T_and_F_tables

T_and_F_tables - 350 Appendix 4 Statistical tables Table...

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Unformatted text preview: 350 Appendix 4 Statistical tables Table A4.1 Critical values for student's t-distribution _ . Probability PM 5 c) Probability PM 2 c) Probability PH 2 c) ‘ _ ‘ tor confidence for two-sided tests tor oneosided tests " Intervals -c 0 c -c 0 c o c Probability Confidence .50 .80 .90 .95 .98 .99 .995 .998 .999 Intervals ~ Two-Sided .50 .20 - .10 .05 .02 .01 .005 .002 .001 Tests , One-Sided df .25‘ .10 .05 .025 .01 .005 .0025 .001 .0005 Tests 1 1.000 3.078 6.314 12.706 31.821 63.637 127.32 - 318.31 636.62 2 .816 1.886 2.920 4.303 6.965 9.925 14.089 22.326 31.598 3 .765 1.638 2.353 3.182 4.541 5.841 7.453 10.213 12.924 4 .741 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610 5 .727 1.476 2.015 ‘ 2.571 3.365 4.032 4.773 5.893 6.869 6 .718 1.440 1.943 2.447 3.143 3.707 4.3 17 5.208 5.959 7 .71 1 1.415 1.895 2.365 2.998 3.499 4.020 4.785 5.408 8. . .706 1.397 1.860 2.306 2.896 3.355 3.833 4.501 5.041 9 .703 1.383 1.833 2.262 2.821 3.250 3.690 4.297 4.78 1 [0 .700 1.372 1.812. 2.228 2.764 3.169 3.581 4.144 4.537 I l .697 1.363 1.796 2.201. 2.718 3.106 ' 3.497 4.025 4.437 [2 .695 1.356 1.782 2.179 2.681 3.055 _ 3.428 3.930 4.318 Q I3 .694 1.350 1.771 2.160 2.650 3.012 3.372 3.852 4.221 14 .692 1.345 1.761 2.145 2.624 2.977 3.326 3.787 4.140 15 .691 1.341 1.753 2.131 2.602 2.947 3.286 3.733 4.073 16 .690 1.337 1.746 2.120 2.583 2.921 3.252 3.686 4.015 17 V .689 1.333 1.740 2.1 10 2.567 2.898 3.222 3.646 3.965 [8 .688 1.330 1.734 2.101 2.552 2.878 3.197 3.610 3.922 19 .688 1.328 1.729 2.093 2.539 2.861 3.174 3.579 3.883 20 .687 1.325 1.725 2.086 2.528 2.845 3.153 3.552 3.850 2] .686 1.323 1.721 2.080 2.518 2.831 3.135 3.527 3.819 22 .686 1.321 1.717 2.074 2.508 2.819 3.1 19 3.505 3.792 23 .685 1.319 1.714 2.069 2.500 2.807 3.104 3.485 3.767 24 .685 1.3 18 1.71 1 2.064 2.492 2.797 3.09 1 3.467 3.745 25 .684 1.316 1.708 2.060 2.485 2.787 3.078 3.450 3.725 26 .684 1.315 1.706 2.056 2.479 2.779 3.067 3.435 3.707 27 .684 1.314 1.703 2.052 2.473 2.771 3.057 3.421 3.690 28 . .683 1.313 1.701 2.048 2.467 2.763 3.047 3.408 3.674 29 .683 1.31 1 1.699 2.045 2.462 2756 3.038 3.396 3.659 30 .683 1.310 1.697 2.042 2.457 2.750 3.030 3.385 3.646 40 .68 1 1.303 1.684 2.021 2423 2704 2.971 3.307 3.551 60 .679 1.296 1.671 2.000 2.390 2.660 2.915 3.232 3.460 I20 .677 1.289 1.658 1.980 2.358 2617 2860 3.160 3.373 a: .674 1.282 1.645 1.960 2326 2.576 2.807 3.090 3.291 Source: Abridged from Table 12 of Biometrika Table: for Slalirlitiam. Vol. I. edited by E. 5. Pearson and H. O. Hartley (London: Cambridge University Press. 