Tables Statistiques

Loi Normale
Fractiles de la Loi Normale
Khideux
Student
Loi de Fisher-Snedecor : Probabilité 0.05
Loi de Fisher-Snedecor : Probabilité 0.025
Loi de Fisher-Snedecor : Probabilité 0.01
Calculateur et dessinateur en ligne de lois de probabilité : http://www.sgcorp.com/probability_distributions.htm

 

 

 

Table de Loi Normale
Fonction de répartition Π de la loi normale centrée réduite.

Probabilité de trouver une valeur inférieure à u .

Π (-u) = 1 - Π (u)

u 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.0 0.50000 0.50399 0.50798 0.51197 0.51595 0.51994 0.52392 0.52790 0.53188 0.53586
0.1 0.53983 0.54380 0.54776 0.55172 0.55567 0.55962 0.56356 0.56749 0.57142 0.57535
0.2 0.57926 0.58317 0.58706 0.59095 0.59483 0.59871 0.60257 0.60642 0.61026 0.61409
0.3 0.61791 0.62172 0.62552 0.62930 0.63307 0.63683 0.64058 0.64431 0.64803 0.65173
0.4 0.65542 0.65910 0.66276 0.66640 0.67003 0.67364 0.67724 0.68082 0.68439 0.68793
0.5 0.69146 0.69497 0.69847 0.70194 0.70540 0.70884 0.71226 0.71566 0.71904 0.72240
0.6 0.72575 0.72907 0.73237 0.73565 0.73891 0.74215 0.74537 0.74857 0.75175 0.75490
0.7 0.75804 0.76115 0.76424 0.76730 0.77035 0.77337 0.77637 0.77935 0.78230 0.78524
0.8 0.78814 0.79103 0.79389 0.79673 0.79955 0.80234 0.80511 0.80785 0.81057 0.81327
0.9 0.81594 0.81859 0.82121 0.82381 0.82639 0.82894 0.83147 0.83398 0.83646 0.83891
1.0 0.84134 0.84375 0.84614 0.84849 0.85083 0.85314 0.85543 0.85769 0.85993 0.86214
1.1 0.86433 0.86650 0.86864 0.87076 0.87286 0.87493 0.87698 0.87900 0.88100 0.88298
1.2 0.88493 0.88686 0.88877 0.89065 0.89251 0.89435 0.89617 0.89796 0.89973 0.90147
1.3 0.90320 0.90490 0.90658 0.90824 0.90988 0.91149 0.91309 0.91466 0.91621 0.91774
1.4 0.91924 0.92073 0.92220 0.92364 0.92507 0.92647 0.92785 0.92922 0.93056 0.93189
1.5 0.93319 0.93448 0.93574 0.93699 0.93822 0.93943 0.94062 0.94179 0.94295 0.94408
1.6 0.94520 0.94630 0.94738 0.94845 0.94950 0.95053 0.95154 0.95254 0.95352 0.95449
1.7 0.95543 0.95637 0.95728 0.95818 0.95907 0.95994 0.96080 0.96164 0.96246 0.96327
1.8 0.96407 0.96485 0.96562 0.96638 0.96712 0.96784 0.96856 0.96926 0.96995 0.97062
1.9 0.97128 0.97193 0.97257 0.97320 0.97381 0.97441 0.97500 0.97558 0.97615 0.97670
2.0 0.97725 0.97778 0.97831 0.97882 0.97932 0.97982 0.98030 0.98077 0.98124 0.98169
2.1 0.98214 0.98257 0.98300 0.98341 0.98382 0.98422 0.98461 0.98500 0.98537 0.98574
2.2 0.98610 0.98645 0.98679 0.98713 0.98745 0.98778 0.98809 0.98840 0.98870 0.98899
2.3 0.98928 0.98956 0.98983 0.99010 0.99036 0.99061 0.99086 0.99111 0.99134 0.99158
2.4 0.99180 0.99202 0.99224 0.99245 0.99266 0.99286 0.99305 0.99324 0.99343 0.99361
2.5 0.99379 0.99396 0.99413 0.99430 0.99446 0.99461 0.99477 0.99492 0.99506 0.99520
2.6 0.99534 0.99547 0.99560 0.99573 0.99585 0.99598 0.99609 0.99621 0.99632 0.99643
2.7 0.99653 0.99664 0.99674 0.99683 0.99693 0.99702 0.99711 0.99720 0.99728 0.99736
2.8 0.99744 0.99752 0.99760 0.99767 0.99774 0.99781 0.99788 0.99795 0.99801 0.99807
2.9 0.99813 0.99819 0.99825 0.99831 0.99836 0.99841 0.99846 0.99851 0.99856 0.99861
3.0 0.99865 0.99869 0.99874 0.99878 0.99882 0.99886 0.99889 0.99893 0.99896 0.99900
3.1 0.99903 0.99906 0.99910 0.99913 0.99916 0.99918 0.99921 0.99924 0.99926 0.99929
3.2 0.99931 0.99934 0.99936 0.99938 0.99940 0.99942 0.99944 0.99946 0.99948 0.99950
3.3 0.99952 0.99953 0.99955 0.99957 0.99958 0.99960 0.99961 0.99962 0.99964 0.99965
3.4 0.99966 0.99968 0.99969 0.99970 0.99971 0.99972 0.99973 0.99974 0.99975 0.99976
3.5 0.99977 0.99978 0.99978 0.99979 0.99980 0.99981 0.99981 0.99982 0.99983 0.99983
3.6 0.99984 0.99985 0.99985 0.99986 0.99986 0.99987 0.99987 0.99988 0.99988 0.99989
3.7 0.99989 0.99990 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992 0.99992 0.99992
3.8 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995
3.9 0.99995 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997

 

 

 

 

Fractiles de la Loi Normale
Pour P < 0.5 (colonne de gauche et ligne supérieure), les fractiles sont négatifs.
Pour P > 0.5 (colonne de droite et ligne inférieure), les fractiles sont positifs.

P 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01  
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.40
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
 infini
2.3263
2.0537
1.8808
1.7507
1.6449
1.5548
1.4758
1.4051
1.3408
1.2816
1.2265
1.1750
1.1264
1.0803
1.0364
0.9945
0.9542
0.9154
0.8779
0.8416
0.8064
0.7722
0.7388
0.7063
0.6745
0.6433
0.6128
0.5828
0.5534
0.5244
0.4958
0.4677
0.4399
0.4125
0.3853
0.3585
0.3319
0.3055
0.2793
0.2533
0.2275
0.2019
0.1764
0.1510
0.1257
0.1004
0.0753
0.0502
0.0251
 3.0902
2.2904
2.0335
1.8663
1.7392
1.6352
1.5464
1.4684
1.3984
1.3346
1.2759
1.2212
1.1700
1.1217
1.0758
1.0322
0.9904
0.9502
0.9116
0.8742
0.8381
0.8030
0.7688
0.7356
0.7031
0.6713
0.6403
0.6098
0.5799
0.5505
0.5215
0.4930
0.4649
0.4372
0.4097
0.3826
0.3558
0.3292
0.3029
0.2767
0.2508
0.2250
0.1993
0.1738
0.1484
0.1231
0.0979
0.0728
0.0476
0.0226
 2.8782
2.2571
2.0141
1.8522
1.7279
1.6258
1.5382
1.4611
1.3917
1.3285
1.2702
1.2160
1.1650
1.1170
1.0714
1.0279
0.9863
0.9463
0.9078
0.8706
0.8345
0.7995
0.7655
0.7323
0.6999
0.6682
0.6372
0.6068
0.5769
0.5476
0.5187
0.4902
0.4621
0.4344
0.4070
0.3799
0.3531
0.3266
0.3002
0.2741
0.2482
0.2224
0.1968
0.1713
0.1459
0.1206
0.0954
0.0702
0.0451
0.0201
 2.7478
2.2262
1.9954
1.8384
1.7169
1.6164
1.5301
1.4538
1.3852
1.3225
1.2646
1.2107
1.1601
1.1123
1.0669
1.0237
0.9822
0.9424
0.9040
0.8669
0.8310
0.7961
0.7621
0.7290
0.6967
0.6651
0.6341
0.6038
0.5740
0.5446
0.5158
0.4874
0.4593
0.4316
0.4043
0.3772
0.3505
0.3239
0.2976
0.2715
0.2456
0.2198
0.1942
0.1687
0.1434
0.1181
0.0929
0.0677
0.0426
0.0175
 2.6521
2.1973
1.9774
1.8250
1.7060
1.6072
1.5220
1.4466
1.3787
1.3165
1.2591
1.2055
1.1552
1.1077
1.0625
1.0194
0.9782
0.9385
0.9002
0.8632
0.8274
0.7926
0.7588
0.7257
0.6935
0.6620
0.6311
0.6008
0.5710
0.5417
0.5129
0.4845
0.4565
0.4289
0.4016
0.3745
0.3478
0.3213
0.2950
0.2689
0.2430
0.2173
0.1917
0.1662
0.1408
0.1156
0.0904
0.0652
0.0401
0.0150
 2.5758
2.1701
1.9600
1.8119
1.6954
1.5982
1.5141
1.4395
1.3722
1.3106
1.2536
1.2004
1.1503
1.1031
1.0581
1.0152
0.9741
0.9346
0.8965
0.8596
0.8239
0.7892
0.7554
0.7225
0.6903
0.6588
0.6280
0.5978
0.5681
0.5388
0.5101
0.4817
0.4538
0.4261
0.3989
0.3719
0.3451
0.3186
0.2924
0.2663
0.2404
0.2147
0.1891
0.1637
0.1383
0.1130
0.0878
0.0627
0.0376
0.0125
 2.5121
2.1444
1.9431
1.7991
1.6849
1.5893
1.5063
1.4325
1.3658
1.3047
1.2481
1.1952
1.1455
1.0985
1.0537
1.0110
0.9701
0.9307
0.8927
0.8560
0.8204
0.7858
0.7521
0.7192
0.6871
0.6557
0.6250
0.5948
0.5651
0.5359
0.5072
0.4789
0.4510
0.4234
0.3961
0.3692
0.3425
0.3160
0.2898
0.2637
0.2378
0.2121
0.1866
0.1611
0.1358
0.1105
0.0853
0.0602
0.0351
0.0100
 2.4573
2.1201
1.9268
1.7866
1.6747
1.5805
1.4985
1.4255
1.3595
1.2988
1.2426
1.1901
1.1407
1.0939
1.0494
1.0069
0.9661
0.9269
0.8890
0.8524
0.8169
0.7824
0.7488
0.7160
0.6840
0.6526
0.6219
0.5918
0.5622
0.5330
0.5044
0.4761
0.4482
0.4207
0.3934
0.3665
0.3398
0.3134
0.2871
0.2611
0.2353
0.2096
0.1840
0.1586
0.1332
0.1080
0.0828
0.0577
0.0326
0.0075
 2.4089
2.0969
1.9110
1.7744
1.6646
1.5718
1.4909
1.4187
1.3532
1.2930
1.2372
1.1850
1.1359
1.0893
1.0451
1.0027
0.9621
0.9230
0.8853
0.8488
0.8134
0.7790
0.7454
0.7128
0.6808
0.6495
0.6189
0.5888
0.5592
0.5302
0.5015
0.4733
0.4454
0.4179
0.3907
0.3638
0.3372
0.3107
0.2845
0.2585
0.2327
0.2070
0.1815
0.1560
0.1307
0.1055
0.0803
0.0552
0.0301
0.0050
 2.3656
2.0748
1.8957
1.7624
1.6546
1.5632
1.4833
1.4118
1.3469
1.2873
1.2319
1.1800
1.1311
1.0848
1.0407
0.9986
0.9581
0.9192
0.8816
0.8452
0.8099
0.7756
0.7421
0.7095
0.6776
0.6464
0.6158
0.5858
0.5563
0.5273
0.4987
0.4705
0.4427
0.4152
0.3880
0.3611
0.3345
0.3081
0.2819
0.2559
0.2301
0.2045
0.1789
0.1535
0.1282
0.1030
0.0778
0.0527
0.0276
0.0025
 2.3263
2.0537
1.8808
1.7507
1.6449
1.5548
1.4758
1.4051
1.3408
1.2816
1.2265
1.1750
1.1264
1.0803
1.0364
0.9945
0.9542
0.9154
0.8779
0.8416
0.8064
0.7722
0.7388
0.7063
0.6745
0.6433
0.6128
0.5828
0.5534
0.5244
0.4958
0.4677
0.4399
0.4125
0.3853
0.3585
0.3319
0.3055
0.2793
0.2533
0.2275
0.2019
0.1764
0.1510
0.1257
0.1004
0.0753
0.0502
0.0251
0.0000
 0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0.90
0.89
0.88
0.87
0.86
0.85
0.84
0.83
0.82
0.81
0.80
0.79
0.78
0.77
0.76
0.75
0.74
0.73
0.72
0.71
0.70
0.69
0.68
0.67
0.66
0.65
0.64
0.63
0.62
0.61
0.60
0.59
0.58
0.57
0.56
0.55
0.54
0.53
0.52
0.51
0.50
  0.01 0.009 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 P

