T-16
26.98 8.331 5.910 5.040
4.602 4.339 4.165 4.041 3.949
3.877 3.820 3.773 3.735 3.702
3.674 3.649 3.628 3.609 3.593
3.578 3.532 3.486 3.442 3.399
3.356 3.314
17.97 6.085 4.501 3.927
3.635 3.461 3.344 3.261 3.199
3.151 3.113 3.082 3.055 3.033
3.014 2.998 2.984 2.971 2.960
2.950 2.919 2.888 2.858 2.829
2.800 2.772
1 2 3 4
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 24 30 40 60
120 `
3.685 3.633
3.958 3.901 3.845 3.791 3.737
4.076 4.046 4.020 3.997 3.977
4.327 4.256 4.199 4.151 4.111
5.218 4.896 4.681 4.529 4.415
32.82 9.798 6.825 5.757
3.917 3.858
4.232 4.166 4.102 4.039 3.977
4.367 4.333 4.303 4.277 4.253
4.654 4.574 4.508 4.453 4.407
5.673 5.305 5.060 4.886 4.756
37.08 10.88 7.502 6.287
4.096 4.030
4.445 4.373 4.302 4.232 4.163
4.595 4.557 4.524 4.495 4.469
4.912 4.823 4.751 4.690 4.639
6.033 5.628 5.359 5.167 5.024
40.41 11.74 8.037 6.707
4.241 4.170
4.620 4.541 4.464 4.389 4.314
4.782 4.741 4.705 4.673 4.645
5.124 5.028 4.950 4.885 4.829
6.330 5.895 5.606 5.399 5.244
43.12 12.44 8.478 7.053
4.363 4.286
4.768 4.684 4.602 4.521 4.441
4.940 4.897 4.858 4.824 4.794
5.305 5.202 5.119 5.049 4.990
6.582 6.122 5.815 5.597 5.432
45.40 13.03 8.853 7.347
4.468 4.387
4.896 4.807 4.720 4.635 4.550
5.077 5.031 4.991 4.956 4.924
5.461 5.353 5.265 5.192 5.131
6.802 6.319 5.998 5.767 5.595
47.36 13.54 9.177 7.602
4.560 4.474
5.008 4.915 4.824 4.735 4.646
5.198 5.150 5.108 5.071 5.038
5.599 5.487 5.395 5.318 5.254
6.995 6.493 6.158 5.918 5.739
49.07 13.99 9.462 7.826
4.641 4.552
5.108 5.012 4.917 4.824 4.732
5.306 5.256 5.212 5.174 5.140
5.722 5.605 5.511 5.431 5.364
7.168 6.649 6.302 6.054 5.867
50.59 14.39 9.717 8.027
4.714 4.622
5.199 5.099 5.001 4.904 4.808
5.404 5.352 5.307 5.267 5.231
5.833 5.713 5.615 5.533 5.463
7.324 6.789 6.431 6.175 5.983
51.96 14.75 9.946 8.208
4.781 4.685
5.282 5.179 5.077 4.977 4.878
5.493 5.439 5.392 5.352 5.315
5.935 5.811 5.710 5.625 5.554
7.466 6.917 6.550 6.287 6.089
53.20 15.08 10.15 8.373
4.842 4.743
5.357 5.251 5.147 5.044 4.942
5.574 5.520 5.471 5.429 5.391
6.028 5.901 5.798 5.711 5.637
7.596 7.034 6.658 6.389 6.186
54.33 15.38 10.35 8.525
4.898 4.796
5.427 5.319 5.211 5.106 5.001
5.649 5.593 5.544 5.501 5.462
6.114 5.984 5.878 5.789 5.714
7.717 7.143 6.759 6.483 6.276
55.36 15.65 10.53 8.664
4.950 4.845
5.493 5.381 5.271 5.163 5.056
5.720 5.662 5.612 5.568 5.528
6.194 6.062 5.953 5.862 5.786
7.828 7.244 6.852 6.571 6.359
56.32 15.91 10.69 8.794
4.998 4.891
5.553 5.439 5.327 5.216 5.107
5.785 5.727 5.675 5.630 5.589