1962). Appendix 4 Statistical Tables 35] Table A4.2 Critical values for the F distribution Probability P (F 2 c) 1 Numerator Degrees of F reedom, df. P 1 2 3 4 5 6 8 10 20 40 no .25, 5.83 7.50 8.21 8.58 8.82 8.98 9.19 9.32 9.58 ~ 9.71 9.85 .10 39.86 49.50 53.59 55.83 57.24 58.20 59.44 60.19 61.74 6253 63.33 .05 161.4 199.5 215.7 224.6 230.2 234.0 238.9 241.9 248.0 251.1 254.3 .25 257 3.00 3.15 3.23 3.28 3.31 3.35 3.38 3.43 3.45 3.48 .10 8.53 9.00 9.16 9.24 9.29 9.33 9.37 9.39 9.44 9.47 9.49 .05 18.51 19.00 19.16 19.25 19.30 19.33 19.37 19.40 19.45 19.47 19.50 .01 98.50 99.00 99.1 7 99.25 99.30 . 99.33 99.37 99.40 99.45 99.47 99.50 .001 998.5 999.0 999.2 9992 999.3 999.3 999.4 999.4 999.4 999.5 999.5 .25 202 2.28 236 2.39 241 242 2.44 244 246 247 247 .10 5.54 5.46 5.39 5.34 5.31 5.28 5.25 5.23 5.18 5.16 5.13 2'; .05 10.13 9.55 9.28 9.12 9.01 8.94 8.85 8.79 8.66 8.59 8.53 E- .01 34.12 30.82 29.46 28.71 28.24 27.91 27.49 27.23 26.69 26.41 26.13 § .001 167.0 148.5 141.1 137.1 134.6 132.8 130.6 129.2 126.4 125.0 123.5 § .25 1.81 ~ 2.00 205 2.06 2.07 2.08 208 208 ' 208 208 208 t .10 4.54 4.32 4.19 4.1 1 4.05 __4,01 , 3.95 3.92 3.84 3.76 f; .05 7.71 6.94 6.59 6.39 6.26 6.16 6.04 5.96 5.80 5.72 . 5.63 § .01 21.20 18.00 16.69 15.98 1552 15.21 14.80 14.55 ' 14.02 13.75 13.46 g .001 74.14 61.25 56.18 53.44 51.71 50.53 49.00 48.05 46.10 45.09 44.05 ._ .25 1.69 1.85 1.88 1.89 1.89 1.89 1.89 1.89 1.88 1.88 1.87 § .10 4.06 3.78 3.62 3.52 3.45 3.40 3.34 3.30 3.21 3.16 3.10 'g .05 6.61 5.79 5.41 5.19 5.05 4.95 4.82 4.74 4.56 4.46 4.36 2 .01 16.26 13.27 12.06 I 1.39 10.97 10.67 10.29 10.05 9.55 9.29 9.02 3 .001 47.18 ' 37.12 33.20 31.09 29.75 28.84 27.64 26.92 25.39 24.60 23.79 .25 1.62 1.76 1.78 1.79 1.79 1.78 1.78 1.77 1.76 1.75 1.74 .10 3.78 3.46 3.29 3.18 3.1 1 3.05 298 294 284 278 272 .05 5.99 5.14 4.76 4.53 4.39 4.28 4.15 4.06 3.87 3.77 3.67 .01 13.75 10.92 9.78 9.15 8.75 8.47 8.10 7.87 7.40 7.14 6.88 .001 35.51 27.00 23.70 21.92 20.81 20.03 19.03 18.41 17.12 16.44 15.75 .25 ‘ 1.57 1.70 1.72 ' 1.72 1.71 1.71 1.70 1.69 1.67 1.66 1.65 .10 3.59 3.26 3.07 296 288 283 275 270 259 254 247 .05 5.59 4.74 4.35 4.12 3.97 3.87 3.73 3.64 3.44 3.34 3.23 .01 1225 9.55 8.45 7.85 7.46 7.19 6.84 6.62 6.16 