 

 

 

Fractiles de la loi du ( ν )
Cette table donne les fractiles FP de la loi de khi-deux
à ν degrés de liberté : P = Probabilité ( < FP )
P
ν
  0.01 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.85 0.9 0.95 0.98 0.99 0.999
1 0.000 0.001 0.004 0.016 0.036 0.064 0.102 0.148 0.275 0.455 0.708 1.074 1.323 1.642 2.072 2.706 3.841 5.412 6.635 10.827
2 0.020 0.040 0.103 0.211 0.325 0.446 0.575 0.713 1.022 1.386 1.833 2.408 2.773 3.219 3.794 4.605 5.991 7.824 9.210 13.815
3 0.115 0.185 0.352 0.584 0.798 1.005 1.213 1.424 1.869 2.366 2.946 3.665 4.108 4.642 5.317 6.251 7.815 9.837 11.345 16.266
4 0.297 0.429 0.711 1.064 1.366 1.649 1.923 2.195 2.753 3.357 4.045 4.878 5.385 5.989 6.745 7.779 9.488 11.668 13.277 18.466
5 0.554 0.752 1.145 1.610 1.994 2.343 2.675 3.000 3.656 4.351 5.132 6.064 6.626 7.289 8.115 9.236 11.070 13.388 15.086 20.515
6 0.872 1.134 1.635 2.204 2.661 3.070 3.455 3.828 4.570 5.348 6.211 7.231 7.841 8.558 9.446 10.645 12.592 15.033 16.812 22.457
7 1.239 1.564 2.167 2.833 3.358 3.822 4.255 4.671 5.493 6.346 7.283 8.383 9.037 9.803 10.748 12.017 14.067 16.622 18.475 24.321
8 1.647 2.032 2.733 3.490 4.078 4.594 5.071 5.527 6.423 7.344 8.351 9.524 10.219 11.030 12.027 13.362 15.507 18.168 20.090 26.124
9 2.088 2.532 3.325 4.168 4.817 5.380 5.899 6.393 7.357 8.343 9.414 10.656 11.389 12.242 13.288 14.684 16.919 19.679 21.666 27.877
10 2.558 3.059 3.940 4.865 5.570 6.179 6.737 7.267 8.295 9.342 10.473 11.781 12.549 13.442 14.534 15.987 18.307 21.161 23.209 29.588
11 3.053 3.609 4.575 5.578 6.336 6.989 7.584 8.148 9.237 10.341 11.530 12.899 13.701 14.631 15.767 17.275 19.675 22.618 24.725 31.264
12 3.571 4.178 5.226 6.304 7.114 7.807 8.438 9.034 10.182 11.340 12.584 14.011 14.845 15.812 16.989 18.549 21.026 24.054 26.217 32.909
13 4.107 4.765 5.892 7.041 7.901 8.634 9.299 9.926 11.129 12.340 13.636 15.119 15.984 16.985 18.202 19.812 22.362 25.471 27.688 34.527
14 4.660 5.368 6.571 7.790 8.696 9.467 10.165 10.821 12.078 13.339 14.685 16.222 17.117 18.151 19.406 21.064 23.685 26.873 29.141 36.124
15 5.229 5.985 7.261 8.547 9.499 10.307 11.037 11.721 13.030 14.339 15.733 17.322 18.245 19.311 20.603 22.307 24.996 28.259 30.578 37.698
16 5.812 6.614 7.962 9.312 10.309 11.152 11.912 12.624 13.983 15.338 16.780 18.418 19.369 20.465 21.793 23.542 26.296 29.633 32.000 39.252
17 6.408 7.255 8.672 10.085 11.125 12.002 12.792 13.531 14.937 16.338 17.824 19.511 20.489 21.615 22.977 24.769 27.587 30.995 33.409 40.791
18 7.015 7.906 9.390 10.865 11.946 12.857 13.675 14.440 15.893 17.338 18.868 20.601 21.605 22.760 24.155 25.989 28.869 32.346 34.805 42.312
19 7.633 8.567 10.117 11.651 12.773 13.716 14.562 15.352 16.850 18.338 19.910 21.689 22.718 23.900 25.329 27.204 30.144 33.687 36.191 43.819
20 8.260 9.237 10.851 12.443 13.604 14.578 15.452 16.266 17.809 19.337 20.951 22.775 23.828 25.038 26.498 28.412 31.410 35.020 37.566 45.314
21 8.897 9.915 11.591 13.240 14.439 15.445 16.344 17.182 18.768 20.337 21.992 23.858 24.935 26.171 27.662 29.615 32.671 36.343 38.932 46.796
22 9.542 10.600 12.338 14.041 15.279 16.314 17.240 18.101 19.729 21.337 23.031 24.939 26.039 27.301 28.822 30.813 33.924 37.659 40.289 48.268
23 10.196 11.293 13.091 14.848 16.122 17.187 18.137 19.021 20.690 22.337 24.069 26.018 27.141 28.429 29.979 32.007 35.172 38.968 41.638 49.728
24 10.856 11.992 13.848 15.659 16.969 18.062 19.037 19.943 21.652 23.337 25.106 27.096 28.241 29.553 31.132 33.196 36.415 40.270 42.980 51.179
25 11.524 12.697 14.611 16.473 17.818 18.940 19.939 20.867 22.616 24.337 26.143 28.172 29.339 30.675 32.282 34.382 37.652 41.566 44.314 52.619
26 12.198 13.409 15.379 17.292 18.671 19.820 20.843 21.792 23.579 25.336 27.179 29.246 30.435 31.795 33.429 35.563 38.885 42.856 45.642 54.051
27 12.878 14.125 16.151 18.114 19.527 20.703 21.749 22.719 24.544 26.336 28.214 30.319 31.528 32.912 34.574 36.741 40.113 44.140 46.963 55.475
28 13.565 14.847 16.928 18.939 20.386 21.588 22.657 23.647 25.509 27.336 29.249 31.391 32.620 34.027 35.715 37.916 41.337 45.419 48.278 56.892
29 14.256 15.574 17.708 19.768 21.247 22.475 23.567 24.577 26.475 28.336 30.283 32.461 33.711 35.139 36.854 39.087 42.557 46.693 49.588 58.301
30 14.953 16.306 18.493 20.599 22.110 23.364 24.478 25.508 27.442 29.336 31.316 33.530 34.800 36.250 37.990 40.256 43.773 47.962 50.892 59.702
31 15.655 17.042 19.281 21.434 22.976 24.255 25.390 26.440 28.409 30.336 32.349 34.598 35.887 37.359 39.124 41.422 44.985 49.226 52.191 61.098
32 16.362 17.783 20.072 22.271 23.844 25.148 26.304 27.373 29.376 31.336 33.381 35.665 36.973 38.466 40.256 42.585 46.194 50.487 53.486 62.487
33 17.073 18.527 20.867 23.110 24.714 26.042 27.219 28.307 30.344 32.336 34.413 36.731 38.058 39.572 41.386 43.745 47.400 51.743 54.775 63.869
34 17.789 19.275 21.664 23.952 25.586 26.938 28.136 29.242 31.313 33.336 35.444 37.795 39.141 40.676 42.514 44.903 48.602 52.995 56.061 65.247
35 18.509 20.027 22.465 24.797 26.460 27.836 29.054 30.178 32.282 34.336 36.475 38.859 40.223 41.778 43.640 46.059 49.802 54.244 57.342 66.619
36 19.233 20.783 23.269 25.643 27.336 28.735 29.973 31.115 33.252 35.336 37.505 39.922 41.304 42.879 44.764 47.212 50.998 55.489 58.619 67.985
37 19.960 21.542 24.075 26.492 28.214 29.635 30.893 32.053 34.222 36.336 38.535 40.984 42.383 43.978 45.886 48.363 52.192 56.730 59.893 69.348
38 20.691 22.304 24.884 27.343 29.093 30.537 31.815 32.992 35.192 37.335 39.564 42.045 43.462 45.076 47.007 49.513 53.384 57.969 61.162 70.704
39 21.426 23.069 25.695 28.196 29.974 31.441 32.737 33.932 36.163 38.335 40.593 43.105 44.539 46.173 48.126 50.660 54.572 59.204 62.428 72.055
40 22.164 23.838 26.509 29.051 30.856 32.345 33.660 34.872 37.134 39.335 41.622 44.165 45.616 47.269 49.244 51.805 55.758 60.436 63.691 73.403
41 22.906 24.609 27.326 29.907 31.740 33.251 34.585 35.813 38.105 40.335 42.651 45.224 46.692 48.363 50.360 52.949 56.942 61.665 64.950 74.744
42 23.650 25.383 28.144 30.765 32.626 34.157 35.510 36.755 39.077 41.335 43.679 46.282 47.766 49.456 51.475 54.090 58.124 62.892 66.206 76.084
43 24.398 26.159 28.965 31.625 33.512 35.065 36.436 37.698 40.050 42.335 44.706 47.339 48.840 50.548 52.588 55.230 59.304 64.116 67.459 77.418
44 25.148 26.939 29.787 32.487 34.400 35.974 37.363 38.641 41.022 43.335 45.734 48.396 49.913 51.639 53.700 56.369 60.481 65.337 68.710 78.749
45 25.901 27.720 30.612 33.350 35.290 36.884 38.291 39.585 41.995 44.335 46.761 49.452 50.985 52.729 54.810 57.505 61.656 66.555 69.957 80.078
46 26.657 28.504 31.439 34.215 36.180 37.795 39.220 40.529 42.968 45.335 47.787 50.507 52.056 53.818 55.920 58.641 62.830 67.771 71.201 81.400
47 27.416 29.291 32.268 35.081 37.072 38.708 40.149 41.474 43.942 46.335 48.814 51.562 53.127 54.906 57.028 59.774 64.001 68.985 72.443 82.720
48 28.177 30.080 33.098 35.949 37.965 39.621 41.079 42.420 44.915 47.335 49.840 52.616 54.196 55.993 58.135 60.907 65.171 70.197 73.683 84.037
49 28.941 30.871 33.930 36.818 38.859 40.534 42.010 43.366 45.889 48.335 50.866 53.670 55.265 57.079 59.241 62.038 66.339 71.406 74.919 85.350
50 29.707 31.664 34.764 37.689 39.754 41.449 42.942 44.313 46.864 49.335 51.892 54.723 56.334 58.164 60.346 63.167 67.505 72.613 76.154 86.660
51 30.475 32.459 35.600 38.560 40.650 42.365 43.874 45.261 47.838 50.335 52.917 55.775 57.401 59.248 61.450 64.295 68.669 73.818 77.386 87.967
