Appendix 3: Statistical Tables

Table A2.1:  t table

cum. prob t .50 t .75 t .80 t .85 t .90 t .95 t .975 t .99 t .995 t .999 t .9995
one-tail 0.50 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 0.001 0.0005
two-tails 1.00 0.50 0.40 0.30 0.20 0.10 0.05 0.02 0.01 0.002 0.001
df
1 0.000 1.000 1.376 1.963 3.078 6.314 12.71 31.82 63.66 318.31 636.62
2 0.000 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 22.327 31.599
3 0.000 0.765 0.978 1.250 1.638 2.353 3.182 4.541 5.841 10.215 12.924
4 0.000 0.741 0.941 1.190 1.533 2.132 2.776 3.747 4.604 7.173 8.610
5 0.000 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 5.893 6.869
6 0.000 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.208 5.959
7 0.000 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 4.785 5.408
8 0.000 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 4.501 5.041
9 0.000 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.297 4.781
10 0.000 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.144 4.587
11 0.000 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.025 4.437
12 0.000 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.930 4.318
13 0.000 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 3.852 4.221
14 0.000 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.787 4.140
15 0.000 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.733 4.073
16 0.000 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 3.686 4.015
17 0.000 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.646 3.965
18 0.000 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.610 3.922
19 0.000 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.579 3.883
20 0.000 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.552 3.850
21 0.000 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.527 3.819
22 0.000 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.505 3.792
23 0.000 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.485 3.768
24 0.000 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.467 3.745
25 0.000 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.450 3.725
26 0.000 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.435 3.707
27 0.000 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.421 3.690
28 0.000 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.408 3.674
29 0.000 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.396 3.659
30 0.000 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.385 3.646
40 0.000 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.307 3.551
60 0.000 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.232 3.460
80 0.000 0.678 0.846 1.043 1.292 1.664 1.990 2.374 2.639 3.195 3.416
100 0.000 0.677 0.845 1.042 1.290 1.660 1.984 2.364 2.626 3.174 3.390
1000 0.000 0.675 0.842 1.037 1.282 1.646 1.962 2.330 2.581 3.098 3.300
z 0.000 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.090 3.291
0% 50% 60% 70% 80% 90% 95% 98% 99% 99.8% 99.9%
Confidence Level

Table A2.2:  chi-square table

Table A2.2:  Table for Chi-square distribution. This table created by the authors using R.
Critical Values for [latex]X^2[/latex]
Probability for a value as large or larger than tables value
Degrees of freedom Tail Probabilities
0.10 0.05 0.01
1 2.71 3.84 6.63
2 4.60 5.99 9.21
3 6.25 7.81 11.34
4 7.78 9.49 13.28
5 9.24 11.07 15.09
6 10.64 12.59 16.81
7 12.02 14.07 18.48
8 13.36 15.51 20.09
9 14.68 16.92 21.67
10 15.99 18.31 23.21

Table A2.3: F table

F distribution critical values

Table entries are critical values for F* with probably p in right tail of the distribution. The numbers in each row correspond to the degrees of freedom in the numerator (df1) and the numbers in the left-most column correspond to the degrees of freedom in the denominator (df2)