6.269 6.134 6.023 5.931 5.852
7.932 7.338 6.939 6.653 6.437
57.22 16.14 10.84 8.914
5.044 4.934
5.610 5.494 5.379 5.266 5.154
5.846 5.786 5.734 5.688 5.647
6.339 6.202 6.089 5.995 5.915
8.030 7.426 7.020 6.729 6.510
58.04 16.37 10.98 9.028
5.086 4.974
5.663 5.545 5.429 5.313 5.199
5.904 5.843 5.790 5.743 5.701
6.405 6.265 6.151 6.055 5.974
8.122 7.508 7.097 6.802 6.579
58.83 16.57 11.11 9.134
5.126 5.012
5.714 5.594 5.475 5.358 5.241
5.958 5.897 5.842 5.794 5.752
6.467 6.326 6.209 6.112 6.029
8.208 7.587 7.170 6.870 6.644
59.56 16.77 11.24 9.233
This table contains critical values associated with the Studentized Range Distribution, Qa, defined by a, and degrees of freedom m and v where m is the number of degrees of freedom in the numerator (the number of treatment groups) and v is the number of degrees of freedom in the denominator. a 5 0.05 m 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 v
Table VIII Critical Values for the Studentized Range Distribution
3199T_Tapp_T1-T27.indd Page T-16 9/15/09 1:46:47 PM user-s131
135.0 19.02 10.62 8.120
6.976 6.331 5.919 5.635 5.428
5.270 5.146 5.046 4.964 4.895
4.836 4.786 4.742 4.703 4.670
4.639 4.546 4.455 4.367 4.282
4.200 4.120
90.03 14.04 8.261 6.512
5.702 5.243 4.949 4.746 4.596
4.482 4.392 4.320 4.260 4.210
4.168 4.131 4.099 4.071 4.046
4.024 3.956 3.889 3.825 3.762
3.702 3.643
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 24 30 40 60
120 `
3
1 2 3 4
a 5 0.01 2 v
4.497 4.403
5.018 4.907 4.799 4.696 4.595
5.252 5.192 5.140 5.094 5.054
5.769 5.621 5.502 5.404 5.322
7.804 7.033 6.543 6.204 5.957
164.3 22.29 12.17 9.173
4
4.709 4.603
5.294 5.168 5.048 4.931 4.818
5.556 5.489 5.430 5.379 5.334
6.136 5.970 5.836 5.727 5.634
8.421 7.556 7.005 6.625 6.348
185.6 24.72 13.33 9.958
5
4.872 4.757
5.510 5.374 5.242 5.114 4.991
5.796 5.722 5.659 5.603 5.554
6.428 6.247 6.101 5.981 5.881
8.913 7.973 7.373 6.960 6.658
202.2 26.63 14.24 10.58
6
5.005 4.882
5.688 5.542 5.401 5.265 5.133
5.994 5.915 5.847 5.788 5.735
6.669 6.476 6.321 6.192 6.085
9.321 8.318 7.679 7.237 6.915
215.8 28.20 15.00 11.10
7
5.118 4.987
5.839 5.685 5.536 5.392 5.253
6.162 6.079 6.007 5.944 5.889
6.875 6.672 6.507 6.372 6.258
9.669 8.613 7.939 7.474 7.134
227.2 29.53 15.64 11.55
8
5.214 5.078
5.970 5.809 5.653 5.502 5.356
6.309 6.222 6.147 6.081 6.022
7.055 6.842 6.670 6.528 6.409
9.972 8.869 8.166 7.681 7.325
237.0 30.68 16.20 11.93
9
5.299 5.157
6.087 5.919 5.756 5.599 5.447
6.439 6.349 6.270 6.201 6.141
7.213 6.992 6.814 6.667 6.543