52 31.246 33.256 36.437 39.433 41.547 43.281 44.807 46.209 48.813 51.335 53.942 56.827 58.468 60.332 62.553 65.422 69.832 75.021 78.616 89.272
53 32.019 34.055 37.276 40.308 42.446 44.199 45.741 47.157 49.788 52.335 54.967 57.879 59.534 61.414 63.654 66.548 70.993 76.223 79.843 90.573
54 32.793 34.856 38.116 41.183 43.345 45.117 46.676 48.106 50.764 53.335 55.992 58.930 60.600 62.496 64.755 67.673 72.153 77.422 81.069 91.871
55 33.571 35.659 38.958 42.060 44.245 46.036 47.610 49.055 51.739 54.335 57.016 59.980 61.665 63.577 65.855 68.796 73.311 78.619 82.292 93.167
56 34.350 36.464 39.801 42.937 45.146 46.955 48.546 50.005 52.715 55.335 58.040 61.031 62.729 64.658 66.954 69.919 74.468 79.815 83.514 94.462
57 35.131 37.270 40.646 43.816 46.048 47.876 49.482 50.956 53.691 56.335 59.064 62.080 63.793 65.737 68.052 71.040 75.624 81.009 84.733 95.750
58 35.914 38.078 41.492 44.696 46.951 48.797 50.419 51.906 54.667 57.335 60.088 63.129 64.857 66.816 69.149 72.160 76.778 82.201 85.950 97.038
59 36.698 38.888 42.339 45.577 47.854 49.718 51.356 52.858 55.643 58.335 61.111 64.178 65.919 67.894 70.246 73.279 77.930 83.391 87.166 98.324
60 37.485 39.699 43.188 46.459 48.759 50.641 52.294 53.809 56.620 59.335 62.135 65.226 66.981 68.972 71.341 74.397 79.082 84.580 88.379 99.608
61 38.273 40.512 44.038 47.342 49.664 51.564 53.232 54.761 57.597 60.335 63.158 66.274 68.043 70.049 72.436 75.514 80.232 85.767 89.591 100.887
62 39.063 41.327 44.889 48.226 50.570 52.487 54.171 55.714 58.574 61.335 64.181 67.322 69.104 71.125 73.530 76.630 81.381 86.953 90.802 102.165
63 39.855 42.143 45.741 49.111 51.477 53.412 55.110 56.666 59.551 62.335 65.204 68.369 70.165 72.201 74.623 77.745 82.529 88.137 92.010 103.442
64 40.649 42.960 46.595 49.996 52.384 54.336 56.050 57.620 60.528 63.335 66.226 69.416 71.225 73.276 75.715 78.860 83.675 89.320 93.217 104.717
65 41.444 43.779 47.450 50.883 53.293 55.262 56.990 58.573 61.506 64.335 67.249 70.462 72.285 74.351 76.807 79.973 84.821 90.501 94.422 105.988
66 42.240 44.599 48.305 51.770 54.202 56.188 57.931 59.527 62.484 65.335 68.271 71.508 73.344 75.424 77.898 81.085 85.965 91.681 95.626 107.257
67 43.038 45.421 49.162 52.659 55.111 57.115 58.872 60.481 63.461 66.335 69.293 72.554 74.403 76.498 78.988 82.197 87.108 92.860 96.828 108.525
68 43.838 46.244 50.020 53.548 56.022 58.042 59.814 61.436 64.440 67.335 70.315 73.600 75.461 77.571 80.078 83.308 88.250 94.037 98.028 109.793
69 44.639 47.068 50.879 54.438 56.933 58.970 60.756 62.391 65.418 68.334 71.337 74.645 76.519 78.643 81.167 84.418 89.391 95.213 99.227 111.055
70 45.442 47.893 51.739 55.329 57.844 59.898 61.698 63.346 66.396 69.334 72.358 75.689 77.577 79.715 82.255 85.527 90.531 96.387 100.425 112.317
71 46.246 48.720 52.600 56.221 58.757 60.827 62.641 64.302 67.375 70.334 73.380 76.734 78.634 80.786 83.343 86.635 91.670 97.561 101.621 113.577
72 47.051 49.548 53.462 57.113 59.670 61.756 63.585 65.258 68.353 71.334 74.401 77.778 79.690 81.857 84.430 87.743 92.808 98.733 102.816 114.834
73 47.858 50.377 54.325 58.006 60.583 62.686 64.528 66.214 69.332 72.334 75.422 78.821 80.747 82.927 85.517 88.850 93.945 99.904 104.010 116.092
74 48.666 51.208 55.189 58.900 61.497 63.616 65.472 67.170 70.311 73.334 76.443 79.865 81.803 83.997 86.602 89.956 95.081 101.074 105.202 117.347
75 49.475 52.039 56.054 59.795 62.412 64.547 66.417 68.127 71.290 74.334 77.464 80.908 82.858 85.066 87.688 91.061 96.217 102.243 106.393 118.599
76 50.286 52.872 56.920 60.690 63.327 65.478 67.362 69.084 72.270 75.334 78.485 81.951 83.913 86.135 88.772 92.166 97.351 103.410 107.582 119.850
77 51.097 53.705 57.786 61.586 64.243 66.409 68.307 70.042 73.249 76.334 79.505 82.994 84.968 87.203 89.857 93.270 98.484 104.576 108.771 121.101
78 51.910 54.540 58.654 62.483 65.159 67.341 69.252 70.999 74.228 77.334 80.526 84.036 86.022 88.271 90.940 94.374 99.617 105.742 109.958 122.347
79 52.725 55.376 59.522 63.380 66.076 68.274 70.198 71.957 75.208 78.334 81.546 85.078 87.077 89.338 92.023 95.476 100.749 106.906 111.144 123.595
80 53.540 56.213 60.391 64.278 66.994 69.207 71.145 72.915 76.188 79.334 82.566 86.120 88.130 90.405 93.106 96.578 101.879 108.069 112.329 124.839
81 54.357 57.051 61.262 65.176 67.912 70.140 72.091 73.874 77.168 80.334 83.586 87.161 89.184 91.472 94.188 97.680 103.010 109.231 113.512 126.084
82 55.174 57.890 62.132 66.076 68.830 71.074 73.038 74.833 78.148 81.334 84.606 88.202 90.237 92.538 95.269 98.780 104.139 110.393 114.695 127.324
83 55.993 58.730 63.004 66.976 69.749 72.008 73.985 75.792 79.128 82.334 85.626 89.243 91.289 93.604 96.350 99.880 105.267 111.553 115.876 128.565
84 56.813 59.570 63.876 67.876 70.669 72.943 74.933 76.751 80.108 83.334 86.646 90.284 92.342 94.669 97.431 100.980 106.395 112.712 117.057 129.802
85 57.634 60.412 64.749 68.777 71.589 73.878 75.881 77.710 81.089 84.334 87.665 91.325 93.394 95.734 98.511 102.079 107.522 113.871 118.236 131.043
86 58.456 61.255 65.623 69.679 72.509 73.813 76.829 78.670 82.069 85.334 88.685 92.365 94.446 96.799 99.590 103.177 108.648 115.028 119.414 132.276
87 59.279 62.098 66.498 70.581 73.430 75.749 77.777 79.630 83.050 86.334 89.704 93.405 95.497 97.863 100.669 104.275 109.773 116.184 120.591 133.511
88 60.103 62.943 67.373 71.484 73.351 76.685 78.726 80.590 84.031 87.334 90.723 94.445 96.548 98.927 101.748 105.372 110.898 117.340 121.767 134.746
89 60.928 63.788 68.249 72.387 75.273 77.622 79.675 81.550 85.012 88.334 91.742 95.484 97.599 99.991 102.826 106.469 112.022 118.495 122.942 135.977
90 61.754 64.635 69.126 73.291 76.195 78.558 80.625 82.511 85.993 89.334 92.761 96.524 98.650 101.054 103.904 107.565 113.145 119.648 124.116 137.208
91 62.581 65.482 70.003 73.196 77.118 79.496 81.574 83.472 86.974 90.334 93.780 97.563 99.700 102.117 104.981 108.661 114.268 120.801 125.289 138.437
92 63.409 66.330 70.882 75.100 78.041 80.433 82.524 84.433 87.955 91.334 94.799 98.602 100.750 103.179 106.058 109.756 115.390 121.953 126.462 139.667
93 64.238 67.179 71.760 76.006 78.965 81.371 83.474 85.394 88.936 92.334 95.818 99.641 101.800 104.241 107.135 110.850 116.511 123.105 127.633 140.894
94 65.068 68.028 72.640 76.912 79.889 82.309 84.425 86.356 89.917 93.334 96.836 100.679 102.850 105.303 108.211 111.944 117.632 124.255 128.803 142.118
95 65.898 68.879 73.520 77.818 80.813 83.248 85.376 87.317 90.899 94.334 97.855 101.717 103.899 106.364 109.286 113.038 118.752 125.405 129.973 143.343
96 66.730 69.730 73.401 78.725 81.738 84.187 86.327 88.279 91.881 95.334 98.873 102.755 104.948 107.425 110.362 114.131 119.871 126.554 131.141 144.566
97 67.562 70.582 75.282 79.633 82.663 85.126 87.278 89.241 92.862 96.334 99.892 103.793 105.997 108.486 111.437 115.223 120.990 127.702 132.309 145.789
98 68.396 71.434 76.164 80.541 83.588 86.065 88.229 90.204 93.844 97.334 100.910 104.831 107.045 109.547 112.511 116.315 122.108 128.849 133.476 147.009
99 69.230 72.288 77.046 81.449 84.514 87.005 89.181 91.166 94.826 98.334 101.928 105.868 108.093 110.607 113.585 117.407 123.225 129.996 134.641 148.230
100 70.065 73.142 77.929 82.358 85.441 87.945 90.133 92.129 95.808 99.334 102.946 106.906 109.141 111.667 114.659 118.498 124.342 131.142 135.807 149.449