5.91 5.65 .001 29.25 21.69 18.77 17.19 16.21 15.52 14.63 14.08 1293 12.33 1 1.70 (continued) 352 Appendix 4 Statistical Tables table A4.2 continued m Numerator Degrees of Freedom. (11'. ______________—_____———\ P 1 2 3 4 S 6 8 IO 20 40 m m 8 .25 1.54 1.66 1.67 1.66 1.66 1.65 1.64 1.63 1.61 1.59 158 JO 3.46 3.1 1 2.92 2.81 2.73 2.67 2.59 2.54 2.42 2.36 2.29 .05 5.32 4.46 4.07 3.84 3.69 3.58 3.44 3.35 3.15 3.04 2.93 .0! 1 1.26 8.65 7.59 7.01 6.63 6.37 6.03 5.8 1 5.36 5.12 4.86 .001 25.42 18.49 15.83 14.39 ' 13.49 12.86 12.04 1 1.54 10.48 9.92 9.33 9 .25 1.51 1.62 1.63 1.63 1.62 1.61 1.60 1.59 1.56 1.54 1.53 .10 . 3.36 3.01 2.81 2.69 2.61 2.55 247 2.42 2.30 2.23 2.16 05 5.12 4.26 3.86 3.63 3.48 3.37 3.23 3.14 2.94 2.83 271 :01 10.56 8.02 6.99 6.42 6.06 5.80 5.47 5.26 4.81 4.57 4.31 .00] 22.86 16.39 13.90 12.56 1 1.71 11.13 10.37 9.89 8.90 8.37 7.81 [0 .25 1.49 1.60 1.60 1.59 1.59 1.58 1.56 1.55 1.52 1.51 1.48 . [0 3.28 2.92 273 2.61 2.52 2.46 2.38 2.32 2.20 2.13 2.06 .05 4.96 4.10 3.71 3.48 3.33 3.22 3.07 2.98 2.77 2.66 2.54 .0] 10.04 7.56 I 6.55 5.99 5.64 5.39 5.06 4.85 4.41 4.17 3.91 .001 21.04 14.91 12.55 1 1.28 10.48 ' 9.92 9.20 8.75 7.80 7.30 6.76 12 .25 1.46 1.56 1.56 1.55 1.54 1.53 1.51 1.50 1.47 1.45 1.42 .l0 3.18 2.81 2.61 2.48 2.39 2.33 2.24 2.19 2.06 1.99 1.90 .05 4.75 3.89 3.49 3.26 3.1 1 3.00 2.85 2.75 2.54 243 2.30 .0 l 9.33 6.93 5.95 5.41 5.06 4.82 4.50 4.30 3.86 3.62 3.36 .001 18.64 12.97 10.80 9.63 8.89 8.38 7.71 7.29 6.40 5.93 5.42 I4 .25 1.44 1.53 1.53 1.52 1.51 1.50 1.48 1.46 1.43 1.41 1.38 .I0 3.10 2.73 2.52 2.39 2.31 2.24 2.15 2.10 1.96 1.89 1.80 .05 4.60 3.74 3.34 3.11 296 2.85 2.70 2.60 2.39 ' 2.27 213 .0] 8.86 5.51 5.56 5.04 4.69 4.46 4.14 3.94 3.51 3.27 3.00 .001 17.14 1 1.78 9.73 8.62 7.92 7.43. 6.80 6.40 5.56 5.10 4.60 16 .25 1.42 1.51 1.51 1.50 1.48 1.48 1.46 1.45 1.40 1.37 1.34 .l0 3.05 2.67 2.46 2.33 2.24 2.18 2.09 2.03 1.89 1.81 1.72 .05 4.49 3.63 3.24 3.01 2.85 2.74 2.59 2.49 2.28 2.15 2.01 .0] 8.53 6.23 5.29 4.77 4.44 4.20 3.89 3.69 3.26 3.02 2.75 .001 16.12 . 10.97 9.00 7.94 7.27 6.81 6.19 5.81 4.99 4.54 4.06 [8 .25 1.41 1.50 1.49 1.48 1.46 1.45 1.43 1.42 1.38 1.35 1.32 .10 3.01 2.62 2.42 2.29 2.20 2.13 2.04 1.98 1.84 1.75 1.66 .05 4.41 3.55 3.16 2.93 2.77 2.66 2.51 241 2.19 2.06 1.92 .01 8.29 6.01 5.09 4.58 4.25 4.01 3.71 3.51 3.08 2.84 2.57 .001 15.38 10.39 8.49 7.46 - 6.81 6.35 5.76 5.39 4.59 4.15 3.67 _—_______________________—________—____— Denominator Degrees of F reedom. df, ‘loole