Appendix B

Quantile and cdf Tables

We provide various tables that might be of use in case you don’t have a computer
handy. Of course, these tables don’t cover every possible probability or quantile,
but they will give you sustenance if you are stranded on a desert island. If you
happen to have your computer wherever you go, you can always use Excel, Minitab,
R, or any other reasonable software package.

• Table B.1: Nor(0, 1) cdf Φ(z) = P Nor(0, 1) ≤ z .

• Table B.2: t(k) distribution (1 − p) quantile tp,k such that P t(k) > tp,k = p.

• Table B.3: χ2 (k) distribution (1 − p) quantile χ2p,k such that

2 2


P χ (k) > χp,k = p.

• Table B.4: F (n, m)
distribution 99% quantile F0.01,n,m such that
P F (n, m) > F0.01,n,m = 0.01.

• Table B.5: F (n, m)
distribution 97.5% quantile F0.025,n,m such that

P F (n, m) > F0.025,n,m = 0.025.

• Table B.6: F (n, m)
distribution 95% quantile F0.05,n,m such that
P F (n, m) > F0.05,n,m = 0.05.

F (n, m) distribution 90% quantile F0.1,n,m such that P F (n, m) >

• Table B.7:
F0.1,n,m = 0.1.

287
288 Chapter B. Quantile and cdf Tables


Table B.1: Nor(0, 1) cdf Φ(z) = P Nor(0, 1) ≤ z , e.g., Φ(1.47) = 0.9292.
Note that the (1 − p)-quantile zp ≡ Φ−1 (1 − p).

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
3.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998
3.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
 289


Table B.2: t distribution (1 − p) quantile tp,k such that P t(k) > tp,k = p,
e.g., t0.005,17 = 2.898.

k\p 0.40 0.30 0.20 0.10 0.05 0.025 0.01 0.005 0.001 0.0005

1 0.325 0.727 1.376 3.078 6.314 12.71 31.821 63.66 318.3 636.6
2 0.289 0.617 1.061 1.886 2.920 4.303 6.965 9.925 22.33 31.60
3 0.277 0.584 0.978 1.638 2.353 3.182 4.541 5.841 10.21 12.92
4 0.271 0.569 0.941 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 0.267 0.559 0.920 1.476 2.015 2.571 3.365 4.032 5.893 6.869
6 0.265 0.553 0.906 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 0.263 0.549 0.896 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 0.262 0.546 0.889 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 0.261 0.543 0.883 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 0.260 0.542 0.879 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 0.260 0.540 0.876 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 0.259 0.539 0.873 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 0.259 0.538 0.870 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 0.258 0.537 0.868 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 0.258 0.536 0.866 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 0.258 0.535 0.865 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 0.257 0.534 0.863 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 0.257 0.534 0.862 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 0.257 0.533 0.861 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 0.257 0.533 0.860 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 0.257 0.532 0.859 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 0.256 0.532 0.858 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 0.256 0.532 0.858 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 0.256 0.531 0.857 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 0.256 0.531 0.856 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 0.256 0.531 0.856 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 0.256 0.531 0.855 1.314 1.703 2.052 2.473 2.771 3.421 3.690
28 0.256 0.530 0.855 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 0.256 0.530 0.854 1.311 1.699 2.045 2.462 2.756 3.396 3.659
30 0.256 0.530 0.854 1.310 1.697 2.042 2.457 2.750 3.385 3.646
31 0.256 0.530 0.853 1.309 1.696 2.040 2.453 2.744 3.375 3.633
32 0.255 0.530 0.853 1.309 1.694 2.037 2.449 2.738 3.365 3.622
33 0.255 0.530 0.853 1.308 1.692 2.035 2.445 2.733 3.356 3.611
34 0.255 0.529 0.852 1.307 1.691 2.032 2.441 2.728 3.348 3.601
35 0.255 0.529 0.852 1.306 1.690 2.030 2.438 2.724 3.340 3.591
40 0.255 0.529 0.851 1.303 1.684 2.021 2.423 2.704 3.307 3.551
50 0.255 0.528 0.849 1.299 1.676 2.009 2.403 2.678 3.261 3.496
60 0.254 0.527 0.848 1.296 1.671 2.000 2.390 2.660 3.232 3.460
80 0.254 0.526 0.846 1.292 1.664 1.990 2.374 2.639 3.195 3.416
100 0.254 0.526 0.845 1.290 1.660 1.984 2.364 2.626 3.174 3.390
200 0.254 0.525 0.843 1.286 1.653 1.972 2.345 2.601 3.131 3.340
290 Chapter B. Quantile and cdf Tables