Table A-II.3: Table for F-Distribution. This table reprinted by permission from B. Bert Gerstman’s StatPrimer 7.0. [pdf version]
Degrees of freedom in numerator (df1)
(df2) p 1 2 3 4 5 6 7 8 12 24 1000
1 0.1 39.86 49.5 53.59 55.83 57.24 58.2 58.91 59.44 60.71 62 63.3
0.05 161.4 199.5 215.7 224.6 230.2 234 236.8 238.9 243.9 249.1 254.2
0.025 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.6 976.7 997.3 1017.8
0.01 4052 4999 5404 5624 5764 5859 5928 5981 6107 6234 6363
0.001 405312 499725 540257 562668 576496 586033 593185 597954 610352 623703 636101
2 0.1 8.53 9 9.16 9.24 9.29 9.33 9.35 9.37 9.41 9.45 9.49
0.05 18.51 19 19.16 19.25 19.3 19.33 19.35 19.37 19.41 19.45 19.49
0.025 38.51 39 39.17 39.25 39.3 39.33 39.36 39.37 39.41 39.46 39.5
0.01 98.5 99 99.16 99.25 99.3 99.33 99.36 99.38 99.42 99.46 99.5
0.001 998.38 998.84 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31
3 0.1 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.22 5.18 5.13
0.05 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.74 8.64 8.53
0.025 17.44 16.04 15.44 15.1 14.88 14.73 14.62 14.54 14.34 14.12 13.91
0.01 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.05 26.6 26.14
0.001 167.06 148.49 141.1 137.08 134.58 132.83 131.61 130.62 128.32 125.93 123.52
4 0.1 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.9 3.83 3.76
0.05 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 5.91 5.77 5.63
0.025 12.22 10.65 9.98 9.6 9.36 9.2 9.07 8.98 8.75 8.51 8.26
0.01 21.2 18 16.69 15.98 15.52 15.21 14.98 14.8 14.37 13.93 13.47
0.001 74.13 61.25 56.17 53.43 51.72 50.52 49.65 49 47.41 45.77 44.09
5 0.1 4.06 3.78 3.62 3.52 3.45 3.4 3.37 3.34 3.27 3.19 3.11
0.05 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.68 4.53 4.37
0.025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.52 6.28 6.02
0.01 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 9.89 9.47 9.03
0.001 47.18 37.12 33.2 31.08 29.75 28.83 28.17 27.65 26.42 25.13 23.82
6 0.1 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.9 2.82 2.72
0.05 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4 3.84 3.67
0.025 8.81 7.26 6.6 6.23 5.99 5.82 5.7 5.6 5.37 5.12 4.86
0.01 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.1 7.72 7.31 6.89
0.001 35.51 27 23.71 21.92 20.8 20.03 19.46 19.03 17.99 16.9 15.77
7 0.1 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.67 2.58 2.47
0.05 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.57 3.41 3.23
0.025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.9 4.67 4.41 4.15
0.01 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.47 6.07 5.66
0.001 29.25 21.69 18.77 17.2 16.21 15.52 15.02 14.63 13.71 12.73 11.72
8 0.1 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.5 2.4 2.3
0.05 5.32 4.46 4.07 3.84 3.69 3.58 3.5 3.44 3.28 3.12 2.93
0.025 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.2 3.95 3.68
0.01 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.67 5.28 4.87
0.001 25.41 18.49 15.83 14.39 13.48 12.86 12.4 12.05 11.19 10.3 9.36
9 0.1 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.38 2.28 2.16
0.05 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.07 2.9 2.71
0.025 7.21 5.71 5.08 4.72 4.48 4.32 4.2 4.1 3.87 3.61 3.34
0.01 10.56 8.02 6.99 6.42 6.06 5.8 5.61 5.47 5.11 4.73 4.32
0.001 22.86 16.39 13.9 12.56 11.71 11.13 10.7 10.37 9.57 8.72 7.84
10 0.1 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.28 2.18 2.06