Pour ν > 100,

 

 

 

 

 

 

 

 

 

Table de la Loi de Student
Cette table donne les fractiles de la loi de Student à ν degrés de liberté : valeur t ayant la probabilité α d'être dépassée en valeur absolue : P ( - t < T < t ) = 1 - α.
Ou : P ( T < - t ) = α / 2 = P ( T > t )
  α bilatéral   1 - α / 2 (unilatéral)   ν (degré de liberté)
  0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.02 0.01 0.005 0.001
  0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 0.975 0.99 0.995 0.9975 0.9995
                             
1 0.1584 0.3249 0.5095 0.7265 1 1.3764 1.9626 3.0777 6.3137 12.706 31.821 63.656 127.32 636.58
2 0.1421 0.2887 0.4447 0.6172 0.8165 1.0607 1.3862 1.8856 2.92 4.3027 6.9645 9.925 14.089 31.6
3 0.1366 0.2767 0.4242 0.5844 0.7649 0.9785 1.2498 1.6377 2.3534 3.1824 4.5407 5.8408 7.4532 12.924
4 0.1338 0.2707 0.4142 0.5686 0.7407 0.941 1.1896 1.5332 2.1318 2.7765 3.7469 4.6041 5.5975 8.6101
5 0.1322 0.2672 0.4082 0.5594 0.7267 0.9195 1.1558 1.4759 2.015 2.5706 3.3649 4.0321 4.7733 6.8685
6 0.1311 0.2648 0.4043 0.5534 0.7176 0.9057 1.1342 1.4398 1.9432 2.4469 3.1427 3.7074 4.3168 5.9587
7 0.1303 0.2632 0.4015 0.5491 0.7111 0.896 1.1192 1.4149 1.8946 2.3646 2.9979 3.4995 4.0294 5.4081
8 0.1297 0.2619 0.3995 0.5459 0.7064 0.8889 1.1081 1.3968 1.8595 2.306 2.8965 3.3554 3.8325 5.0414
9 0.1293 0.261 0.3979 0.5435 0.7027 0.8834 1.0997 1.383 1.8331 2.2622 2.8214 3.2498 3.6896 4.7809
10 0.1289 0.2602 0.3966 0.5415 0.6998 0.8791 1.0931 1.3722 1.8125 2.2281 2.7638 3.1693 3.5814 4.5868
11 0.1286 0.2596 0.3956 0.5399 0.6974 0.8755 1.0877 1.3634 1.7959 2.201 2.7181 3.1058 3.4966 4.4369
12 0.1283 0.259 0.3947 0.5386 0.6955 0.8726 1.0832 1.3562 1.7823 2.1788 2.681 3.0545 3.4284 4.3178
13 0.1281 0.2586 0.394 0.5375 0.6938 0.8702 1.0795 1.3502 1.7709 2.1604 2.6503 3.0123 3.3725 4.2209
14 0.128 0.2582 0.3933 0.5366 0.6924 0.8681 1.0763 1.345 1.7613 2.1448 2.6245 2.9768 3.3257 4.1403
15 0.1278 0.2579 0.3928 0.5357 0.6912 0.8662 1.0735 1.3406 1.7531 2.1315 2.6025 2.9467 3.286 4.0728
16 0.1277 0.2576 0.3923 0.535 0.6901 0.8647 1.0711 1.3368 1.7459 2.1199 2.5835 2.9208 3.252 4.0149
17 0.1276 0.2573 0.3919 0.5344 0.6892 0.8633 1.069 1.3334 1.7396 2.1098 2.5669 2.8982 3.2224 3.9651
18 0.1274 0.2571 0.3915 0.5338 0.6884 0.862 1.0672 1.3304 1.7341 2.1009 2.5524 2.8784 3.1966 3.9217
19 0.1274 0.2569 0.3912 0.5333 0.6876 0.861 1.0655 1.3277 1.7291 2.093 2.5395 2.8609 3.1737 3.8833
20 0.1273 0.2567 0.3909 0.5329 0.687 0.86 1.064 1.3253 1.7247 2.086 2.528 2.8453 3.1534 3.8496
21 0.1272 0.2566 0.3906 0.5325 0.6864 0.8591 1.0627 1.3232 1.7207 2.0796 2.5176 2.8314 3.1352 3.8193
22 0.1271 0.2564 0.3904 0.5321 0.6858 0.8583 1.0614 1.3212 1.7171 2.0739 2.5083 2.8188 3.1188 3.7922
23 0.1271 0.2563 0.3902 0.5317 0.6853 0.8575 1.0603 1.3195 1.7139 2.0687 2.4999 2.8073 3.104 3.7676
24 0.127 0.2562 0.39 0.5314 0.6848 0.8569 1.0593 1.3178 1.7109 2.0639 2.4922 2.797 3.0905 3.7454
25 0.1269 0.2561 0.3898 0.5312 0.6844 0.8562 1.0584 1.3163 1.7081 2.0595 2.4851 2.7874 3.0782 3.7251
26 0.1269 0.256 0.3896 0.5309 0.684 0.8557 1.0575 1.315 1.7056 2.0555 2.4786 2.7787 3.0669 3.7067
27 0.1268 0.2559 0.3894 0.5306 0.6837 0.8551 1.0567 1.3137 1.7033 2.0518 2.4727 2.7707 3.0565 3.6895
28 0.1268 0.2558 0.3893 0.5304 0.6834 0.8546 1.056 1.3125 1.7011 2.0484 2.4671 2.7633 3.047 3.6739
29 0.1268 0.2557 0.3892 0.5302 0.683 0.8542 1.0553 1.3114 1.6991 2.0452 2.462 2.7564 3.038 3.6595
30 0.1267 0.2556 0.389 0.53 0.6828 0.8538 1.0547 1.3104 1.6973 2.0423 2.4573 2.75 3.0298 3.646
31 0.1267 0.2555 0.3889 0.5298 0.6825 0.8534 1.0541 1.3095 1.6955 2.0395 2.4528 2.744 3.0221 3.6335
32 0.1267 0.2555 0.3888 0.5297 0.6822 0.853 1.0535 1.3086 1.6939 2.0369 2.4487 2.7385 3.0149 3.6218
33 0.1266 0.2554 0.3887 0.5295 0.682 0.8526 1.053 1.3077 1.6924 2.0345 2.4448 2.7333 3.0082 3.6109
34 0.1266 0.2553 0.3886 0.5294 0.6818 0.8523 1.0525 1.307 1.6909 2.0322 2.4411 2.7284 3.002 3.6007
35 0.1266 0.2553 0.3885 0.5292 0.6816 0.852 1.052 1.3062 1.6896 2.0301 2.4377 2.7238 2.9961 3.5911
36 0.1266 0.2552 0.3884 0.5291 0.6814 0.8517 1.0516 1.3055 1.6883 2.0281 2.4345 2.7195 2.9905 3.5821
37 0.1265 0.2552 0.3883 0.5289 0.6812 0.8514 1.0512 1.3049 1.6871 2.0262 2.4314 2.7154 2.9853 3.5737
38 0.1265 0.2551 0.3882 0.5288 0.681 0.8512 1.0508 1.3042 1.686 2.0244 2.4286 2.7116 2.9803 3.5657
39 0.1265 0.2551 0.3882 0.5287 0.6808 0.8509 1.0504 1.3036 1.6849 2.0227 2.4258 2.7079 2.9756 3.5581
40 0.1265 0.255 0.3881 0.5286 0.6807 0.8507 1.05 1.3031 1.6839 2.0211 2.4233 2.7045 2.9712 3.551
41 0.1264 0.255 0.388 0.5285 0.6805 0.8505 1.0497 1.3025 1.6829 2.0195 2.4208 2.7012 2.967 3.5443
42 0.1264 0.255 0.388 0.5284 0.6804 0.8503 1.0494 1.302 1.682 2.0181 2.4185 2.6981 2.963 3.5377
43 0.1264 0.2549 0.3879 0.5283 0.6802 0.8501 1.0491 1.3016 1.6811 2.0167 2.4163 2.6951 2.9592 3.5316
44 0.1264 0.2549 0.3878 0.5282 0.6801 0.8499 1.0488 1.3011 1.6802 2.0154 2.4141 2.6923 2.9555 3.5258
45 0.1264 0.2549 0.3878 0.5281 0.68 0.8497 1.0485 1.3007 1.6794 2.0141 2.4121 2.6896 2.9521 3.5203
46 0.1264 0.2548 0.3877 0.5281 0.6799 0.8495 1.0482 1.3002 1.6787 2.0129 2.4102 2.687 2.9488 3.5149
47 0.1263 0.2548 0.3877 0.528 0.6797 0.8493 1.048 1.2998 1.6779 2.0117 2.4083 2.6846 2.9456 3.5099
48 0.1263 0.2548 0.3876 0.5279 0.6796 0.8492 1.0478 1.2994 1.6772 2.0106 2.4066 2.6822 2.9426 3.505
49 0.1263 0.2547 0.3876 0.5278 0.6795 0.849 1.0475 1.2991 1.6766 2.0096 2.4049 2.68 2.9397 3.5005
50 0.1263 0.2547 0.3875 0.5278 0.6794 0.8489 1.0473 1.2987 1.6759 2.0086 2.4033 2.6778 2.937 3.496
60 0.1262 0.2545 0.3872 0.5272 0.6786 0.8477 1.0455 1.2958 1.6706 2.0003 2.3901 2.6603 2.9146 3.4602
70 0.1261 0.2543 0.3869 0.5268 0.678 0.8468 1.0442 1.2938 1.6669 1.9944 2.3808 2.6479 2.8987 3.435
80 0.1261 0.2542 0.3867 0.5265 0.6776 0.8461 1.0432 1.2922 1.6641 1.9901 2.3739 2.6387 2.887 3.4164
90 0.126 0.2541 0.3866 0.5263 0.6772 0.8456 1.0424 1.291 1.662 1.9867 2.3685 2.6316 2.8779 3.4019
100 0.126 0.254 0.3864 0.5261 0.677 0.8452 1.0418 1.2901 1.6602 1.984 2.3642 2.6259 2.8707 3.3905
110 0.126 0.254 0.3863 0.5259 0.6767 0.8449 1.0413 1.2893 1.6588 1.9818 2.3607 2.6213 2.8648 3.3811
120 0.1259 0.2539 0.3862 0.5258 0.6765 0.8446 1.0409 1.2886 1.6576 1.9799 2.3578 2.6174 2.8599 3.3734
130 0.1259 0.2539 0.3862 0.5257 0.6764 0.8444 1.0406 1.2881 1.6567 1.9784 2.3554 2.6142 2.8557 3.367
140 0.1259 0.2538 0.3861 0.5256 0.6762 0.8442 1.0403 1.2876 1.6558 1.9771 2.3533 2.6114 2.8522 3.3613
infini (loi normale) 0.1257 0.2533 0.3853 0.5244 0.6744 0.8416 1.0364 1.2816 1.6449 1.96 2.3264 2.5759 2.8072 3.2908

 

 

 

 

 

