.306 1.690 2.030 2.133 2.262 2.438 2.724 3.591
40 .126 .255 .388 .529 .681 .851 1.050 1.303 1.684 2.021 2.123 2.250 2.423 2.704 3.551
45 .126 .255 .388 .528 .680 .850 1.049 1.301 1.679 2.014 2.115 2.241 2.412 2.690 3.520
50 .126 .255 .388 .528 .679 .849 1.047 1.299 1.676 2.009 2.109 2.234 2.403 2.678 3.496
55 .126 .255 .387 .527 .679 .848 1.046 1.297 1.673 2.004 2.104 2.228 2.396 2.668 3.476
60 .126 .254 .387 .527 .679 .848 1.045 1.296 1.671 2.000 2.099 2.223 2.390 2.660 3.460
70 .126 .254 .387 .527 .678 .847 1.044 1.294 1.667 1.994 2.093 2.215 2.381 2.648 3.435
80 .126 .254 .387 .526 .678 .846 1.043 1.292 1.664 1.990 2.088 2.209 2.374 2.639 3.416
90 .126 .254 .387 .526 .677 .846 1.042 1.291 1.662 1.987 2.084 2.205 2.368 2.632 3.402
100 .126 .254 .386 .526 .677 .845 1.042 1.290 1.660 1.984 2.081 2.201 2.364 2.626 3.390
120 .126 .254 .386 .526 .677 .845 1.041 1.289 1.658 1.980 2.076 2.196 2.358 2.617 3.373
240 .126 .254 .386 .525 .676 .843 1.039 1.285 1.651 1.970 2.065 2.183 2.342 2.596 3.332
∞ .126 .253 .385 .524 .674 .842 1.036 1.282 1.645 1.960 2.054 2.170 2.326 2.576 3.291