0.05 4.96 4.1 3.71 3.48 3.33 3.22 3.14 3.07 2.91 2.74 2.54
0.025 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.62 3.37 3.09
0.01 10.04 7.56 6.55 5.99 5.64 5.39 5.2 5.06 4.71 4.33 3.92
0.001 21.04 14.9 12.55 11.28 10.48 9.93 9.52 9.2 8.45 7.64 6.78
12 0.1 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.15 2.04 1.91
0.05 4.75 3.89 3.49 3.26 3.11 3 2.91 2.85 2.69 2.51 2.3
0.025 6.55 5.1 4.47 4.12 3.89 3.73 3.61 3.51 3.28 3.02 2.73
0.01 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.5 4.16 3.78 3.37
0.001 18.64 12.97 10.8 9.63 8.89 8.38 8 7.71 7 6.25 5.44
14 0.1 3.1 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.05 1.94 1.8
0.05 4.6 3.74 3.34 3.11 2.96 2.85 2.76 2.7 2.53 2.35 2.14
0.025 6.3 4.86 4.24 3.89 3.66 3.5 3.38 3.29 3.05 2.79 2.5
0.01 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 3.8 3.43 3.02
0.001 17.14 11.78 9.73 8.62 7.92 7.44 7.08 6.8 6.13 5.41 4.62
16 0.1 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 1.99 1.87 1.72
0.05 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.42 2.24 2.02
0.025 6.12 4.69 4.08 3.73 3.5 3.34 3.22 3.12 2.89 2.63 2.32
0.01 8.53 6.23 5.29 4.77 4.44 4.2 4.03 3.89 3.55 3.18 2.76
0.001 16.12 10.97 9.01 7.94 7.27 6.8 6.46 6.2 5.55 4.85 4.08
18 0.1 3.01 2.62 2.42 2.29 2.2 2.13 2.08 2.04 1.93 1.81 1.66
0.05 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.34 2.15 1.92
0.025 5.98 4.56 3.95 3.61 3.38 3.22 3.1 3.01 2.77 2.5 2.2
0.01 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.37 3 2.58
0.001 15.38 10.39 8.49 7.46 6.81 6.35 6.02 5.76 5.13 4.45 3.69
20 0.1 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2 1.89 1.77 1.61
0.05 4.35 3.49 3.1 2.87 2.71 2.6 2.51 2.45 2.28 2.08 1.85
0.025 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.68 2.41 2.09
0.01 8.1 5.85 4.94 4.43 4.1 3.87 3.7 3.56 3.23 2.86 2.43
0.001 14.82 9.95 8.1 7.1 6.46 6.02 5.69 5.44 4.82 4.15 3.4
30 0.1 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.77 1.64 1.46
0.05 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.09 1.89 1.63
0.025 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.41 2.14 1.8
0.01 7.56 5.39 4.51 4.02 3.7 3.47 3.3 3.17 2.84 2.47 2.02
0.001 13.29 8.77 7.05 6.12 5.53 5.12 4.82 4.58 4 3.36 2.61
50 0.1 2.81 2.41 2.2 2.06 1.97 1.9 1.84 1.8 1.68 1.54 1.33
0.05 4.03 3.18 2.79 2.56 2.4 2.29 2.2 2.13 1.95 1.74 1.45
0.025 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.22 1.93 1.56
0.01 7.17 5.06 4.2 3.72 3.41 3.19 3.02 2.89 2.56 2.18 1.7
0.001 12.22 7.96 6.34 5.46 4.9 4.51 4.22 4 3.44 2.82 2.05
100 0.1 2.76 2.36 2.14 2 1.91 1.83 1.78 1.73 1.61 1.46 1.22
0.05 3.94 3.09 2.7 2.46 2.31 2.19 2.1 2.03 1.85 1.63 1.3
0.025 5.18 3.83 3.25 2.92 2.7 2.54 2.42 2.32 2.08 1.78 1.36
0.01 6.9 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.37 1.98 1.45
0.001 11.5 7.41 5.86 5.02 4.48 4.11 3.83 3.61 3.07 2.46 1.64
1000 0.1 2.71 2.31 2.09 1.95 1.85 1.78 1.72 1.68 1.55 1.39 1.08
0.05 3.85 3 2.61 2.38 2.22 2.11 2.02 1.95 1.76 1.53 1.11
0.025 5.04 3.7 3.13 2.8 2.58 2.42 2.3 2.2 1.96 1.65 1.13
0.01 6.66 4.63 3.8 3.34 3.04 2.82 2.66 2.53 2.2 1.81 1.16
0.001 10.89 6.96 5.46 4.65 4.14 3.78 3.51 3.3 2.77 2.16 1.22

License

Icon for the Creative Commons Attribution-NonCommercial 4.0 International License

Process of Science Companion: Data Analysis, Statistics and Experimental Design Copyright © 2019 by University of Wisconsin-Madison Biocore Program is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

Share This Book