10.24 9.097 8.368 7.863 7.495
245.6 31.69 16.69 12.27
10
m
5.375 5.227
6.191 6.017 5.849 5.686 5.528
6.555 6.462 6.381 6.310 6.247
7.356 7.128 6.943 6.791 6.664
10.48 9.301 8.548 8.027 7.647
253.2 32.59 17.13 12.57
11
5.443 5.290
6.285 6.106 5.932 5.764 5.601
6.660 6.564 6.480 6.407 6.342
7.485 7.250 7.060 6.903 6.772
10.70 9.485 8.711 8.176 7.784
260.0 33.40 17.53 12.84
12
Table VIII Critical Values for the Studentized Range Distribution (Continued)
5.505 5.348
6.371 6.186 6.008 5.835 5.667
6.757 6.658 6.572 6.497 6.430
7.603 7.362 7.167 7.006 6.871
10.89 9.653 8.860 8.312 7.910
266.2 34.13 17.89 13.09
13
5.562 5.400
6.450 6.261 6.078 5.900 5.728
6.845 6.744 6.656 6.579 6.510
7.712 7.465 7.265 7.101 6.962
11.08 9.808 8.997 8.436 8.025
271.8 34.81 18.22 13.32
14
5.614 5.448
6.523 6.330 6.143 5.961 5.785
6.927 6.823 6.734 6.655 6.585
7.812 7.560 7.356 7.188 7.047
11.24 9.951 9.124 8.552 8.132
277.0 35.43 18.52 13.53
15
5.662 5.493
6.591 6.394 6.203 6.017 5.837
7.003 6.898 6.806 6.725 6.654
7.906 7.649 7.441 7.269 7.126
11.40 10.08 9.242 8.659 8.232
281.8 36.00 18.81 13.73
16
5.708 5.535
6.654 6.453 6.259 6.069 5.886
7.074 6.967 6.873 6.792 6.719
7.993 7.732 7.520 7.345 7.199
11.55 10.21 9.353 8.760 8.325
286.3 36.53 19.07 13.91
17
5.750 5.574
6.714 6.510 6.311 6.119 5.931
7.142 7.032 6.937 6.854 6.780
8.076 7.809 7.594 7.417 7.268
11.68 10.32 9.456 8.854 8.412
290.4 37.03 19.32 14.08
18
5.790 5.611
6.771 6.563 6.361 6.165 5.974
7.204 7.093 6.997 6.912 6.837
8.153 7.883 7.665 7.485 7.333
11.81 10.43 9.554 8.943 8.495
294.3 37.50 19.55 14.24
19
5.827 5.645
6.823 6.612 6.407 6.209 6.015
7.264 7.152 7.053 6.968 6.891
8.226 7.952 7.731 7.548 7.395
11.93 10.54 9.646 9.027 8.573
298.0 37.95 19.77 14.40
20
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T-17
T-18
1351. 60.42 23.32 14.99
11.67 9.960 8.930 8.250 7.768
7.411 7.136 6.917 6.740 6.594
6.470 6.365 6.275 6.196 6.127
6.065 5.877 5.698 5.528 5.365
5.211 5.063
900.3 44.69 18.28 12.18
9.714 8.427 7.648 7.130 6.762
6.487 6.275 6.106 5.970 5.856
5.760 5.678 5.608 5.546 5.492
5.444 5.297 5.156 5.022 4.894
4.771 4.654
5 6 7 8 9
10 11 12 13 14
15 16 17 18 19
20 24 30 40 60
120 `
3
1 2 3 4
a 5 0.001 2 v
5.476 5.309
6.454 6.238 6.033 5.838 5.653
6.920 6.799 6.695 6.604 6.525
8.006 7.687 7.436 7.231 7.062
12.96 10.97 9.768 8.978 8.419
1643. 70.77 26.65 16.84
4
5.667 5.484
6.740 6.503 6.278 6.063 5.860
7.252 7.119 7.005 6.905 6.817
8.450 8.098 7.821 7.595 7.409
13.93 11.72 10.40 9.522 8.906
1856. 78.43 29.13 18.23
5
5.815 5.619
