100 STATISTICAL TESTS phần 9 docx

GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 192 — #8 192 100 STATISTICAL TESTS Table 3 continued Level of significance α = 0.01 ν 1 ν 2 123456789 1 4052 4999 5403 5625 5764 5859 5928 5981 6022 2 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 ∞ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 193 — #9 TABLES 193 Table 3 continued Level of significance α = 0.01 ν 1 ν 2 10 12 15 20 24 30 40 60 120 ∞ 1 6056 6106 6157 6209 6235 6261 6287 6313 6339 6366 2 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 3 27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13 4 14.55 14.37 14.20 14.02 13.39 13.84 13.75 13.65 13.56 13.46 5 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02 6 7.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88 7 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65 8 5.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4.86 9 5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.31 10 4.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.91 11 4.54 4.40 4.25 4.10 4.02 3.94 3.86 3.78 3.69 3.60 12 4.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.36 13 4.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17 14 3.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.00 15 3.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87 16 3.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.75 17 3.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.65 18 3.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.57 19 3.43 3.30 3.15 3.00 2.92 2.84 2.76 2.67 2.58 2.49 20 3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42 21 3.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.36 22 3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.31 23 3.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.26 24 3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.21 25 3.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.17 26 3.09 2.96 2.81 2.66 2.58 2.50 2.42 2.33 2.23 2.13 27 3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.10 28 3.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.06 29 3.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03 30 2.98 2.84 2.70 2.55 2.47 2.39 2.30 2.21 2.11 2.01 40 2.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.80 60 2.63 2.50 2.35 2.20 2.12 2.03 1.94 1.84 1.73 1.60 120 2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1.38 ∞ 2.32 2.18 2.04 1.88 1.79 1.70 1.59 1.47 1.32 1.00 Source: Pearson and Hartley, 1970 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 194 — #10 194 100 STATISTICAL TESTS Table 4 Fisher z-transformation z(r) = 1 2 log e  1 +r 1 −r  = tanh −1 r = 1.1513 log 10  1 +r 1 −r  z 0123456789 0.0 0.0000 0.0100 0.0200 0.0300 0.0400 0.0500 0.0601 0.0701 0.0802 0.0902 0.1 0.1003 0.1104 0.1206 0.1307 0.1409 0.1511 0.1614 0.1717 0.1820 0.1923 0.2 0.2027 0.2132 0.2237 0.2341 0.2448 0.2554 0.2661 0.2769 0.2877 0.2986 0.3 0.3095 0.3205 0.3316 0.3428 0.3541 0.3654 0.3769 0.3884 0.4001 0.4118 0.4 0.4236 0.4356 0.4477 0.4599 0.4722 0.4847 0.4973 0.5101 0.5230 0.5361 0.5 0.5493 0.5627 0.5763 0.5901 0.6042 0.6184 0.6328 0.6475 0.6625 0.6777 0.6 0.6931 0.7089 0.7250 0.7414 0.7582 0.7753 0.7928 0.8107 0.8291 0.8480 0.7 0.8673 0.8872 0.9076 0.9287 0.9505 0.9730 0.9962 1.0203 1.0454 1.0714 0.8 1.0986 1.1270 1.1568 1.1881 1.2212 1.2562 1.2933 1.3331 1.3758 1.4219 0.90 1.4722 1.4775 1.4828 1.4882 1.4937 1.4992 1.5047 1.5103 1.5160 