Values of Tukey's HSD Statistic

Tabled Values are HSD Statistics for the Given Probabilities and dfEFFECT = 2

dfERROR .90 .80 .70 .60 .50 .40 .30 .20 .10 .05 .04 .03 .02 .01 .001
2 .449 .674 .883 1.10 1.35 1.65 2.063 2.701 4.054 5.891 6.621 7.685 9.461 13.45 42.765
3 .445 .661 .855 1.05 1.27 1.52 1.835 2.295 3.159 4.179 4.550 5.066 5.873 7.508 16.487
4 .443 .655 .842 1.03 1.23 1.45 1.735 2.124 2.811 3.564 3.826 4.180 4.715 5.742 10.595
5 .442 .651 .835 1.02 1.21 1.42 1.679 2.030 2.628 3.254 3.465 3.746 4.162 4.933 8.253
6 .441 .649 .830 1.01 1.19 1.40 1.643 1.972 2.516 3.068 3.251 3.492 3.842 4.476 7.042
7 .441 .647 .826 1.00 1.18 1.38 1.618 1.931 2.440 2.945 3.110 3.325 3.634 4.186 6.315
8 .440 .646 .823 .995 1.17 1.37 1.600 1.902 2.386 2.857 3.010 3.207 3.489 3.985 5.833
9 .440 .644 .821 .992 1.17 1.36 1.586 1.879 2.345 2.792 2.935 3.120 3.382 3.838 5.493
10 .440 .644 .820 .989 1.16 1.35 1.575 1.861 2.312 2.741 2.877 3.053 3.300 3.727 5.240
11 .439 .643 .818 .986 1.16 1.35 1.566 1.847 2.287 2.701 2.832 2.999 3.235 3.639 5.045
12 .439 .642 .817 .984 1.16 1.34 1.559 1.835 2.266 2.668 2.794 2.956 3.182 3.568 4.891
13 .439 .642 .816 .983 1.15 1.34 1.553 1.826 2.248 2.640 2.763 2.920 3.139 3.510 4.766
14 .439 .642 .815 .981 1.15 1.33 1.547 1.817 2.233 2.617 2.737 2.890 3.102 3.461 4.662
15 .439 .641 .815 .980 1.15 1.33 1.543 1.810 2.220 2.597 2.715 2.864 3.071 3.420 4.575
16 .439 .641 .814 .979 1.15 1.33 1.539 1.804 2.209 2.580 2.695 2.841 3.044 3.384 4.501
17 .439 .641 .813 .978 1.15 1.33 1.535 1.798 2.199 2.565 2.679 2.822 3.021 3.353 4.437
18 .439 .640 .813 .977 1.14 1.33 1.532 1.793 2.191 2.552 2.664 2.805 3.000 3.326 4.381
19 .438 .640 .813 .977 1.14 1.32 1.529 1.789 2.183 2.540 2.651 2.790 2.982 3.302 4.332
20 .438 .640 .812 .976 1.14 1.32 1.527 1.785 2.176 2.530 2.639 2.776 2.966 3.280 4.289
21 .438 .640 .812 .975 1.14 1.32 1.525 1.782 2.170 2.521 2.628 2.764 2.951 3.261 4.250
22 .438 .640 .811 .975 1.14 1.32 1.523 1.778 2.164 2.512 2.619 2.753 2.938 3.244 4.215
23 .438 .640 .811 .974 1.14 1.32 1.521 1.775 2.159 2.504 2.610 2.743 2.926 3.228 4.184
24 .438 .639 .811 .974 1.14 1.32 1.519 1.773 2.155 2.497 2.602 2.734 2.915 3.214 4.156
25 .438 .639 .811 .973 1.14 1.32 1.518 1.770 2.150 2.491 2.595 2.726 2.905 3.201 4.130
26 .438 .639 .810 .973 1.14 1.31 1.516 1.768 2.146 2.485 2.588 2.718 2.896 3.189 4.106
27 .438 .639 .810 .973 1.14 1.31 1.515 1.766 2.143 2.479 2.582 2.711 2.888 3.178 4.084
28 .438 .639 .810 .972 1.14 1.31 1.514 1.764 2.140 2.474 2.576 2.704 2.880 3.168 4.065
29 .438 .639 .810 .972 1.14 1.31 1.512 1.762 2.136 2.470 2.571 2.698 2.873 3.159 4.046
30 .438 .639 .810 .972 1.14 1.31 1.511 1.761 2.134 2.465 2.566 2.693 2.866 3.150 4.029
35 .438 .639 .809 .971 1.13 1.31 1.507 1.754 2.122 2.447 2.546 2.670 2.838 3.114 3.959
40 .438 .638 .808 .970 1.13 1.31 1.504 1.749 2.113 2.434 2.531 2.653 2.818 3.088 3.909
45 .438 .638 .808 .969 1.13 1.30 1.501 1.745 2.106 2.424 2.519 2.639 2.802 3.068 3.870
50 .438 .638 .808 .968 1.13 1.30 1.499 1.742 2.100 2.415 2.510 2.629 2.790 3.052 3.839
55 .438 .638 .808 .968 1.13 1.30 1.498 1.739 2.096 2.409 2.503 2.620 2.780 3.039 3.814
60 .438 .638 .807 .968 1.13 1.30 1.496 1.737 2.092 2.403 2.497 2.613 2.772 3.028 3.794
70 .438 .637 .807 .967 1.13 1.30 1.494 1.734 2.086 2.395 2.487 2.602 2.759 3.011 3.762
80 .438 .637 .807 .967 1.13 1.30 1.492 1.731 2.082 2.388 2.480 2.594 2.749 2.999 3.738
90 .437 .637 .806 .966 1.13 1.30 1.491 1.729 2.079 2.383 2.474 2.588 2.741 2.989 3.720
100 .437 .637 .806 .966 1.13 1.30 1.490 1.728 2.076 2.379 2.470 2.583 2.735 2.981 3.706
120 .437 .637 .806 .966 1.13 1.30 1.489 1.725 2.072 2.373 2.463 2.575 2.726 2.970 3.684
240 .437 .637 .805 .965 1.12 1.29 1.485 1.719 2.062 2.358 2.447 2.556 2.704 2.941 3.632
∞ .437 .636 .805 .964 1.12 1.29 1.481 1.714 2.052 2.344 2.430 2.538 2.682 2.914 3.581