Table : Loi de Fisher-Snedecor
Valeur f de la variable de Fisher-Snedecor F ( ν1 ; ν2 ) ayant la probabilité 0.05 d'être dépassée
ν1 : degrés de liberté du numérateur
ν2 : degrés de liberté du dénominateur
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 35 40 45 50 60 80 100 200 500 1000
1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 242.98 243.90 244.69 245.36 245.95 246.47 246.92 247.32 247.69 248.02 248.58 249.05 249.45 249.80 250.10 250.69 251.14 251.49 251.77 252.20 252.72 253.04 253.68 254.06 254.19
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.40 19.41 19.42 19.42 19.43 19.43 19.44 19.44 19.44 19.45 19.45 19.45 19.46 19.46 19.46 19.47 19.47 19.47 19.48 19.48 19.48 19.49 19.49 19.49 19.49
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.76 8.74 8.73 8.71 8.70 8.69 8.68 8.67 8.67 8.66 8.65 8.64 8.63 8.62 8.62 8.60 8.59 8.59 8.58 8.57 8.56 8.55 8.54 8.53 8.53
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.94 5.91 5.89 5.87 5.86 5.84 5.83 5.82 5.81 5.80 5.79 5.77 5.76 5.75 5.75 5.73 5.72 5.71 5.70 5.69 5.67 5.66 5.65 5.64 5.63
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.70 4.68 4.66 4.64 4.62 4.60 4.59 4.58 4.57 4.56 4.54 4.53 4.52 4.50 4.50 4.48 4.46 4.45 4.44 4.43 4.41 4.41 4.39 4.37 4.37
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.03 4.00 3.98 3.96 3.94 3.92 3.91 3.90 3.88 3.87 3.86 3.84 3.83 3.82 3.81 3.79 3.77 3.76 3.75 3.74 3.72 3.71 3.69 3.68 3.67
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.60 3.57 3.55 3.53 3.51 3.49 3.48 3.47 3.46 3.44 3.43 3.41 3.40 3.39 3.38 3.36 3.34 3.33 3.32 3.30 3.29 3.27 3.25 3.24 3.23
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.31 3.28 3.26 3.24 3.22 3.20 3.19 3.17 3.16 3.15 3.13 3.12 3.10 3.09 3.08 3.06 3.04 3.03 3.02 3.01 2.99 2.97 2.95 2.94 2.93
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.10 3.07 3.05 3.03 3.01 2.99 2.97 2.96 2.95 2.94 2.92 2.90 2.89 2.87 2.86 2.84 2.83 2.81 2.80 2.79 2.77 2.76 2.73 2.72 2.71
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.94 2.91 2.89 2.86 2.85 2.83 2.81 2.80 2.79 2.77 2.75 2.74 2.72 2.71 2.70 2.68 2.66 2.65 2.64 2.62 2.60 2.59 2.56 2.55 2.54
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.69 2.67 2.66 2.65 2.63 2.61 2.59 2.58 2.57 2.55 2.53 2.52 2.51 2.49 2.47 2.46 2.43 2.42 2.41
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.72 2.69 2.66 2.64 2.62 2.60 2.58 2.57 2.56 2.54 2.52 2.51 2.49 2.48 2.47 2.44 2.43 2.41 2.40 2.38 2.36 2.35 2.32 2.31 2.30
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.63 2.60 2.58 2.55 2.53 2.51 2.50 2.48 2.47 2.46 2.44 2.42 2.41 2.39 2.38 2.36 2.34 2.33 2.31 2.30 2.27 2.26 2.23 2.22 2.21
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.57 2.53 2.51 2.48 2.46 2.44 2.43 2.41 2.40 2.39 2.37 2.35 2.33 2.32 2.31 2.28 2.27 2.25 2.24 2.22 2.20 2.19 2.16 2.14 2.14
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.51 2.48 2.45 2.42 2.40 2.38 2.37 2.35 2.34 2.33 2.31 2.29 2.27 2.26 2.25 2.22 2.20 2.19 2.18 2.16 2.14 2.12 2.10 2.08 2.07
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.46 2.42 2.40 2.37 2.35 2.33 2.32 2.30 2.29 2.28 2.25 2.24 2.22 2.21 2.19 2.17 2.15 2.14 2.12 2.11 2.08 2.07 2.04 2.02 2.02
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.41 2.38 2.35 2.33 2.31 2.29 2.27 2.26 2.24 2.23 2.21 2.19 2.17 2.16 2.15 2.12 2.10 2.09 2.08 2.06 2.03 2.02 1.99 1.97 1.97
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.37 2.34 2.31 2.29 2.27 2.25 2.23 2.22 2.20 2.19 2.17 2.15 2.13 2.12 2.11 2.08 2.06 2.05 2.04 2.02 1.99 1.98 1.95 1.93 1.92
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.34 2.31 2.28 2.26 2.23 2.21 2.20 2.18 2.17 2.16 2.13 2.11 2.10 2.08 2.07 2.05 2.03 2.01 2.00 1.98 1.96 1.94 1.91 1.89 1.88
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.31 2.28 2.25 2.22 2.20 2.18 2.17 2.15 2.14 2.12 2.10 2.08 2.07 2.05 2.04 2.01 1.99 1.98 1.97 1.95 1.92 1.91 1.88 1.86 1.85
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.28 2.25 2.22 2.20 2.18 2.16 2.14 2.12 2.11 2.10 2.07 2.05 2.04 2.02 2.01 1.98 1.96 1.95 1.94 1.92 1.89 1.88 1.84 1.83 1.82
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.26 2.23 2.20 2.17 2.15 2.13 2.11 2.10 2.08 2.07 2.05 2.03 2.01 2.00 1.98 1.96 1.94 1.92 1.91 1.89 1.86 1.85 1.82 1.80 1.79
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.24 2.20 2.18 2.15 2.13 2.11 2.09 2.08 2.06 2.05 2.02 2.01 1.99 1.97 1.96 1.93 1.91 1.90 1.88 1.86 1.84 1.82 1.79 1.77 1.76
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.22 2.18 2.15 2.13 2.11 2.09 2.07 2.05 2.04 2.03 2.00 1.98 1.97 1.95 1.94 1.91 1.89 1.88 1.86 1.84 1.82 1.80 1.77 1.75 1.74
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.20 2.16 2.14 2.11 2.09 2.07 2.05 2.04 2.02 2.01 1.98 1.96 1.95 1.93 1.92 1.89 1.87 1.86 1.84 1.82 1.80 1.78 1.75 1.73 1.72
26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.18 2.15 2.12 2.09 2.07 2.05 2.03 2.02 2.00 1.99 1.97 1.95 1.93 1.91 1.90 1.87 1.85 1.84 1.82 1.80 1.78 1.76 1.73 1.71 1.70
27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.17 2.13 2.10 2.08 2.06 2.04 2.02 2.00 1.99 1.97 1.95 1.93 1.91 1.90 1.88 1.86 1.84 1.82 1.81 1.79 1.76 1.74 1.71 1.69 1.68
28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.15 2.12 2.09 2.06 2.04 2.02 2.00 1.99 1.97 1.96 1.93 1.91 1.90 1.88 1.87 1.84 1.82 1.80 1.79 1.77 1.74 1.73 1.69 1.67 1.66
29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.14 2.10 2.08 2.05 2.03 2.01 1.99 1.97 1.96 1.94 1.92 1.90 1.88 1.87 1.85 1.83 1.81 1.79 1.77 1.75 1.73 1.71 1.67 1.65 1.65
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.13 2.09 2.06 2.04 2.01 1.99 1.98 1.96 1.95 1.93 1.91 1.89 1.87 1.85 1.84 1.81 1.79 1.77 1.76 1.74 1.71 1.70 1.66 1.64 1.63
32 4.15 3.29 2.90 2.67 2.51 2.40 2.31 2.24 2.19 2.14 2.10 2.07 2.04 2.01 1.99 1.97 1.95 1.94 1.92 1.91 1.88 1.86 1.85 1.83 1.82 1.79 1.77 1.75 1.74 1.71 1.69 1.67 1.63 1.61 1.60
34 4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17 2.12 2.08 2.05 2.02 1.99 1.97 1.95 1.93 1.92 1.90 1.89 1.86 1.84 1.82 1.81 1.80 1.77 1.75 1.73 1.71 1.69 1.66 1.65 1.61 1.59 1.58
36 4.11 3.26 2.87 2.63 2.48 2.36 2.28 2.21 2.15 2.11 2.07 2.03 2.00 1.98 1.95 1.93 1.92 1.90 1.88 1.87 1.85 1.82 1.81 1.79 1.78 1.75 1.73 1.71 1.69 1.67 1.64 1.62 1.59 1.56 1.56
38 4.10 3.24 2.85 2.62 2.46 2.35 2.26 2.19 2.14 2.09 2.05 2.02 1.99 1.96 1.94 1.92 1.90 1.88 1.87 1.85 1.83 1.81 1.79 1.77 1.76 1.73 1.71 1.69 1.68 1.65 1.62 1.61 1.57 1.54 1.54
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.04 2.00 1.97 1.95 1.92 1.90 1.89 1.87 1.85 1.84 1.81 1.79 1.77 1.76 1.74 1.72 1.69 1.67 1.66 1.64 1.61 1.59 1.55 1.53 1.52
42 4.07 3.22 2.83 2.59 2.44 2.32 2.24 2.17 2.11 2.06 2.03 1.99 1.96 1.94 1.91 1.89 1.87 1.86 1.84 1.83 1.80 1.78 1.76 1.75 1.73 1.70 1.68 1.66 1.65 1.62 1.59 1.57 1.53 1.51 1.50
44 4.06 3.21 2.82 2.58 2.43 2.31 2.23 2.16 2.10 2.05 2.01 1.98 1.95 1.92 1.90 1.88 1.86 1.84 1.83 1.81 1.79 1.77 1.75 1.73 1.72 1.69 1.67 1.65 1.63 1.61 1.58 1.56 1.52 1.49 1.49
46 4.05 3.20 2.81 2.57 2.42 2.30 2.22 2.15 2.09 2.04 2.00 1.97 1.94 1.91 1.89 1.87 1.85 1.83 1.82 1.80 1.78 1.76 1.74 1.72 1.71 1.68 1.65 1.64 1.62 1.60 1.57 1.55 1.51 1.48 1.47
48 4.04 3.19 2.80 2.57 2.41 2.29 2.21 2.14 2.08 2.03 1.99 1.96 1.93 1.90 1.88 1.86 1.84 1.82 1.81 1.79 1.77 1.75 1.73 1.71 1.70 1.67 1.64 1.62 1.61 1.59 1.56 1.54 1.49 1.47 1.46
50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03 1.99 1.95 1.92 1.89 1.87 1.85 1.83 1.81 1.80 1.78 1.76 1.74 1.72 1.70 1.69 1.66 1.63 1.61 1.60 1.58 1.54 1.52 1.48 1.46 1.45
55 4.02 3.16 2.77 2.54 2.38 2.27 2.18 2.11 2.06 2.01 1.97 1.93 1.90 1.88 1.85 1.83 1.81 1.79 1.78 1.76 1.74 1.72 1.70 1.68 1.67 1.64 1.61 1.59 1.58 1.55 1.52 1.50 1.46 1.43 1.42
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.95 1.92 1.89 1.86 1.84 1.82 1.80 1.78 1.76 1.75 1.72 1.70 1.68 1.66 1.65 1.62 1.59 1.57 1.56 1.53 1.50 1.48 1.44 1.41 1.40
65 3.99 3.14 2.75 2.51 2.36 2.24 2.15 2.08 2.03 1.98 1.94 1.90 1.87 1.85 1.82 1.80 1.78 1.76 1.75 1.73 1.71 1.69 1.67 1.65 1.63 1.60 1.58 1.56 1.54 1.52 1.49 1.46 1.42 1.39 1.38
70 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.07 2.02 1.97 1.93 1.89 1.86 1.84 1.81 1.79 1.77 1.75 1.74 1.72 1.70 1.67 1.65 1.64 1.62 1.59 1.57 1.55 1.53 1.50 1.47 1.45 1.40 1.37 1.36
75 3.97 3.12 2.73 2.49 2.34 2.22 2.13 2.06 2.01 1.96 1.92 1.88 1.85 1.83 1.80 1.78 1.76 1.74 1.73 1.71 1.69 1.66 1.64 1.63 1.61 1.58 1.55 1.53 1.52 1.49 1.46 1.44 1.39 1.36 1.35
80 3.96 3.11 2.72 2.49 2.33 2.21 2.13 2.06 2.00 1.95 1.91 1.88 1.84 1.82 1.79 1.77 1.75 1.73 1.72 1.70 1.68 1.65 1.63 1.62 1.60 1.57 1.54 1.52 1.51 1.48 1.45 1.43 1.38 1.35 1.34
85 3.95 3.10 2.71 2.48 2.32 2.21 2.12 2.05 1.99 1.94 1.90 1.87 1.84 1.81 1.79 1.76 1.74 1.73 1.71 1.70 1.67 1.65 1.63 1.61 1.59 1.56 1.54 1.52 1.50 1.47 1.44 1.42 1.37 1.34 1.32
90 3.95 3.10 2.71 2.47 2.32 2.20 2.11 2.04 1.99 1.94 1.90 1.86 1.83 1.80 1.78 1.76 1.74 1.72 1.70 1.69 1.66 1.64 1.62 1.60 1.59 1.55 1.53 1.51 1.49 1.46 1.43 1.41 1.36 1.33 1.31
95 3.94 3.09 2.70 2.47 2.31 2.20 2.11 2.04 1.98 1.93 1.89 1.86 1.82 1.80 1.77 1.75 1.73 1.71 1.70 1.68 1.66 1.63 1.61 1.59 1.58 1.55 1.52 1.50 1.48 1.46 1.42 1.40 1.35 1.32 1.30
100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97 1.93 1.89 1.85 1.82 1.79 1.77 1.75 1.73 1.71 1.69 1.68 1.65 1.63 1.61 1.59 1.57 1.54 1.52 1.49 1.48 1.45 1.41 1.39 1.34 1.31 1.30
125 3.92 3.07 2.68 2.44 2.29 2.17 2.08 2.01 1.96 1.91 1.87 1.83 1.80 1.77 1.75 1.73 1.71 1.69 1.67 1.66 1.63 1.60 1.58 1.57 1.55 1.52 1.49 1.47 1.45 1.42 1.39 1.36 1.31 1.27 1.26
150 3.90 3.06 2.66 2.43 2.27 2.16 2.07 2.00 1.94 1.89 1.85 1.82 1.79 1.76 1.73 1.71 1.69 1.67 1.66 1.64 1.61 1.59 1.57 1.55 1.54 1.50 1.48 1.45 1.44 1.41 1.37 1.34 1.29 1.25 1.24
200 3.89 3.04 2.65 2.42 2.26 2.14 2.06 1.98 1.93 1.88 1.84 1.80 1.77 1.74 1.72 1.69 1.67 1.66 1.64 1.62 1.60 1.57 1.55 1.53 1.52 1.48 1.46 1.43 1.41 1.39 1.35 1.32 1.26 1.22 1.21
300 3.87 3.03 2.63 2.40 2.24 2.13 2.04 1.97 1.91 1.86 1.82 1.78 1.75 1.72 1.70 1.68 1.66 1.64 1.62 1.61 1.58 1.55 1.53 1.51 1.50 1.46 1.43 1.41 1.39 1.36 1.32 1.30 1.23 1.19 1.17
500 3.86 3.01 2.62 2.39 2.23 2.12 2.03 1.96 1.90 1.85 1.81 1.77 1.74 1.71 1.69 1.66 1.64 1.62 1.61 1.59 1.56 1.54 1.52 1.50 1.48 1.45 1.42 1.40 1.38 1.35 1.30 1.28 1.21 1.16 1.14
1000 3.85 3.00 2.61 2.38 2.22 2.11 2.02 1.95 1.89 1.84 1.80 1.76 1.73 1.70 1.68 1.65 1.63 1.61 1.60 1.58 1.55 1.53 1.51 1.49 1.47 1.43 1.41 1.38 1.36 1.33 1.29 1.26 1.19 1.13 1.11
2000 3.85 3.00 2.61 2.38 2.22 2.10 2.01 1.94 1.88 1.84 1.79 1.76 1.73 1.70 1.67 1.65 1.63 1.61 1.59 1.58 1.55 1.52 1.50 1.48 1.46 1.43 1.40 1.38 1.36 1.32 1.28 1.25 1.18 1.12 1.09