Table B.3: χ2 distribution (1−p) quantile χ2p,k such that P χ2 (k) > χ2p,k = p,
e.g., χ20.025,12 = 23.34.

k\p 0.999 0.995 0.99 0.975 0.95 0.9 0.1 0.05 0.025 0.01 0.005 0.001

1 0.000 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 10.83
2 0.002 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.60 13.82
3 0.024 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.34 12.84 16.27
4 0.091 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.14 13.28 14.86 18.47
5 0.210 0.412 0.554 0.831 1.145 1.610 9.236 11.07 12.83 15.09 16.75 20.52
6 0.381 0.676 0.872 1.237 1.635 2.204 10.64 12.59 14.45 16.81 18.55 22.46
7 0.598 0.989 1.239 1.690 2.167 2.833 12.02 14.07 16.01 18.48 20.28 24.32
8 0.857 1.344 1.646 2.180 2.733 3.490 13.36 15.51 17.53 20.09 21.95 26.12
9 1.152 1.735 2.088 2.700 3.325 4.168 14.68 16.92 19.02 21.67 23.59 27.88
10 1.479 2.156 2.558 3.247 3.940 4.865 15.99 18.31 20.48 23.21 25.19 29.59
11 1.834 2.603 3.053 3.816 4.575 5.578 17.28 19.68 21.92 24.72 26.76 31.26
12 2.214 3.074 3.571 4.404 5.226 6.304 18.55 21.03 23.34 26.22 28.30 32.91
13 2.617 3.565 4.107 5.009 5.892 7.042 19.81 22.36 24.74 27.69 29.82 34.53
14 3.041 4.075 4.660 5.629 6.571 7.790 21.06 23.68 26.12 29.14 31.32 36.12
15 3.483 4.601 5.229 6.262 7.261 8.547 22.31 25.00 27.49 30.58 32.80 37.70
16 3.942 5.142 5.812 6.908 7.962 9.312 23.54 26.30 28.85 32.00 34.27 39.25
17 4.416 5.697 6.408 7.564 8.672 10.09 24.77 27.59 30.19 33.41 35.72 40.79
18 4.905 6.265 7.015 8.231 9.390 10.86 25.99 28.87 31.53 34.81 37.16 42.31
19 5.407 6.844 7.633 8.907 10.12 11.65 27.20 30.14 32.85 36.19 38.58 43.82
20 5.921 7.434 8.260 9.591 10.85 12.44 28.41 31.41 34.17 37.57 40.00 45.31
21 6.447 8.034 8.897 10.28 11.59 13.24 29.62 32.67 35.48 38.93 41.40 46.80
22 6.983 8.643 9.542 10.98 12.34 14.04 30.81 33.92 36.78 40.29 42.80 48.27
23 7.529 9.260 10.20 11.69 13.09 14.85 32.01 35.17 38.08 41.64 44.18 49.73
24 8.085 9.886 10.86 12.40 13.85 15.66 33.20 36.42 39.36 42.98 45.56 51.18
25 8.649 10.52 11.52 13.12 14.61 16.47 34.38 37.65 40.65 44.31 46.93 52.62
26 9.222 11.16 12.20 13.84 15.38 17.29 35.56 38.89 41.92 45.64 48.29 54.05
27 9.803 11.81 12.88 14.57 16.15 18.11 36.74 40.11 43.19 46.96 49.64 55.48
28 10.39 12.46 13.56 15.31 16.93 18.94 37.92 41.34 44.46 48.28 50.99 56.89
29 10.99 13.12 14.26 16.05 17.71 19.77 39.09 42.56 45.72 49.59 52.34 58.30
30 11.59 13.79 14.95 16.79 18.49 20.60 40.26 43.77 46.98 50.89 53.67 59.70
31 12.20 14.46 15.66 17.54 19.28 21.43 41.42 44.99 48.23 52.19 55.00 61.10
32 12.81 15.13 16.36 18.29 20.07 22.27 42.58 46.19 49.48 53.49 56.33 62.49
33 13.43 15.82 17.07 19.05 20.87 23.11 43.75 47.40 50.73 54.78 57.65 63.87
34 14.06 16.50 17.79 19.81 21.66 23.95 44.90 48.60 51.97 56.06 58.96 65.25
35 14.69 17.19 18.51 20.57 22.47 24.80 46.06 49.80 53.20 57.34 60.27 66.62
40 17.92 20.71 22.16 24.43 26.51 29.05 51.81 55.76 59.34 63.69 66.77 73.40
50 24.67 27.99 29.71 32.36 34.76 37.69 63.17 67.50 71.42 76.15 79.49 86.66
60 31.74 35.53 37.48 40.48 43.19 46.46 74.40 79.08 83.30 88.38 91.95 99.61
80 46.52 51.17 53.54 57.15 60.39 64.28 96.58 101.9 106.6 112.3 116.3 124.8
100 61.92 67.33 70.06 74.22 77.93 82.36 118.5 124.3 129.6 135.8 140.2 149.4
200 143.8 152.2 156.4 162.7 168.3 174.8 226.0 234.0 241.1 249.4 255.3 267.5
 Table B.4: F distribution 99% quantile F0.01,n,m such that P(F (n, m) >
F0.01,n,m ) = 0.01, e.g., F0.01,9,5 = 10.16.