Values of Tukey's HSD Statistic

Tabled Values are HSD Statistics for the Given Probabilities and dfEFFECT = 3

dfERROR .90 .80 .70 .60 .50 .40 .30 .20 .10 .05 .04 .03 .02 .01 .001
2 .672 .926 1.16 1.40 1.68 2.02 2.490 3.223 4.789 6.928 7.780 9.023 11.10 15.76 50.056
3 .676 .918 1.13 1.34 1.58 1.85 2.201 2.710 3.676 4.826 5.246 5.830 6.746 8.605 18.839
4 .679 .914 1.12 1.32 1.53 1.77 2.073 2.494 3.243 4.071 4.360 4.752 5.345 6.486 11.906
5 .681 .913 1.11 1.30 1.50 1.73 2.001 2.375 3.015 3.690 3.919 4.224 4.676 5.518 9.166
6 .683 .912 1.10 1.29 1.48 1.70 1.955 2.300 2.874 3.462 3.657 3.914 4.290 4.973 7.753
7 .684 .911 1.10 1.28 1.47 1.68 1.924 2.248 2.780 3.310 3.484 3.711 4.039 4.626 6.907
8 .685 .911 1.10 1.28 1.46 1.66 1.900 2.210 2.711 3.202 3.361 3.568 3.864 4.387 6.348
9 .686 .911 1.10 1.27 1.45 1.65 1.882 2.182 2.660 3.122 3.270 3.462 3.735 4.212 5.953
10 .686 .910 1.10 1.27 1.45 1.64 1.868 2.159 2.619 3.059 3.200 3.380 3.636 4.079 5.661
11 .687 .910 1.09 1.27 1.44 1.63 1.856 2.141 2.587 3.010 3.143 3.315 3.558 3.974 5.436
12 .687 .910 1.09 1.27 1.44 1.63 1.847 2.125 2.560 2.969 3.098 3.263 3.494 3.890 5.258
13 .688 .910 1.09 1.26 1.44 1.62 1.839 2.113 2.538 2.935 3.060 3.219 3.442 3.821 5.113
14 .688 .910 1.09 1.26 1.43 1.62 1.832 2.102 2.519 2.907 3.028 3.182 3.398 3.763 4.993
15 .688 .910 1.09 1.26 1.43 1.62 1.826 2.093 2.503 2.882 3.000 3.151 3.360 3.714 4.893
16 .688 .910 1.09 1.26 1.43 1.61 1.821 2.085 2.489 2.861 2.977 3.124 3.328 3.671 4.808
17 .689 .910 1.09 1.26 1.43 1.61 1.816 2.078 2.477 2.843 2.956 3.100 3.299 3.634 4.734
18 .689 .910 1.09 1.26 1.43 1.61 1.812 2.071 2.466 2.826 2.938 3.079 3.275 3.602 4.670
19 .689 .910 1.09 1.26 1.42 1.60 1.809 2.066 2.456 2.812 2.922 3.061 3.253 3.574 4.613
20 .689 .910 1.09 1.26 1.42 1.60 1.805 2.061 2.448 2.799 2.907 3.044 3.233 3.548 4.564
21 .689 .910 1.09 1.26 1.42 1.60 1.803 2.056 2.440 2.787 2.894 3.029 3.216 3.526 4.519
22 .689 .909 1.09 1.25 1.42 1.60 1.800 2.052 2.433 2.777 2.882 3.016 3.200 3.505 4.479
23 .690 .909 1.09 1.25 1.42 1.60 1.797 2.048 2.426 2.767 2.872 3.004 3.185 3.487 4.444
24 .690 .909 1.09 1.25 1.42 1.60 1.795 2.045 2.421 2.759 2.862 2.993 3.172 3.470 4.411
25 .690 .909 1.09 1.25 1.42 1.59 1.793 2.042 2.415 2.751 2.853 2.983 3.160 3.454 4.381
26 .690 .909 1.09 1.25 1.42 1.59 1.791 2.039 2.410 2.743 2.845 2.973 3.149 3.440 4.354
27 .690 .909 1.09 1.25 1.42 1.59 1.790 2.036 2.406 2.737 2.838 2.965 3.139 3.427 4.330
28 .690 .909 1.09 1.25 1.42 1.59 1.788 2.034 2.402 2.730 2.831 2.957 3.130 3.415 4.307
29 .690 .909 1.09 1.25 1.42 1.59 1.787 2.031 2.398 2.725 2.824 2.949 3.121 3.404 4.286
30 .690 .909 1.09 1.25 1.42 1.59 1.785 2.029 2.394 2.719 2.818 2.943 3.113 3.394 4.266
35 .691 .909 1.09 1.25 1.41 1.59 1.780 2.020 2.379 2.697 2.793 2.915 3.080 3.351 4.186
40 .691 .909 1.09 1.25 1.41 1.58 1.775 2.014 2.368 2.680 2.775 2.894 3.056 3.320 4.128
45 .691 .909 1.09 1.25 1.41 1.58 1.772 2.009 2.359 2.668 2.761 2.878 3.037 3.296 4.084
50 .691 .909 1.09 1.25 1.41 1.58 1.769 2.005 2.352 2.658 2.750 2.865 3.022 3.277 4.049
55 .691 .909 1.09 1.25 1.41 1.58 1.767 2.001 2.347 2.649 2.741 2.855 3.010 3.262 4.020
60 .691 .909 1.08 1.25 1.41 1.58 1.765 1.999 2.342 2.643 2.733 2.846 3.000 3.249 3.997
70 .692 .909 1.08 1.25 1.41 1.57 1.763 1.994 2.335 2.632 2.721 2.833 2.984 3.229 3.961
80 .692 .909 1.08 1.25 1.40 1.57 1.760 1.991 2.329 2.624 2.712 2.823 2.972 3.214 3.934
90 .692 .909 1.08 1.25 1.40 1.57 1.759 1.988 2.325 2.618 2.705 2.815 2.963 3.203 3.913
100 .692 .909 1.08 1.24 1.40 1.57 1.757 1.986 2.321 2.613 2.700 2.809 2.956 3.193 3.897
120 .692 .909 1.08 1.24 1.40 1.57 1.755 1.983 2.316 2.605 2.692 2.800 2.945 3.180 3.872
240 .692 .909 1.08 1.24 1.40 1.57 1.751 1.976 2.304 2.587 2.672 2.777 2.918 3.146 3.812
∞ .693 .909 1.08 1.24 1.40 1.56 1.746 1.968 2.291 2.569 2.652 2.754 2.892 3.113 3.754

