Appendix B Tables A9 TABLE 4 Percentiles of the t Distribution tP P d f t.60 t.70 t.80 t.90 t.95 t.975 t.99 t.995 1 .325 .727 1.376 3.078 6.314 12.706 31.821 63.657 2 .289 .617 1.061 1.886 2.920 4.303 6.965 9.925 3 .277 .584 .978 1.638 2.353 3.182 4.541 5.841 4 .271 .569 .941 1.533 2.132 2.776 3.747 4.604 5 .267 .559 .920 1.476 2.015 2.571 3.365 4.032 6 .265 .553 .906 1.440 1.943 2.447 3.143 3.707 7 .263 .549 .896 1.415 1.895 2.365 2.998 3.499 8 .262 .546 .889 1.397 1.860 2.306 2.896 3.355 9 .261 .543 .883 1.383 1.833 2.262 2.821 3.250 10 .260 .542 .879 1.372 1.812 2.228 2.764 3.169 11 .260 .540 .876 1.363 1.796 2.201 2.718 3.106 12 .259 .539 .873 1.356 1.782 2.179 2.681 3.055 13 .259 .538 .870 1.350 1.771 2.160 2.650 3.012 14 .258 .537 .868 1.345 1.761 2.145 2.624 2.977 15 .258 .536 .866 1.341 1.753 2.131 2.602 2.947 16 .258 .535 .865 1.337 1.746 2.120 2.583 2.921 17 .257 .534 .863 1.333 1.740 2.110 2.567 2.898 18 .257 .534 .862 1.330 1.734 2.101 2.552 2.878 19 .257 .533 .861 1.328 1.729 2.093 2.539 2.861 20 .257 .533 .860 1.325 1.725 2.086 2.528 2.845 21 .257 .532 .859 1.323 1.721 2.080 2.518 2.831 22 .256 .532 .858 1.321 1.717 2.074 2.508 2.819 23 .256 .532 .858 1.319 1.714 2.069 2.500 2.807 24 .256 .531 .857 1.318 1.711 2.064 2.492 2.797 25 .256 .531 .856 1.316 1.708 2.060 2.485 2.787 26 .256 .531 .856 1.315 1.706 2.056 2.479 2.779 27 .256 .531 .855 1.314 1.703 2.052 2.473 2.771 28 .256 .530 .855 1.313 1.701 2.048 2.467 2.763 29 .256 .530 .854 1.311 1.699 2.045 2.462 2.756 30 .256 .530 .854 1.310 1.697 2.042 2.457 2.750 40 .255 .529 .851 1.303 1.684 2.021 2.423 2.704 60 .254 .527 .848 1.296 1.671 2.000 2.390 2.660 120 .254 .526 .845 1.289 1.658 1.980 2.358 2.617 ∞ .253 .524 .842 1.282 1.645 1.960 2.326 2.576 TABLE 5 Percentiles of the F Distribution: F .95(n1, n2) (Continued) n1 = degrees of freedom for numerator n1 n2 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254.3 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 19.45 19.46 19.47 19.48 19.49 19.50 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 8.64 8.62 8.59 8.57 8.55 8.53 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 5.72 5.69 5.66 5.63 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 4.53 4.50 4.46 4.43 4.40 4.36 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 3.84 3.81 3.77 3.74 3.70 3.67 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 3.41 3.38 3.34 3.30 3.27 3.23 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 3.12 3.08 3.04 3.01 2.97 2.93 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 2.90 2.86 2.83 2.79 2.75 2.71 10 4.96 4.10 3.71 3.48 3.83 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54 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 2.61 2.57 2.53 2.49 2.45 2.40 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 2.51 2.47 2.43 2.38 2.34 2.30 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 2.42 2.38 2.34 2.30 2.25 2.21 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 2.35 2.31 2.27 2.22 2.18 2.13 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 2.29 2.25 2.20 2.16 2.11 2.07 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 2.24 2.19 2.15 2.11 2.06 2.01 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 2.19 2.15 2.10 2.06 2.01 1.96 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 2.15 2.11 2.06 2.02 1.97 1.92 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 2.03 1.98 1.93 1.88 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 2.08 2.04 1.99 1.95 1.90 1.84 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 1.96 1.92 1.87 1.81 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 2.03 1.98 1.94 1.89 1.84 1.78 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 2.01 1.96 1.91 1.86 1.81 1.76 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 1.98 1.94 1.89 1.84 1.79 1.73 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 1.87 1.82 1.77 1.71 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.15 2.07 1.99 1.95 1.90 1.85 1.80 1.75 1.69 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.67 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.64 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 1.89 1.84 1.79 1.74 1.68 1.62 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 1.79 1.74 1.69 1.64 1.58 1.51 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 1.70 1.65 1.59 1.53 1.47 1.39 120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1.25 n 2 = d e g r e e s o f f r e e d o m f o r d e n o m i n a t o r ∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00 A 11