F Statistical Tables

Table F.1: Cumulative standard normal distribution, z = -3.49 to 0
-0.09 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0
-3.40 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
-3.30 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005
-3.20 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 0.0007
-3.10 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 0.0010
-3.00 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 0.0013
-2.90 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 0.0019
-2.80 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 0.0026
-2.70 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035
-2.60 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 0.0047
-2.50 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 0.0062
-2.40 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 0.0082
-2.30 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 0.0107
-2.20 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 0.0139
-2.10 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 0.0179
-2.00 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 0.0228
-1.90 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 0.0287
-1.80 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 0.0359
-1.70 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 0.0446
-1.60 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 0.0548
-1.50 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 0.0668
-1.40 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 0.0808
-1.30 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 0.0968
-1.20 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 0.1151
-1.10 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 0.1357
-1.00 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 0.1587
-0.90 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 0.1841
-0.80 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 0.2119
-0.70 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 0.2420
-0.60 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 0.2743
-0.50 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 0.3085
-0.40 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 0.3446
-0.30 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 0.3821
-0.20 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 0.4207
-0.10 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 0.4602
-0.00 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 0.5000
Table F.2: Cumulative standard normal distribution, z = 0.0 to 3.49
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.00 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.10 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.20 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.30 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.40 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.50 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
0.60 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.70 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.80 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.90 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.00 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.10 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830
1.20 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.30 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.40 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319
1.50 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.60 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.70 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.80 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.90 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767
2.00 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.10 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857
2.20 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890
2.30 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.40 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.50 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.60 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.70 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
2.80 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.90 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.00 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990
3.10 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.20 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.30 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.40 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
Table F.3: Percentage Points \(t_{\nu,\alpha}\) of the Student-t Distribution
\(\nu \backslash \alpha\) 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
1 3.078 6.314 12.706 31.821 63.657 127.321 318.309 636.619
2 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.599
3 1.638 2.353 3.182 4.541 5.841 7.453 10.215 12.924
4 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869
6 1.440 1.943 2.447 3.143 3.707 4.317 5.208 5.959
7 1.415 1.895 2.365 2.998 3.499 4.029 4.785 5.408
8 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.041