1.5217 0.91 1.5275 1.5334 1.5393 1.5453 1.5513 1.5574 1.5636 1.5698 1.5762 1.5826 0.92 1.5890 1.5956 1.6022 1.6089 1.6157 1.6226 1.6296 1.6366 1.6438 1.6510 0.93 1.6584 1.6658 1.6734 1.6811 1.6888 1.6967 1.7047 1.7129 1.7211 1.7295 0.94 1.7380 1.7467 1.7555 1.7645 1.7736 1.7828 1.7923 1.8019 1.8117 1.8216 0.95 1.8318 1.8421 1.8527 1.8635 1.8745 1.8857 1.8972 1.9090 1.9210 1.9333 0.96 1.9459 1.9588 1.9721 1.9857 1.9996 2.0139 2.0287 2.0439 2.0595 2.0756 0.97 2.0923 2.1095 2.1273 2.1457 2.1649 2.1847 2.2054 2.2269 2.2494 2.2729 0.98 2.2976 2.3235 2.3507 2.3796 2.4101 2.4427 2.4774 2.5147 2.5550 2.5987 0.99 2.6467 2.6995 2.7587 2.8257 2.9031 2.9945 3.1063 3.2504 3.4534 3.8002 Source: Neave, 1978 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 195 — #11 TABLES 195 Table 5 Critical values for the χ 2 -distribution Columns a denote the lower boundaries or the left-sided critical values. Columns b denote the upper boundaries or the right-sided critical values. Level of significance α Two-sided 0.20 0.10 0.05 0.01 One-sided 0.10 0.05 0.025 0.005 ν abababab 1 0.016 2.71 39.10 −4 3.84 98.10 −5 5.02 16.10 −5 6.63 2 0.21 4.61 0.10 5.99 0.05 7.38 0.02 9.21 3 0.58 6.25 0.35 7.81 0.22 9.35 0.11 11.34 4 1.06 7.78 0.71 9.49 0.48 11.14 0.30 13.28 5 1.61 9.24 1.15 11.07 0.83 12.83 0.55 15.09 6 2.20 10.64 1.64 12.59 1.24 14.45 0.87 16.81 7 2.83 12.02 2.17 14.07 1.69 16.01 1.24 18.48 8 3.49 13.36 2.73 15.51 2.18 17.53 1.65 20.09 9 4.17 14.68 3.33 16.92 2.70 19.02 2.09 21.67 10 4.87 15.99 3.94 18.31 3.25 20.48 2.56 23.21 11 5.58 17.28 4.57 19.68 3.82 21.92 3.05 24.73 12 6.30 18.55 5.23 21.03 4.40 23.34 3.57 26.22 13 7.04 19.81 5.89 22.36 5.01 24.74 4.11 27.69 14 7.79 21.06 6.57 23.68 5.63 26.12 4.66 29.14 15 8.55 22.31 7.26 25.00 6.26 27.49 5.23 30.58 16 9.31 23.54 7.96 26.30 6.91 28.85 5.81 32.00 17 10.09 24.77 8.67 27.59 7.56 30.19 6.41 33.41 18 10.86 25.99 9.39 28.87 8.23 31.53 7.01 34.81 19 11.65 27.20 10.12 30.14 8.91 32.85 7.63 36.19 20 12.44 28.41 10.85 31.41 9.59 34.17 8.26 37.57 21 13.24 29.62 11.59 32.67 10.28 35.48 8.90 38.93 22 14.04 30.81 12.34 33.92 10.98 36.78 9.54 40.29 23 14.85 32.01 13.09 35.17 11.69 38.08 10.20 41.64 24 15.66 33.20 13.85 36.42 12.40 39.36 10.86 42.98 25 16.47 34.38 14.61 37.65 13.12 40.65 11.52 44.31 26 17.29 35.56 15.38 38.89 13.84 41.92 12.20 45.64 27 18.11 36.74 16.15 40.11 14.57 43.19 12.88 46.96 28 18.94 37.92 16.93 41.34 15.31 44.46 13.56 48.28 29 19.77 39.09 17.71 42.56 16.05 45.72 14.26 49.59 30 20.60 40.26 18.49 43.77 16.79 46.98 14.95 50.89 40 29.05 51.81 26.51 55.76 24.43 59.34 22.16 63.69 50 37.69 63.17 34.76 67.50 32.36 71.42 29.71 76.15 60 46.46 74.40 43.19 79.08 40.48 83.30 37.48 88.38 70 55.33 85.53 51.74 90.53 48.76 95.02 45.44 100.43 80 64.28 96.58 60.39 101.88 57.15 106.63 53.54 112.33 90 73.29 107.57 69.13 113.15 65.65 118.14 61.75 124.12 100 82.36 118.50 77.93 124.34 74.22 129.56 70.06 135.81 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 196 — #12 196 100 STATISTICAL TESTS Table 6 Critical values of r for the correlation test with ρ = 0 The distribution is symmetrical with respect to ρ = 0. Level of significance α Two-sided 0.10 0.05 0.02 0.01 0.001 One-sided 0.05 0.025 0.01 0.005 0.0005 ν = n − 2 1 0.988 0.997 0.9995 0.9999 1.000 2 0.900 0.950 0.980 0.990 0.999 3 0.805 0.878 0.934 0.959 0.991 4 0.729 0.811 0.882 0.917 0.974 5 0.669 0.754 0.833 0.874 0.951 6 0.622 0.707 0.789 0.834 0.925 7 0.582 0.666 0.750 0.798 0.898 8 0.549 0.632 