A42 continued m Numerator Degrees of Freedom. (if, m r 1 2 3 4 s 6 8 1o 20 40 a, m. 20 25 1.40 1.49 1.48 1.46 1.45 ‘ 1.44 1.42 1.40 1.36 1.33 1.29 .l0 2.97 2.59 2.38 2.25 2.16 2.09 2.00 1.94 1.79 1.71 1.61 .05 4.35 3.49 3.10 2.87 2.71 2.60 2.45 2.35 2.12 1.99 1.84 .0] 8.10 5.85 4.94 4.43 4.10 3.87 3.56 3.37 2.94 2.69 2.42 .001 14.82 9.95 8.10 7.10 6.46 6.02 5.44 5.08 4.29 3.86 3.38 30 .25 1.38 1.45 1.44 1.42 1.41 1.39 1.37 1.35 1.30 1.27 1.23 .l0 2.88 2.49 2.28 2.14 2.05 1.98 1.88 1.82 1.67 1.57 1.46 .05 4.17 3.32 2.92 2.69 2.53 2.42 2.27 2.16 1.93 1.79 1.62 .0] 7.56 5.39 4.51 4.02 3.70 3.47 3.17 2.98 2.55 2.30 2.01 "'5_ .001 13.29 8.77 7.05 6.12 5.53 5.12 4.58 4.24 3.49 3.07 259 E 40 .25 1.36 1.44 1.42 1.40 1.39 1.37 1.35 1.33 1.28 1.24 1.19 E .10 2.84 2.44 223 209 200 1.93 1.83 1.76 1.61 1.51 1.38 L: .05 4.08 3.23 284 2.61 2.45 234 218 2.08 1.84 1.69 1.51 ‘3. .01 7.31 5.18 4.31 3.83 3.51 329 299 280 237 2.11 1.80 .001 12.61 8.25 6.60 5.70 5.13 4.73 4.21 3.87 3.15 273 223 1% 60 .25 1.35 1.42 1.41 1.38 1.37 1.35 1.32 1.30 1.25 1.21 1.15 a .10 279 2.39 218 204 1.95 1.87 1.77 1.71 ~ 1.54 1.44 1.29 .5. .05 4.00 3.15 276 253 237 225 210 1.99 1.75 1.59 139 g .01 7.08 4.98 4.13 3.65 3.34 3.12 282 263 220 1.94 1.60 § .001 11.97 7.76 6.17 5.31 4.76 4.37 3.87 3.54 283 241 1.89 55 120 .25 1.34 1.40 1.39 1.37 1.35 1.33 1.30 1.28 1.22 1.18 1.10 .10 2.75 2.35 2.13 1.99 1.90 1.82 1.72 1.65 1.48 1.37 1.19 .05 33.92 3.07 2.68 2.45 2.29 2.1 7 2.02 1.9 1 1.66 1.50 1.25 .01 6.85 4.79 3.95 3.48 3.1 7 2.96 2.66 2.47 2.03 1.76 1.38 .001 1 1.38 7.32 5.79 4.95 4.42 ‘ 4.04 3.55 3.24 2.53 2.11 1.54 :1: .25 1.32 1.39 1.37 1.35 1.33 1.31 1.28 1.25 1.19 1.14 1.00 .I0 2.71 2.30 2.08 1.94 1.85 1.77 1.67 1.60 1.42 1.30 1.00 .05 3.84 3.00 2.60 2.37 2.21 2.10 1.94 1.83 1.57 1.39 1.00 .01 6.64 4.61 3.78 3.32 3.02 2.80 2.51 2.32 1.88 1.59 1.00 .001 10.83 6.91 5.42 4.62 4.10 3.74 3.27 2.96 2.27 1.84 1.00 Source: Abridged from Table 18 of Biomem'ka Table: jar Statisticians. Vol. I. edited by E. S. Pearson and H. 0. Hartley (London: Cambridge University Press. 1962). _______—___________——_———— ...
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This note was uploaded on 03/27/2012 for the course ECON 2280 taught by Professor Daniel during the Spring '12 term at Dalhousie.

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T_and_F_tables - 350 Appendix 4 Statistical tables Table...

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