m\n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 60 120

1 4052 5000 5403 5625 5764 5859 5928 5981 6022 6056 6106 6157 6209 6240 6261 6313 6339
2 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.42 99.43 99.45 99.46 99.47 99.48 99.49
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05 26.87 26.69 26.58 26.50 26.32 26.22
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.37 14.20 14.02 13.91 13.84 13.65 13.56
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.89 9.72 9.55 9.45 9.38 9.20 9.11
6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.72 7.56 7.40 7.30 7.23 7.06 6.97
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.47 6.31 6.16 6.06 5.99 5.82 5.74
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.67 5.52 5.36 5.26 5.20 5.03 4.95
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.11 4.96 4.81 4.71 4.65 4.48 4.40
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.71 4.56 4.41 4.31 4.25 4.08 4.00
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.40 4.25 4.10 4.01 3.94 3.78 3.69
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.16 4.01 3.86 3.76 3.70 3.54 3.45
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.96 3.82 3.66 3.57 3.51 3.34 3.25
14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.80 3.66 3.51 3.41 3.35 3.18 3.09
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.67 3.52 3.37 3.28 3.21 3.05 2.96
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.55 3.41 3.26 3.16 3.10 2.93 2.84
17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.46 3.31 3.16 3.07 3.00 2.83 2.75
18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.37 3.23 3.08 2.98 2.92 2.75 2.66
19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.30 3.15 3.00 2.91 2.84 2.67 2.58
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.23 3.09 2.94 2.84 2.78 2.61 2.52
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.17 3.03 2.88 2.79 2.72 2.55 2.46
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.12 2.98 2.83 2.73 2.67 2.50 2.40
23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.07 2.93 2.78 2.69 2.62 2.45 2.35
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.03 2.89 2.74 2.64 2.58 2.40 2.31
25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.99 2.85 2.70 2.60 2.54 2.36 2.27
30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.84 2.70 2.55 2.45 2.39 2.21 2.11
40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.66 2.52 2.37 2.27 2.20 2.02 1.92
60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.50 2.35 2.20 2.10 2.03 1.84 1.73
120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.34 2.19 2.03 1.93 1.86 1.66 1.53
291
 Table B.5: F distribution 97.5% quantile F0.025,n,m such that P(F (n, m) >
292

F0.025,n,m ) = 0.025, e.g., F0.025,9,5 = 6.68.

m\n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 60 120

1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.6 976.7 984.9 993.1 998.1 1001 1010 1014
2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43 39.45 39.46 39.46 39.48 39.49
3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25 14.17 14.12 14.08 13.99 13.95
4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.75 8.66 8.56 8.50 8.46 8.36 8.31
5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43 6.33 6.27 6.23 6.12 6.07
6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.37 5.27 5.17 5.11 5.07 4.96 4.90
7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.67 4.57 4.47 4.40 4.36 4.25 4.20
8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.20 4.10 4.00 3.94 3.89 3.78 3.73
9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.87 3.77 3.67 3.60 3.56 3.45 3.39
10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52 3.42 3.35 3.31 3.20 3.14
11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.43 3.33 3.23 3.16 3.12 3.00 2.94
12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.28 3.18 3.07 3.01 2.96 2.85 2.79
13 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.15 3.05 2.95 2.88 2.84 2.72 2.66
14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.05 2.95 2.84 2.78 2.73 2.61 2.55
15 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 2.96 2.86 2.76 2.69 2.64 2.52 2.46
16 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.89 2.79 2.68 2.61 2.57 2.45 2.38
17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.82 2.72 2.62 2.55 2.50 2.38 2.32
18 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.77 2.67 2.56 2.49 2.44 2.32 2.26
19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.72 2.62 2.51 2.44 2.39 2.27 2.20
20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.68 2.57 2.46 2.40 2.35 2.22 2.16
21 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 2.64 2.53 2.42 2.36 2.31 2.18 2.11
22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.60 2.50 2.39 2.32 2.27 2.14 2.08
23 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.57 2.47 2.36 2.29 2.24 2.11 2.04
24 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.54 2.44 2.33 2.26 2.21 2.08 2.01
25 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.51 2.41 2.30 2.23 2.18 2.05 1.98
30 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.41 2.31 2.20 2.12 2.07 1.94 1.87
40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.29 2.18 2.07 1.99 1.94 1.80 1.72
60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.17 2.06 1.94 1.87 1.82 1.67 1.58
120 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 2.05 1.94 1.82 1.75 1.69 1.53 1.43
Chapter B. Quantile and cdf Tables
 Table B.6: F distribution 95% quantile F0.05,n,m such that P(F (n, m) >
F0.05,n,m ) = 0.05, e.g., F0.05,9,5 = 4.77.