6.966 6.712 6.470 6.240 6.022
7.517 7.374 7.250 7.143 7.049
8.804 8.426 8.127 7.885 7.685
14.71 12.32 10.90 9.958 9.295
2022. 84.49 31.11 19.34
6
5.937 5.730
7.154 6.884 6.628 6.386 6.155
7.736 7.585 7.454 7.341 7.242
9.099 8.699 8.383 8.126 7.915
15.35 12.83 11.32 10.32 9.619
2158. 89.46 32.74 20.26
7
6.039 5.823
7.313 7.031 6.763 6.509 6.268
7.925 7.766 7.629 7.510 7.405
9.352 8.933 8.601 8.333 8.110
15.90 13.26 11.68 10.64 9.897
2272. 93.67 34.12 21.04
8
6.128 5.903
7.453 7.159 6.880 6.616 6.366
8.088 7.923 7.781 7.657 7.549
9.573 9.138 8.793 8.513 8.282
16.38 13.63 11.99 10.91 10.14
2370. 97.30 35.33 21.73
9
6.206 5.973
7.577 7.272 6.984 6.711 6.451
8.234 8.063 7.916 7.788 7.676
9.769 9.319 8.962 8.673 8.434
16.81 13.97 12.27 11.15 10.36
2455. 100.5 36.39 22.33
10
m
6.276 6.036
7.688 7.374 7.077 6.796 6.528
8.365 8.189 8.037 7.906 7.790
9.946 9.482 9.115 8.817 8.571
17.18 14.27 12.52 11.36 10.55
2532. 103.3 37.34 22.87
11
6.339 6.092
7.788 7.467 7.162 6.872 6.598
8.483 8.303 8.148 8.012 7.893
10.11 9.630 9.254 8.948 8.696
17.53 14.54 12.74 11.56 10.73
2600. 105.9 38.20 23.36
12
Table VIII Critical Values for the Studentized Range Distribution (Continued)
6.396 6.144
7.880 7.551 7.239 6.942 6.661
8.592 8.407 8.248 8.110 7.988
10.25 9.766 9.381 9.068 8.809
17.85 14.79 12.95 11.74 10.89
2662. 108.2 38.98 23.81
13
6.448 6.191
7.966 7.629 7.310 7.007 6.720
8.693 8.504 8.342 8.199 8.075
10.39 9.892 9.498 9.178 8.914
18.13 15.01 13.14 11.91 11.03
2718. 110.4 39.69 24.21
14
6.496 6.234
8.044 7.701 7.375 7.067 6.774
8.786 8.593 8.427 8.283 8.156
10.52 10.01 9.606 9.281 9.012
18.41 15.22 13.32 12.06 11.18
2770. 112.3 40.35 24.59
15
6.542 6.274
8.118 7.768 7.437 7.122 6.824
8.872 8.676 8.508 8.361 8.232
10.64 10.12 9.707 9.376 9.103
18.66 15.42 13.48 12.21 11.30
2818. 114.2 40.97 24.94
16
6.583 6.312
8.186 7.831 7.494 7.174 6.871
8.954 8.755 8.583 8.434 8.303
10.75 10.22 9.802 9.466 9.188
18.89 15.60 13.64 12.34 11.42
2863. 115.9 41.54 25.27
17
6.623 6.347
8.251 7.890 7.548 7.223 6.914
9.030 8.828 8.654 8.502 8.369
10.85 10.31 9.891 9.550 9.267
19.10 15.78 13.78 12.47 11.54
2904. 117.4 42.07 25.58
18
6.660 6.380
8.312 7.946 7.599 7.269 6.956
9.102 8.897 8.720 8.567 8.432
10.95 10.41 9.975 9.629 9.343
19.31 15.94 13.92 12.59 11.64
2943. 118.9 42.58 25.87
19
6.695 6.411
8.370 7.999 7.647 7.312 6.995
9.170 8.963 8.784 8.628 8.491
11.03 10.49 10.06 9.704 9.414
19.51 16.09 14.04 12.70 11.75
2980. 120.3 43.05 26.14
20
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