Values of Tukey's HSD Statistic

Tabled Values are HSD Statistics for the Given Probabilities and dfEFFECT = 4

dfERROR .90 .80 .70 .60 .50 .40 .30 .20 .10 .05 .04 .03 .02 .01 .001
2 .834 1.11 1.36 1.62 1.92 2.29 2.800 3.605 5.330 7.694 8.637 10.01 12.31 17.48 55.467
3 .847 1.10 1.33 1.55 1.80 2.09 2.466 3.013 4.057 5.304 5.762 6.397 7.394 9.422 20.596
4 .855 1.10 1.31 1.52 1.75 2.00 2.317 2.762 3.560 4.446 4.756 5.176 5.813 7.042 12.888
5 .861 1.10 1.31 1.51 1.71 1.95 2.234 2.624 3.298 4.012 4.254 4.578 5.059 5.955 9.850
6 .865 1.10 1.30 1.49 1.69 1.91 2.180 2.537 3.136 3.751 3.956 4.227 4.622 5.343 8.287
7 .868 1.10 1.30 1.49 1.68 1.89 2.143 2.477 3.027 3.578 3.759 3.996 4.339 4.953 7.351
8 .871 1.10 1.30 1.48 1.67 1.87 2.115 2.433 2.948 3.455 3.619 3.834 4.141 4.684 6.733
9 .873 1.11 1.30 1.48 1.66 1.86 2.094 2.399 2.888 3.363 3.515 3.713 3.995 4.488 6.297
10 .874 1.11 1.30 1.47 1.65 1.85 2.077 2.373 2.841 3.291 3.435 3.620 3.883 4.339 5.975
11 .876 1.11 1.29 1.47 1.65 1.84 2.064 2.351 2.804 3.234 3.371 3.546 3.794 4.222 5.726
12 .877 1.11 1.29 1.47 1.64 1.83 2.052 2.333 2.773 3.187 3.318 3.486 3.722 4.127 5.530
13 .878 1.11 1.29 1.47 1.64 1.83 2.043 2.318 2.747 3.149 3.275 3.437 3.663 4.049 5.370
14 .879 1.11 1.29 1.46 1.64 1.82 2.035 2.306 2.725 3.116 3.238 3.395 3.613 3.984 5.239
15 .880 1.11 1.29 1.46 1.63 1.82 2.028 2.295 2.706 3.088 3.207 3.359 3.570 3.929 5.128
16 .880 1.11 1.29 1.46 1.63 1.81 2.022 2.285 2.690 3.064 3.180 3.328 3.534 3.881 5.034
17 .881 1.11 1.29 1.46 1.63 1.81 2.016 2.277 2.676 3.042 3.156 3.301 3.502 3.840 4.953
18 .882 1.11 1.29 1.46 1.63 1.81 2.012 2.270 2.663 3.024 3.135 3.277 3.474 3.803 4.882
19 .882 1.11 1.29 1.46 1.63 1.80 2.007 2.263 2.652 3.007 3.117 3.256 3.449 3.771 4.820
20 .883 1.11 1.29 1.46 1.62 1.80 2.004 2.257 2.642 2.992 3.101 3.237 3.427 3.743 4.766
21 .883 1.11 1.29 1.46 1.62 1.80 2.000 2.252 2.633 2.979 3.086 3.221 3.407 3.717 4.717