m\n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 60 120

1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.3 250.1 252.2 253.3
2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.46 19.46 19.48 19.49
3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.63 8.62 8.57 8.55
4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.69 5.66
5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.52 4.50 4.43 4.40
6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.83 3.81 3.74 3.70
7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.40 3.38 3.30 3.27
8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3.15 3.11 3.08 3.01 2.97
9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.89 2.86 2.79 2.75
10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.73 2.70 2.62 2.58
11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.60 2.57 2.49 2.45
12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.50 2.47 2.38 2.34
13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.41 2.38 2.30 2.25
14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.34 2.31 2.22 2.18
15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.28 2.25 2.16 2.11
16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.42 2.35 2.28 2.23 2.19 2.11 2.06
17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.18 2.15 2.06 2.01
18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.14 2.11 2.02 1.97
19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 1.98 1.93
20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.07 2.04 1.95 1.90
21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.92 1.87
22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.02 1.98 1.89 1.84
23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.00 1.96 1.86 1.81
24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.97 1.94 1.84 1.79
25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.82 1.77
30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.88 1.84 1.74 1.68
40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.78 1.74 1.64 1.58
60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.69 1.65 1.53 1.47
120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.60 1.55 1.43 1.35
293
 Table B.7: F distribution 90% quantile F0.1,n,m such that P(F (n, m) >
294

F0.1,n,m ) = 0.1, e.g., F0.1,9,5 = 3.32.

m\n 1 2 3 4 5 6 7 8 9 10 12 15 20 25 30 60 120

1 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 60.19 60.71 61.22 61.74 62.05 62.26 62.79 63.06
2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.48
3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 5.22 5.20 5.18 5.17 5.17 5.15 5.14
4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 3.90 3.87 3.84 3.83 3.82 3.79 3.78
5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30 3.27 3.24 3.21 3.19 3.17 3.14 3.12
6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94 2.90 2.87 2.84 2.81 2.80 2.76 2.74
7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70 2.67 2.63 2.59 2.57 2.56 2.51 2.49
8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54 2.50 2.46 2.42 2.40 2.38 2.34 2.32
9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 2.38 2.34 2.30 2.27 2.25 2.21 2.18
10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32 2.28 2.24 2.20 2.17 2.16 2.11 2.08
11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 2.21 2.17 2.12 2.10 2.08 2.03 2.00
12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19 2.15 2.10 2.06 2.03 2.01 1.96 1.93
13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14 2.10 2.05 2.01 1.98 1.96 1.90 1.88
14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10 2.05 2.01 1.96 1.93 1.91 1.86 1.83
15 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06 2.02 1.97 1.92 1.89 1.87 1.82 1.79
16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 1.99 1.94 1.89 1.86 1.84 1.78 1.75
17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00 1.96 1.91 1.86 1.83 1.81 1.75 1.72
18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98 1.93 1.89 1.84 1.80 1.78 1.72 1.69
19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96 1.91 1.86 1.81 1.78 1.76 1.70 1.67
20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94 1.89 1.84 1.79 1.76 1.74 1.68 1.64
21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 1.87 1.83 1.78 1.74 1.72 1.66 1.62
22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90 1.86 1.81 1.76 1.73 1.70 1.64 1.60
23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 1.84 1.80 1.74 1.71 1.69 1.62 1.59
24 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88 1.83 1.78 1.73 1.70 1.67 1.61 1.57
25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87 1.82 1.77 1.72 1.68 1.66 1.59 1.56
30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 1.77 1.72 1.67 1.63 1.61 1.54 1.50
40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76 1.71 1.66 1.61 1.57 1.54 1.47 1.42
60 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71 1.66 1.60 1.54 1.50 1.48 1.40 1.35
120 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65 1.60 1.55 1.48 1.44 1.41 1.32 1.26
Chapter B. Quantile and cdf Tables