 

 

 

Table : Loi de Fisher-Snedecor
Valeur f de la variable de Fisher-Snedecor F ( ν1 ; ν2 ) ayant la probabilité 0.025 d'être dépassée
ν1 : degrés de liberté du numérateur
ν2 : degrés de liberté du dénominateur
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 35 40 45 50 60 80 100 200 500 2000
1 647.79 799.48 864.15 899.60 921.83 937.11 948.20 956.64 963.28 968.63 973.03 976.72 979.84 982.55 984.87 986.91 988.72 990.35 991.80 993.08 995.35 997.27 998.84 1000.24 1001.40 1003.79 1005.60 1006.99 1008.10 1009.79 1011.91 1013.16 1015.72 1017.24 1017.99
2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.41 39.42 39.43 39.43 39.44 39.44 39.44 39.45 39.45 39.45 39.46 39.46 39.46 39.46 39.47 39.47 39.48 39.48 39.48 39.49 39.49 39.49 39.50 39.50
3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.37 14.34 14.30 14.28 14.25 14.23 14.21 14.20 14.18 14.17 14.14 14.12 14.11 14.09 14.08 14.06 14.04 14.02 14.01 13.99 13.97 13.96 13.93 13.91 13.90
4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.79 8.75 8.72 8.68 8.66 8.63 8.61 8.59 8.58 8.56 8.53 8.51 8.49 8.48 8.46 8.43 8.41 8.39 8.38 8.36 8.33 8.32 8.29 8.27 8.26
5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.57 6.52 6.49 6.46 6.43 6.40 6.38 6.36 6.34 6.33 6.30 6.28 6.26 6.24 6.23 6.20 6.18 6.16 6.14 6.12 6.10 6.08 6.05 6.03 6.02
6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.41 5.37 5.33 5.30 5.27 5.24 5.22 5.20 5.18 5.17 5.14 5.12 5.10 5.08 5.07 5.04 5.01 4.99 4.98 4.96 4.93 4.92 4.88 4.86 4.85
7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.71 4.67 4.63 4.60 4.57 4.54 4.52 4.50 4.48 4.47 4.44 4.41 4.39 4.38 4.36 4.33 4.31 4.29 4.28 4.25 4.23 4.21 4.18 4.16 4.15
8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.24 4.20 4.16 4.13 4.10 4.08 4.05 4.03 4.02 4.00 3.97 3.95 3.93 3.91 3.89 3.86 3.84 3.82 3.81 3.78 3.76 3.74 3.70 3.68 3.67
9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.91 3.87 3.83 3.80 3.77 3.74 3.72 3.70 3.68 3.67 3.64 3.61 3.59 3.58 3.56 3.53 3.51 3.49 3.47 3.45 3.42 3.40 3.37 3.35 3.34
10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.66 3.62 3.58 3.55 3.52 3.50 3.47 3.45 3.44 3.42 3.39 3.37 3.34 3.33 3.31 3.28 3.26 3.24 3.22 3.20 3.17 3.15 3.12 3.09 3.08
11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.47 3.43 3.39 3.36 3.33 3.30 3.28 3.26 3.24 3.23 3.20 3.17 3.15 3.13 3.12 3.09 3.06 3.04 3.03 3.00 2.97 2.96 2.92 2.90 2.89
12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.32 3.28 3.24 3.21 3.18 3.15 3.13 3.11 3.09 3.07 3.04 3.02 3.00 2.98 2.96 2.93 2.91 2.89 2.87 2.85 2.82 2.80 2.76 2.74 2.73
13 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.20 3.15 3.12 3.08 3.05 3.03 3.00 2.98 2.96 2.95 2.92 2.89 2.87 2.85 2.84 2.80 2.78 2.76 2.74 2.72 2.69 2.67 2.63 2.61 2.60
14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.09 3.05 3.01 2.98 2.95 2.92 2.90 2.88 2.86 2.84 2.81 2.79 2.77 2.75 2.73 2.70 2.67 2.65 2.64 2.61 2.58 2.56 2.53 2.50 2.49
15 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 3.01 2.96 2.92 2.89 2.86 2.84 2.81 2.79 2.77 2.76 2.73 2.70 2.68 2.66 2.64 2.61 2.59 2.56 2.55 2.52 2.49 2.47 2.44 2.41 2.40
16 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.93 2.89 2.85 2.82 2.79 2.76 2.74 2.72 2.70 2.68 2.65 2.63 2.60 2.58 2.57 2.53 2.51 2.49 2.47 2.45 2.42 2.40 2.36 2.33 2.32
17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.87 2.82 2.79 2.75 2.72 2.70 2.67 2.65 2.63 2.62 2.59 2.56 2.54 2.52 2.50 2.47 2.44 2.42 2.41 2.38 2.35 2.33 2.29 2.26 2.25
18 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.81 2.77 2.73 2.70 2.67 2.64 2.62 2.60 2.58 2.56 2.53 2.50 2.48 2.46 2.44 2.41 2.38 2.36 2.35 2.32 2.29 2.27 2.23 2.20 2.19
19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.76 2.72 2.68 2.65 2.62 2.59 2.57 2.55 2.53 2.51 2.48 2.45 2.43 2.41 2.39 2.36 2.33 2.31 2.30 2.27 2.24 2.22 2.18 2.15 2.14
20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.72 2.68 2.64 2.60 2.57 2.55 2.52 2.50 2.48 2.46 2.43 2.41 2.39 2.37 2.35 2.31 2.29 2.27 2.25 2.22 2.19 2.17 2.13 2.10 2.09
21 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 2.68 2.64 2.60 2.56 2.53 2.51 2.48 2.46 2.44 2.42 2.39 2.37 2.34 2.33 2.31 2.27 2.25 2.23 2.21 2.18 2.15 2.13 2.09 2.06 2.05
22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.65 2.60 2.56 2.53 2.50 2.47 2.45 2.43 2.41 2.39 2.36 2.33 2.31 2.29 2.27 2.24 2.21 2.19 2.17 2.14 2.11 2.09 2.05 2.02 2.01
23 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.62 2.57 2.53 2.50 2.47 2.44 2.42 2.39 2.37 2.36 2.33 2.30 2.28 2.26 2.24 2.20 2.18 2.15 2.14 2.11 2.08 2.06 2.01 1.99 1.97
24 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.59 2.54 2.50 2.47 2.44 2.41 2.39 2.36 2.35 2.33 2.30 2.27 2.25 2.23 2.21 2.17 2.15 2.12 2.11 2.08 2.05 2.02 1.98 1.95 1.94
25 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.56 2.51 2.48 2.44 2.41 2.38 2.36 2.34 2.32 2.30 2.27 2.24 2.22 2.20 2.18 2.15 2.12 2.10 2.08 2.05 2.02 2.00 1.95 1.92 1.91
26 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.54 2.49 2.45 2.42 2.39 2.36 2.34 2.31 2.29 2.28 2.24 2.22 2.19 2.17 2.16 2.12 2.09 2.07 2.05 2.03 1.99 1.97 1.92 1.90 1.88
27 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 2.51 2.47 2.43 2.39 2.36 2.34 2.31 2.29 2.27 2.25 2.22 2.19 2.17 2.15 2.13 2.10 2.07 2.05 2.03 2.00 1.97 1.94 1.90 1.87 1.86
28 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.49 2.45 2.41 2.37 2.34 2.32 2.29 2.27 2.25 2.23 2.20 2.17 2.15 2.13 2.11 2.08 2.05 2.03 2.01 1.98 1.94 1.92 1.88 1.85 1.83
29 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.48 2.43 2.39 2.36 2.32 2.30 2.27 2.25 2.23 2.21 2.18 2.15 2.13 2.11 2.09 2.06 2.03 2.01 1.99 1.96 1.92 1.90 1.86 1.83 1.81
30 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.46 2.41 2.37 2.34 2.31 2.28 2.26 2.23 2.21 2.20 2.16 2.14 2.11 2.09 2.07 2.04 2.01 1.99 1.97 1.94 1.90 1.88 1.84 1.81 1.79
32 5.53 4.15 3.56 3.22 3.00 2.84 2.71 2.62 2.54 2.48 2.43 2.38 2.34 2.31 2.28 2.25 2.22 2.20 2.18 2.16 2.13 2.10 2.08 2.06 2.04 2.00 1.98 1.95 1.93 1.91 1.87 1.85 1.80 1.77 1.75
34 5.50 4.12 3.53 3.19 2.97 2.81 2.69 2.59 2.52 2.45 2.40 2.35 2.31 2.28 2.25 2.22 2.20 2.17 2.15 2.13 2.10 2.07 2.05 2.03 2.01 1.97 1.95 1.92 1.90 1.88 1.84 1.82 1.77 1.74 1.72
36 5.47 4.09 3.50 3.17 2.94 2.78 2.66 2.57 2.49 2.43 2.37 2.33 2.29 2.25 2.22 2.20 2.17 2.15 2.13 2.11 2.08 2.05 2.03 2.00 1.99 1.95 1.92 1.90 1.88 1.85 1.81 1.79 1.74 1.71 1.69
38 5.45 4.07 3.48 3.15 2.92 2.76 2.64 2.55 2.47 2.41 2.35 2.31 2.27 2.23 2.20 2.17 2.15 2.13 2.11 2.09 2.05 2.03 2.00 1.98 1.96 1.93 1.90 1.87 1.85 1.82 1.79 1.76 1.71 1.68 1.67
40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.33 2.29 2.25 2.21 2.18 2.15 2.13 2.11 2.09 2.07 2.03 2.01 1.98 1.96 1.94 1.90 1.88 1.85 1.83 1.80 1.76 1.74 1.69 1.66 1.64
42 5.40 4.03 3.45 3.11 2.89 2.73 2.61 2.51 2.43 2.37 2.32 2.27 2.23 2.20 2.16 2.14 2.11 2.09 2.07 2.05 2.02 1.99 1.96 1.94 1.92 1.89 1.86 1.83 1.81 1.78 1.74 1.72 1.67 1.64 1.62
44 5.39 4.02 3.43 3.09 2.87 2.71 2.59 2.50 2.42 2.36 2.30 2.26 2.22 2.18 2.15 2.12 2.10 2.07 2.05 2.03 2.00 1.97 1.95 1.93 1.91 1.87 1.84 1.82 1.80 1.77 1.73 1.70 1.65 1.62 1.60
46 5.37 4.00 3.42 3.08 2.86 2.70 2.58 2.48 2.41 2.34 2.29 2.24 2.20 2.17 2.13 2.11 2.08 2.06 2.04 2.02 1.99 1.96 1.93 1.91 1.89 1.85 1.82 1.80 1.78 1.75 1.71 1.69 1.63 1.60 1.58
48 5.35 3.99 3.40 3.07 2.84 2.69 2.56 2.47 2.39 2.33 2.27 2.23 2.19 2.15 2.12 2.09 2.07 2.05 2.02 2.01 1.97 1.94 1.92 1.90 1.88 1.84 1.81 1.79 1.77 1.73 1.69 1.67 1.62 1.58 1.57
50 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.38 2.32 2.26 2.22 2.18 2.14 2.11 2.08 2.06 2.03 2.01 1.99 1.96 1.93 1.91 1.89 1.87 1.83 1.80 1.77 1.75 1.72 1.68 1.66 1.60 1.57 1.55
55 5.31 3.95 3.36 3.03 2.81 2.65 2.53 2.43 2.36 2.29 2.24 2.19 2.15 2.11 2.08 2.05 2.03 2.01 1.99 1.97 1.93 1.90 1.88 1.86 1.84 1.80 1.77 1.74 1.72 1.69 1.65 1.62 1.57 1.54 1.52
60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.22 2.17 2.13 2.09 2.06 2.03 2.01 1.98 1.96 1.94 1.91 1.88 1.86 1.83 1.82 1.78 1.74 1.72 1.70 1.67 1.63 1.60 1.54 1.51 1.49
65 5.26 3.91 3.32 2.99 2.77 2.61 2.49 2.39 2.32 2.25 2.20 2.15 2.11 2.07 2.04 2.01 1.99 1.97 1.95 1.93 1.89 1.86 1.84 1.82 1.80 1.76 1.72 1.70 1.68 1.65 1.60 1.58 1.52 1.48 1.46
70 5.25 3.89 3.31 2.97 2.75 2.59 2.47 2.38 2.30 2.24 2.18 2.14 2.10 2.06 2.03 2.00 1.97 1.95 1.93 1.91 1.88 1.85 1.82 1.80 1.78 1.74 1.71 1.68 1.66 1.63 1.59 1.56 1.50 1.46 1.44
75 5.23 3.88 3.30 2.96 2.74 2.58 2.46 2.37 2.29 2.22 2.17 2.12 2.08 2.05 2.01 1.99 1.96 1.94 1.92 1.90 1.86 1.83 1.81 1.78 1.76 1.72 1.69 1.67 1.65 1.61 1.57 1.54 1.48 1.44 1.42
80 5.22 3.86 3.28 2.95 2.73 2.57 2.45 2.35 2.28 2.21 2.16 2.11 2.07 2.03 2.00 1.97 1.95 1.92 1.90 1.88 1.85 1.82 1.79 1.77 1.75 1.71 1.68 1.65 1.63 1.60 1.55 1.53 1.47 1.43 1.41
85 5.21 3.85 3.27 2.94 2.72 2.56 2.44 2.35 2.27 2.20 2.15 2.10 2.06 2.02 1.99 1.96 1.94 1.91 1.89 1.87 1.84 1.81 1.78 1.76 1.74 1.70 1.67 1.64 1.62 1.59 1.54 1.51 1.45 1.41 1.39
90 5.20 3.84 3.26 2.93 2.71 2.55 2.43 2.34 2.26 2.19 2.14 2.09 2.05 2.02 1.98 1.95 1.93 1.91 1.88 1.86 1.83 1.80 1.77 1.75 1.73 1.69 1.66 1.63 1.61 1.58 1.53 1.50 1.44 1.40 1.38
95 5.19 3.84 3.26 2.92 2.70 2.54 2.42 2.33 2.25 2.19 2.13 2.08 2.04 2.01 1.98 1.95 1.92 1.90 1.88 1.86 1.82 1.79 1.77 1.74 1.72 1.68 1.65 1.62 1.60 1.57 1.52 1.49 1.43 1.39 1.37
100 5.18 3.83 3.25 2.92 2.70 2.54 2.42 2.32 2.24 2.18 2.12 2.08 2.04 2.00 1.97 1.94 1.91 1.89 1.87 1.85 1.81 1.78 1.76 1.74 1.71 1.67 1.64 1.61 1.59 1.56 1.51 1.48 1.42 1.38 1.36
125 5.15 3.80 3.22 2.89 2.67 2.51 2.39 2.30 2.22 2.15 2.10 2.05 2.01 1.97 1.94 1.91 1.89 1.86 1.84 1.82 1.79 1.75 1.73 1.71 1.68 1.64 1.61 1.58 1.56 1.52 1.48 1.45 1.38 1.34 1.31
150 5.13 3.78 3.20 2.87 2.65 2.49 2.37 2.28 2.20 2.13 2.08 2.03 1.99 1.95 1.92 1.89 1.87 1.84 1.82 1.80 1.77 1.74 1.71 1.69 1.67 1.62 1.59 1.56 1.54 1.50 1.45 1.42 1.35 1.31 1.28
200 5.10 3.76 3.18 2.85 2.63 2.47 2.35 2.26 2.18 2.11 2.06 2.01 1.97 1.93 1.90 1.87 1.84 1.82 1.80 1.78 1.74 1.71 1.68 1.66 1.64 1.60 1.56 1.53 1.51 1.47 1.42 1.39 1.32 1.27 1.24
300 5.07 3.73 3.16 2.83 2.61 2.45 2.33 2.23 2.16 2.09 2.04 1.99 1.95 1.91 1.88 1.85 1.82 1.80 1.77 1.75 1.72 1.69 1.66 1.64 1.62 1.57 1.54 1.51 1.48 1.45 1.39 1.36 1.28 1.23 1.19
500 5.05 3.72 3.14 2.81 2.59 2.43 2.31 2.22 2.14 2.07 2.02 1.97 1.93 1.89 1.86 1.83 1.80 1.78 1.76 1.74 1.70 1.67 1.64 1.62 1.60 1.55 1.52 1.49 1.46 1.42 1.37 1.34 1.25 1.19 1.15
1000 5.04 3.70 3.13 2.80 2.58 2.42 2.30 2.20 2.13 2.06 2.01 1.96 1.92 1.88 1.85 1.82 1.79 1.77 1.74 1.72 1.69 1.65 1.63 1.60 1.58 1.54 1.50 1.47 1.45 1.41 1.35 1.32 1.23 1.16 1.11
2000 5.03 3.70 3.12 2.79 2.57 2.41 2.29 2.20 2.12 2.05 2.00 1.95 1.91 1.87 1.84 1.81 1.78 1.76 1.74 1.72 1.68 1.65 1.62 1.60 1.57 1.53 1.49 1.46 1.44 1.40 1.34 1.31 1.22 1.15 1.09

