# Appendix 2: 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

 Critical Values for $X^2$ 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 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)

 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

This chapter is adapted from Appendix 2: Statistical Tables in Process of Science Companion: Data Analysis, Statistics and Experimental Design by Michelle Harris, Rick Nordheim, and Janet Batzli.