9 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.781
10 1.372 1.812 2.228 2.764 3.169 3.581 4.144 4.587
11 1.363 1.796 2.201 2.718 3.106 3.497 4.025 4.437
12 1.356 1.782 2.179 2.681 3.055 3.428 3.930 4.318
13 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.221
14 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.140
15 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073
16 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015
17 1.333 1.740 2.110 2.567 2.898 3.222 3.646 3.965
18 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.922
19 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883
20 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.850
21 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819
22 1.321 1.717 2.074 2.508 2.819 3.119 3.505 3.792
23 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.768
24 1.318 1.711 2.064 2.492 2.797 3.091 3.467 3.745
25 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.725
26 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707
27 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690
28 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674
29 1.311 1.699 2.045 2.462 2.756 3.038 3.396 3.659
30 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646
31 1.309 1.696 2.040 2.453 2.744 3.022 3.375 3.633
32 1.309 1.694 2.037 2.449 2.738 3.015 3.365 3.622
33 1.308 1.692 2.035 2.445 2.733 3.008 3.356 3.611
34 1.307 1.691 2.032 2.441 2.728 3.002 3.348 3.601
35 1.306 1.690 2.030 2.438 2.724 2.996 3.340 3.591
40 1.303 1.684 2.021 2.423 2.704 2.971 3.307 3.551
45 1.301 1.679 2.014 2.412 2.690 2.952 3.281 3.520
50 1.299 1.676 2.009 2.403 2.678 2.937 3.261 3.496
\(\infty\) 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291
Table F.4: Percentage Points \(\chi^{2}_{\nu,\alpha}\) of the Chi-Square Distribution (\(\nu\)) degrees of freedom
\(\nu \backslash \alpha\) 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
1 2.706 3.841 5.024 6.635 7.879 9.141 10.828 12.116
2 4.605 5.991 7.378 9.210 10.597 11.983 13.816 15.202
3 6.251 7.815 9.348 11.345 12.838 14.320 16.266 17.730
4 7.779 9.488 11.143 13.277 14.860 16.424 18.467 19.997
5 9.236 11.070 12.833 15.086 16.750 18.386 20.515 22.105
6 10.645 12.592 14.449 16.812 18.548 20.249 22.458 24.103
7 12.017 14.067 16.013 18.475 20.278 22.040 24.322 26.018
8 13.362 15.507 17.535 20.090 21.955 23.774 26.124 27.868
9 14.684 16.919 19.023 21.666 23.589 25.462 27.877 29.666
10 15.987 18.307 20.483 23.209 25.188 27.112 29.588 31.420
11 17.275 19.675 21.920 24.725 26.757 28.729 31.264 33.137
12 18.549 21.026 23.337 26.217 28.300 30.318 32.909 34.821
13 19.812 22.362 24.736 27.688 29.819 31.883 34.528 36.478
14 21.064 23.685 26.119 29.141 31.319 33.426 36.123 38.109
15 22.307 24.996 27.488 30.578 32.801 34.950 37.697 39.719
16 23.542 26.296 28.845 32.000 34.267 36.456 39.252 41.308
17 24.769 27.587 30.191 33.409 35.718 37.946 40.790 42.879
18 25.989 28.869 31.526 34.805 37.156 39.422 42.312 44.434
19 27.204 30.144 32.852 36.191 38.582 40.885 43.820 45.973
20 28.412 31.410 34.170 37.566 39.997 42.336 45.315 47.498
21 29.615 32.671 35.479 38.932 41.401 43.775 46.797 49.011
22 30.813 33.924 36.781 40.289 42.796 45.204 48.268 50.511
23 32.007 35.172 38.076 41.638 44.181 46.623 49.728 52.000
24 33.196 36.415 39.364 42.980 45.559 48.034 51.179 53.479
25 34.382 37.652 40.646 44.314 46.928 49.435 52.620 54.947
26 35.563 38.885 41.923 45.642 48.290 50.829 54.052 56.407
27 36.741 40.113 43.195 46.963 49.645 52.215 55.476 57.858
28 37.916 41.337 44.461 48.278 50.993 53.594 56.892 59.300
29 39.087 42.557 45.722 49.588 52.336 54.967 58.301 60.735
30 40.256 43.773 46.979 50.892 53.672 56.332 59.703 62.162
31 41.422 44.985 48.232 52.191 55.003 57.692 61.098 63.582
32 42.585 46.194 49.480 53.486 56.328 59.046 62.487 64.995
33 43.745 47.400 50.725 54.776 57.648 60.395 63.870 66.403
34 44.903 48.602 51.966 56.061 58.964 61.738 65.247 67.803
35 46.059 49.802 53.203 57.342 60.275 63.076 66.619 69.199
40 51.805 55.758 59.342 63.691 66.766 69.699 73.402 76.095
50 63.167 67.505 71.420 76.154 79.490 82.664 86.661 89.561
60 74.397 79.082 83.298 88.379 91.952 95.344 99.607 102.695
70 85.527 90.531 95.023 100.425 104.215 107.808 112.317 115.578
80 96.578 101.879 106.629 112.329 116.321 120.102 124.839 128.261
90 107.565 113.145 118.136 124.116 128.299 132.256 137.208 140.782
100 118.498 124.342 129.561 135.807 140.169 144.293 149.449 153.167
Table F.5: Kolmogorov-Smirnov Test Critical Values
n \(D_{0.1}\) \(D_{0.05}\) \(D_{0.01}\)
10 0.36866 0.40925 0.48893
11 0.35242 0.39122 0.46770
12 0.33815 0.37543 0.44905
13 0.32549 0.36143 0.43247
14 0.31417 0.34890 0.41762
15 0.30397 0.33760 0.40420
16 0.29472 0.32733 0.39201
17 0.28627 0.31796 0.38086
18 0.27851 0.30936 0.37062
19 0.27136 0.30143 0.36117
20 0.26473 0.29408 0.35241
25 0.23768 0.26404 0.31657
30 0.21756 0.24170 0.28987
35 0.20185 0.22425 0.26897
over 35 \(1.22/\sqrt{n}\) \(1.36/\sqrt{n}\) \(1.63/\sqrt{n}\)


See (Miller 1956). Additional values can be computed at:

http://www.ciphersbyritter.com/JAVASCRP/NORMCHIK.HTM#KolSmir

References

Miller, L. H. 1956. “Table of Percentage Points of Kolmogorov Statistics.” Journal of the American Statistical Association, 111–21.