 

 

 

Table : Loi de Fisher-Snedecor
Valeur f de la variable de Fisher-Snedecor F ( ν1 ; ν2 ) ayant la probabilité 0.01 d'être dépassée
ν1 : degrés de liberté du numérateur
ν2 : degrés de liberté du dénominateur
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 35 40 45 50 60 80 100 200 500 1000
1 4052.18 4999.34 5403.53 5624.26 5763.96 5858.95 5928.33 5980.95 6022.40 6055.93 6083.40 6106.68 6125.77 6143.00 6156.97 6170.01 6181.19 6191.43 6200.75 6208.66 6223.10 6234.27 6244.52 6252.90 6260.35 6275.25 6286.43 6295.74 6302.26 6312.97 6326.47 6333.92 6349.76 6359.54 6362.80
2 98.50 99.00 99.16 99.25 99.30 99.33 99.36 99.38 99.39 99.40 99.41 99.42 99.42 99.43 99.43 99.44 99.44 99.44 99.45 99.45 99.46 99.46 99.46 99.46 99.47 99.47 99.48 99.48 99.48 99.48 99.48 99.49 99.49 99.50 99.50
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.34 27.23 27.13 27.05 26.98 26.92 26.87 26.83 26.79 26.75 26.72 26.69 26.64 26.60 26.56 26.53 26.50 26.45 26.41 26.38 26.35 26.32 26.27 26.24 26.18 26.15 26.14
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.45 14.37 14.31 14.25 14.20 14.15 14.11 14.08 14.05 14.02 13.97 13.93 13.89 13.86 13.84 13.79 13.75 13.71 13.69 13.65 13.61 13.58 13.52 13.49 13.47
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.96 9.89 9.82 9.77 9.72 9.68 9.64 9.61 9.58 9.55 9.51 9.47 9.43 9.40 9.38 9.33 9.29 9.26 9.24 9.20 9.16 9.13 9.08 9.04 9.03
6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.79 7.72 7.66 7.60 7.56 7.52 7.48 7.45 7.42 7.40 7.35 7.31 7.28 7.25 7.23 7.18 7.14 7.11 7.09 7.06 7.01 6.99 6.93 6.90 6.89
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.54 6.47 6.41 6.36 6.31 6.28 6.24 6.21 6.18 6.16 6.11 6.07 6.04 6.02 5.99 5.94 5.91 5.88 5.86 5.82 5.78 5.75 5.70 5.67 5.66
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.73 5.67 5.61 5.56 5.52 5.48 5.44 5.41 5.38 5.36 5.32 5.28 5.25 5.22 5.20 5.15 5.12 5.09 5.07 5.03 4.99 4.96 4.91 4.88 4.87
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.18 5.11 5.05 5.01 4.96 4.92 4.89 4.86 4.83 4.81 4.77 4.73 4.70 4.67 4.65 4.60 4.57 4.54 4.52 4.48 4.44 4.41 4.36 4.33 4.32
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.77 4.71 4.65 4.60 4.56 4.52 4.49 4.46 4.43 4.41 4.36 4.33 4.30 4.27 4.25 4.20 4.17 4.14 4.12 4.08 4.04 4.01 3.96 3.93 3.92
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.46 4.40 4.34 4.29 4.25 4.21 4.18 4.15 4.12 4.10 4.06 4.02 3.99 3.96 3.94 3.89 3.86 3.83 3.81 3.78 3.73 3.71 3.66 3.62 3.61
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.22 4.16 4.10 4.05 4.01 3.97 3.94 3.91 3.88 3.86 3.82 3.78 3.75 3.72 3.70 3.65 3.62 3.59 3.57 3.54 3.49 3.47 3.41 3.38 3.37
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 4.02 3.96 3.91 3.86 3.82 3.78 3.75 3.72 3.69 3.66 3.62 3.59 3.56 3.53 3.51 3.46 3.43 3.40 3.38 3.34 3.30 3.27 3.22 3.19 3.18
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.86 3.80 3.75 3.70 3.66 3.62 3.59 3.56 3.53 3.51 3.46 3.43 3.40 3.37 3.35 3.30 3.27 3.24 3.22 3.18 3.14 3.11 3.06 3.03 3.02
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.73 3.67 3.61 3.56 3.52 3.49 3.45 3.42 3.40 3.37 3.33 3.29 3.26 3.24 3.21 3.17 3.13 3.10 3.08 3.05 3.00 2.98 2.92 2.89 2.88
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.62 3.55 3.50 3.45 3.41 3.37 3.34 3.31 3.28 3.26 3.22 3.18 3.15 3.12 3.10 3.05 3.02 2.99 2.97 2.93 2.89 2.86 2.81 2.78 2.76
17 8.40 6.11 5.19 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.52 3.46 3.40 3.35 3.31 3.27 3.24 3.21 3.19 3.16 3.12 3.08 3.05 3.03 3.00 2.96 2.92 2.89 2.87 2.83 2.79 2.76 2.71 2.68 2.66
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.43 3.37 3.32 3.27 3.23 3.19 3.16 3.13 3.10 3.08 3.03 3.00 2.97 2.94 2.92 2.87 2.84 2.81 2.78 2.75 2.70 2.68 2.62 2.59 2.58
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.36 3.30 3.24 3.19 3.15 3.12 3.08 3.05 3.03 3.00 2.96 2.92 2.89 2.87 2.84 2.80 2.76 2.73 2.71 2.67 2.63 2.60 2.55 2.51 2.50
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.29 3.23 3.18 3.13 3.09 3.05 3.02 2.99 2.96 2.94 2.90 2.86 2.83 2.80 2.78 2.73 2.69 2.67 2.64 2.61 2.56 2.54 2.48 2.44 2.43
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.24 3.17 3.12 3.07 3.03 2.99 2.96 2.93 2.90 2.88 2.84 2.80 2.77 2.74 2.72 2.67 2.64 2.61 2.58 2.55 2.50 2.48 2.42 2.38 2.37
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.18 3.12 3.07 3.02 2.98 2.94 2.91 2.88 2.85 2.83 2.78 2.75 2.72 2.69 2.67 2.62 2.58 2.55 2.53 2.50 2.45 2.42 2.36 2.33 2.32
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.14 3.07 3.02 2.97 2.93 2.89 2.86 2.83 2.80 2.78 2.74 2.70 2.67 2.64 2.62 2.57 2.54 2.51 2.48 2.45 2.40 2.37 2.32 2.28 2.27
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.09 3.03 2.98 2.93 2.89 2.85 2.82 2.79 2.76 2.74 2.70 2.66 2.63 2.60 2.58 2.53 2.49 2.46 2.44 2.40 2.36 2.33 2.27 2.24 2.22
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 3.06 2.99 2.94 2.89 2.85 2.81 2.78 2.75 2.72 2.70 2.66 2.62 2.59 2.56 2.54 2.49 2.45 2.42 2.40 2.36 2.32 2.29 2.23 2.19 2.18
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 3.02 2.96 2.90 2.86 2.81 2.78 2.75 2.72 2.69 2.66 2.62 2.58 2.55 2.53 2.50 2.45 2.42 2.39 2.36 2.33 2.28 2.25 2.19 2.16 2.14
27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.99 2.93 2.87 2.82 2.78 2.75 2.71 2.68 2.66 2.63 2.59 2.55 2.52 2.49 2.47 2.42 2.38 2.35 2.33 2.29 2.25 2.22 2.16 2.12 2.11