22 .883 1.11 1.29 1.46 1.62 1.80 1.997 2.247 2.625 2.967 3.072 3.205 3.389 3.694 4.673
23 .884 1.11 1.29 1.46 1.62 1.80 1.994 2.243 2.617 2.956 3.060 3.192 3.373 3.674 4.634
24 .884 1.11 1.29 1.45 1.62 1.79 1.992 2.238 2.611 2.946 3.049 3.179 3.358 3.655 4.598
25 .884 1.11 1.29 1.45 1.62 1.79 1.989 2.235 2.604 2.937 3.039 3.167 3.344 3.637 4.565
26 .885 1.11 1.29 1.45 1.62 1.79 1.987 2.231 2.599 2.928 3.029 3.157 3.332 3.621 4.536
27 .885 1.11 1.29 1.45 1.62 1.79 1.985 2.228 2.593 2.921 3.021 3.147 3.320 3.607 4.508
28 .885 1.11 1.29 1.45 1.62 1.79 1.983 2.225 2.588 2.913 3.013 3.138 3.310 3.593 4.483
29 .885 1.11 1.29 1.45 1.62 1.79 1.981 2.223 2.584 2.907 3.005 3.130 3.300 3.581 4.460
30 .886 1.11 1.29 1.45 1.61 1.79 1.980 2.220 2.579 2.901 2.999 3.122 3.291 3.569 4.439
35 .886 1.11 1.29 1.45 1.61 1.78 1.973 2.210 2.562 2.875 2.970 3.090 3.253 3.522 4.351
40 .887 1.11 1.29 1.45 1.61 1.78 1.968 2.202 2.549 2.856 2.949 3.066 3.226 3.487 4.287
45 .888 1.11 1.29 1.45 1.61 1.78 1.964 2.196 2.539 2.841 2.933 3.048 3.204 3.460 4.239
50 .888 1.11 1.29 1.45 1.61 1.77 1.961 2.191 2.531 2.830 2.920 3.033 3.187 3.438 4.200
55 .888 1.11 1.29 1.45 1.61 1.77 1.958 2.187 2.524 2.820 2.910 3.022 3.174 3.421 4.169
60 .889 1.11 1.29 1.45 1.61 1.77 1.956 2.184 2.519 2.812 2.901 3.012 3.162 3.407 4.144
70 .889 1.11 1.29 1.45 1.60 1.77 1.953 2.178 2.510 2.800 2.887 2.996 3.144 3.384 4.104
80 .889 1.11 1.29 1.45 1.60 1.77 1.950 2.175 2.504 2.791 2.877 2.985 3.131 3.368 4.074
90 .890 1.11 1.29 1.45 1.60 1.77 1.948 2.172 2.499 2.784 2.869 2.976 3.121 3.355 4.052
100 .890 1.11 1.29 1.45 1.60 1.76 1.946 2.169 2.495 2.778 2.863 2.969 3.113 3.345 4.034
120 .890 1.11 1.29 1.44 1.60 1.76 1.944 2.166 2.489 2.770 2.854 2.959 3.100 3.329 4.007
240 .891 1.11 1.29 1.44 1.60 1.76 1.938 2.157 2.474 2.749 2.831 2.933 3.070 3.292 3.942
∞ .892 1.11 1.29 1.44 1.60 1.76 1.932 2.148 2.460 2.728 2.808 2.907 3.040 3.255 3.878