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.96 2.90 2.84 2.79 2.75 2.72 2.68 2.65 2.63 2.60 2.56 2.52 2.49 2.46 2.44 2.39 2.35 2.32 2.30 2.26 2.22 2.19 2.13 2.09 2.08
29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.93 2.87 2.81 2.77 2.73 2.69 2.66 2.63 2.60 2.57 2.53 2.49 2.46 2.44 2.41 2.36 2.33 2.30 2.27 2.23 2.19 2.16 2.10 2.06 2.05
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.91 2.84 2.79 2.74 2.70 2.66 2.63 2.60 2.57 2.55 2.51 2.47 2.44 2.41 2.39 2.34 2.30 2.27 2.25 2.21 2.16 2.13 2.07 2.03 2.02
32 7.50 5.34 4.46 3.97 3.65 3.43 3.26 3.13 3.02 2.93 2.86 2.80 2.74 2.70 2.65 2.62 2.58 2.55 2.53 2.50 2.46 2.42 2.39 2.36 2.34 2.29 2.25 2.22 2.20 2.16 2.11 2.08 2.02 1.98 1.97
34 7.44 5.29 4.42 3.93 3.61 3.39 3.22 3.09 2.98 2.89 2.82 2.76 2.70 2.66 2.61 2.58 2.54 2.51 2.49 2.46 2.42 2.38 2.35 2.32 2.30 2.25 2.21 2.18 2.16 2.12 2.07 2.04 1.98 1.94 1.92
36 7.40 5.25 4.38 3.89 3.57 3.35 3.18 3.05 2.95 2.86 2.79 2.72 2.67 2.62 2.58 2.54 2.51 2.48 2.45 2.43 2.38 2.35 2.32 2.29 2.26 2.21 2.18 2.14 2.12 2.08 2.03 2.00 1.94 1.90 1.89
38 7.35 5.21 4.34 3.86 3.54 3.32 3.15 3.02 2.92 2.83 2.75 2.69 2.64 2.59 2.55 2.51 2.48 2.45 2.42 2.40 2.35 2.32 2.28 2.26 2.23 2.18 2.14 2.11 2.09 2.05 2.00 1.97 1.90 1.86 1.85
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.73 2.66 2.61 2.56 2.52 2.48 2.45 2.42 2.39 2.37 2.33 2.29 2.26 2.23 2.20 2.15 2.11 2.08 2.06 2.02 1.97 1.94 1.87 1.83 1.82
42 7.28 5.15 4.29 3.80 3.49 3.27 3.10 2.97 2.86 2.78 2.70 2.64 2.59 2.54 2.50 2.46 2.43 2.40 2.37 2.34 2.30 2.26 2.23 2.20 2.18 2.13 2.09 2.06 2.03 1.99 1.94 1.91 1.85 1.80 1.79
44 7.25 5.12 4.26 3.78 3.47 3.24 3.08 2.95 2.84 2.75 2.68 2.62 2.56 2.52 2.47 2.44 2.40 2.37 2.35 2.32 2.28 2.24 2.21 2.18 2.15 2.10 2.07 2.03 2.01 1.97 1.92 1.89 1.82 1.78 1.76
46 7.22 5.10 4.24 3.76 3.44 3.22 3.06 2.93 2.82 2.73 2.66 2.60 2.54 2.50 2.45 2.42 2.38 2.35 2.33 2.30 2.26 2.22 2.19 2.16 2.13 2.08 2.04 2.01 1.99 1.95 1.90 1.86 1.80 1.76 1.74
48 7.19 5.08 4.22 3.74 3.43 3.20 3.04 2.91 2.80 2.71 2.64 2.58 2.53 2.48 2.44 2.40 2.37 2.33 2.31 2.28 2.24 2.20 2.17 2.14 2.12 2.06 2.02 1.99 1.97 1.93 1.88 1.84 1.78 1.73 1.72
50 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70 2.63 2.56 2.51 2.46 2.42 2.38 2.35 2.32 2.29 2.27 2.22 2.18 2.15 2.12 2.10 2.05 2.01 1.97 1.95 1.91 1.86 1.82 1.76 1.71 1.70
55 7.12 5.01 4.16 3.68 3.37 3.15 2.98 2.85 2.75 2.66 2.59 2.53 2.47 2.42 2.38 2.34 2.31 2.28 2.25 2.23 2.18 2.15 2.11 2.08 2.06 2.01 1.97 1.94 1.91 1.87 1.82 1.78 1.71 1.67 1.65
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.56 2.50 2.44 2.39 2.35 2.31 2.28 2.25 2.22 2.20 2.15 2.12 2.08 2.05 2.03 1.98 1.94 1.90 1.88 1.84 1.78 1.75 1.68 1.63 1.62
65 7.04 4.95 4.10 3.62 3.31 3.09 2.93 2.80 2.69 2.61 2.53 2.47 2.42 2.37 2.33 2.29 2.26 2.23 2.20 2.17 2.13 2.09 2.06 2.03 2.00 1.95 1.91 1.88 1.85 1.81 1.75 1.72 1.65 1.60 1.59
70 7.01 4.92 4.07 3.60 3.29 3.07 2.91 2.78 2.67 2.59 2.51 2.45 2.40 2.35 2.31 2.27 2.23 2.20 2.18 2.15 2.11 2.07 2.03 2.01 1.98 1.93 1.89 1.85 1.83 1.78 1.73 1.70 1.62 1.57 1.56
75 6.99 4.90 4.05 3.58 3.27 3.05 2.89 2.76 2.65 2.57 2.49 2.43 2.38 2.33 2.29 2.25 2.22 2.18 2.16 2.13 2.09 2.05 2.02 1.99 1.96 1.91 1.87 1.83 1.81 1.76 1.71 1.67 1.60 1.55 1.53
80 6.96 4.88 4.04 3.56 3.26 3.04 2.87 2.74 2.64 2.55 2.48 2.42 2.36 2.31 2.27 2.23 2.20 2.17 2.14 2.12 2.07 2.03 2.00 1.97 1.94 1.89 1.85 1.82 1.79 1.75 1.69 1.65 1.58 1.53 1.51
85 6.94 4.86 4.02 3.55 3.24 3.02 2.86 2.73 2.62 2.54 2.46 2.40 2.35 2.30 2.26 2.22 2.19 2.15 2.13 2.10 2.06 2.02 1.98 1.95 1.93 1.88 1.83 1.80 1.77 1.73 1.67 1.64 1.56 1.51 1.49
90 6.93 4.85 4.01 3.53 3.23 3.01 2.84 2.72 2.61 2.52 2.45 2.39 2.33 2.29 2.24 2.21 2.17 2.14 2.11 2.09 2.04 2.00 1.97 1.94 1.92 1.86 1.82 1.79 1.76 1.72 1.66 1.62 1.55 1.49 1.48
95 6.91 4.84 3.99 3.52 3.22 3.00 2.83 2.70 2.60 2.51 2.44 2.38 2.32 2.28 2.23 2.20 2.16 2.13 2.10 2.08 2.03 1.99 1.96 1.93 1.90 1.85 1.81 1.77 1.75 1.70 1.65 1.61 1.53 1.48 1.46
100 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.59 2.50 2.43 2.37 2.31 2.27 2.22 2.19 2.15 2.12 2.09 2.07 2.02 1.98 1.95 1.92 1.89 1.84 1.80 1.76 1.74 1.69 1.63 1.60 1.52 1.47 1.45
125 6.84 4.78 3.94 3.47 3.17 2.95 2.79 2.66 2.55 2.47 2.39 2.33 2.28 2.23 2.19 2.15 2.11 2.08 2.05 2.03 1.98 1.94 1.91 1.88 1.85 1.80 1.76 1.72 1.69 1.65 1.59 1.55 1.47 1.41 1.39
150 6.81 4.75 3.91 3.45 3.14 2.92 2.76 2.63 2.53 2.44 2.37 2.31 2.25 2.20 2.16 2.12 2.09 2.06 2.03 2.00 1.96 1.92 1.88 1.85 1.83 1.77 1.73 1.69 1.66 1.62 1.56 1.52 1.43 1.38 1.35
200 6.76 4.71 3.88 3.41 3.11 2.89 2.73 2.60 2.50 2.41 2.34 2.27 2.22 2.17 2.13 2.09 2.06 2.03 2.00 1.97 1.93 1.89 1.85 1.82 1.79 1.74 1.69 1.66 1.63 1.58 1.52 1.48 1.39 1.33 1.30
300 6.72 4.68 3.85 3.38 3.08 2.86 2.70 2.57 2.47 2.38 2.31 2.24 2.19 2.14 2.10 2.06 2.03 1.99 1.97 1.94 1.89 1.85 1.82 1.79 1.76 1.70 1.66 1.62 1.59 1.55 1.48 1.44 1.35 1.28 1.25
500 6.69 4.65 3.82 3.36 3.05 2.84 2.68 2.55 2.44 2.36 2.28 2.22 2.17 2.12 2.07 2.04 2.00 1.97 1.94 1.92 1.87 1.83 1.79 1.76 1.74 1.68 1.63 1.60 1.57 1.52 1.45 1.41 1.31 1.23 1.20
1000 6.66 4.63 3.80 3.34 3.04 2.82 2.66 2.53 2.43 2.34 2.27 2.20 2.15 2.10 2.06 2.02 1.98 1.95 1.92 1.90 1.85 1.81 1.77 1.74 1.72 1.66 1.61 1.58 1.54 1.50 1.43 1.38 1.28 1.19 1.16
2000 6.65 4.62 3.79 3.33 3.03 2.81 2.65 2.52 2.42 2.33 2.26 2.19 2.14 2.09 2.05 2.01 1.97 1.94 1.91 1.89 1.84 1.80 1.76 1.73 1.71 1.65 1.60 1.57 1.53 1.48 1.42 1.37 1.26 1.17 1.13