0.716 0.765 0.872 9 0.521 0.602 0.685 0.735 0.847 10 0.497 0.576 0.658 0.708 0.823 11 0.476 0.553 0.634 0.684 0.801 12 0.458 0.532 0.612 0.661 0.780 13 0.441 0.514 0.592 0.641 0.760 14 0.426 0.497 0.574 0.623 0.742 15 0.412 0.482 0.558 0.606 0.725 16 0.400 0.468 0.542 0.590 0.708 17 0.389 0.456 0.528 0.575 0.693 18 0.378 0.444 0.516 0.561 0.679 19 0.369 0.433 0.503 0.549 0.665 20 0.360 0.423 0.492 0.537 0.652 22 0.344 0.404 0.472 0.515 0.629 24 0.330 0.388 0.453 0.496 0.607 25 0.323 0.381 0.445 0.487 0.597 30 0.296 0.349 0.409 0.449 0.554 35 0.275 0.325 0.381 0.418 0.519 40 0.257 0.304 0.358 0.372 0.490 45 0.243 0.288 0.338 0.372 0.415 50 0.231 0.273 0.322 0.354 0.443 55 0.220 0.261 0.307 0.338 0.424 60 0.211 0.250 0.295 0.325 0.408 65 0.203 0.240 0.284 0.312 0.393 70 0.195 0.232 0.274 0.302 0.380 75 0.189 0.224 0.264 0.292 0.368 80 0.183 0.217 0.256 0.283 0.357 85 0.178 0.211 0.249 0.275 0.347 90 0.173 0.205 0.242 0.267 0.338 95 0.168 0.200 0.236 0.260 0.329 100 0.164 0.195 0.230 0.254 0.321 125 0.147 0.174 0.206 0.228 0.288 150 0.134 0.159 0.189 0.208 0.264 175 0.124 0.148 0.174 0.194 0.248 200 0.116 0.138 0.164 0.181 0.235 300 0.095 0.113 0.134 0.148 0.188 500 0.074 0.088 0.104 0.115 0.148 1000 0.052 0.062 0.073 0.081 0.104 2000 0.037 0.044 0.056 0.058 0.074 Source: De Jonge, 1963–4 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 197 — #13 TABLES 197 Table 7 Critical values of g 1 and g 2 for Fisher’s cumulant test The g 1 distribution may be considered as symmetrical with respect to 0; the g 2 distribution has to be considered as asymmetrical. The columns a denote the lower boundaries or left-sided critical values. The columns b denote the upper boundaries or right-sided critical values. g 1 g 2 Level of significance α Two-sided 0.10 0.02 0.10 0.02 One-sided 0.05 0.01 0.05 0.01 n abab 50 0.550 0.812 –––– 75 0.454 0.664 –––– 100 0.395 0.576 −0.62 1.53 −0.80 1.53 125 0.354 0.514 −0.57 1.34 −0.74 1.34 150 0.324 0.469 −0.53 1.22 −0.69 1.22 175 0.301 0.434 −0.50 1.11 −0.66 1.11 200 0.282 0.406 −0.47 1.04 −0.62 1.04 250 0.253 0.362 −0.44 0.91 −0.57 0.91 300 0.231 0.331 −0.40 0.82 −0.53 0.82 350 0.214 0.306 −0.37 0.75 −0.49 0.75 400 0.201 0.286 −0.35 0.69 −0.48 0.69 450 0.189 0.270 −0.33 0.65 −0.44 0.65 500 0.180 0.256 −0.32 0.62 −0.42 0.62 550 0.171 0.244 −0.30 0.59 −0.41 0.59 600 0.163 0.234 −0.29 0.55 −0.39 0.55 650 0.157 0.225 −0.28 0.53 −0.38 0.53 700 0.151 0.215 −0.27 0.51 −0.37 0.51 750 0.146 0.208 −0.26 0.49 −0.35 0.49 800 0.142 0.202 −0.25 0.47 −0.34 0.47 850 0.138 0.196 −0.25 0.46 −0.33 0.46 900 0.134 0.190 −0.24 0.44 −0.33 0.44 950 0.130 0.185 −0.23 0.43 −0.32 0.43 1000 0.127 0.180 −0.23 0.42 −0.31 0.42 Source: Geary and Pearson, n.d.; Bennett and Franklin, 1961 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 198 — #14 198 100 STATISTICAL TESTS Table 8 Critical values for the Dixon test of outliers Test Level of significance α Statistic n 0.30 0.20 0.10 0.05 0.02 0.01 0.005 3 0.684 0.781 0.886 0.941 0.976 0.988 0.994 4 0.471 0.560 0.679 0.765 0.846 0.889 0.926 5 0.373 0.451 0.557 0.642 0.729 0.780 0.821 r 10 = x 2 − x 1 x n − x 1 6 0.318 0.386 0.482 0.560 0.644 0.698 0.740 7 0.281 0.344 0.434 0.507 0.586 0.637 0.680 8 0.318 0.385 0.479 0.554 0.631 0.683 0.725 9 0.288 0.352 0.441 0.512 0.587 0.635 0.677 r 11 = x 2 − x 1 x n−1 − x 1 10 0.265 0.325 0.409 0.477 0.551 0.597 0.639 11 0.391 0.442 0.517 0.576 0.638 0.679 0.713 12 0.370 0.419 0.490 0.546 0.605 0.642 0.675 r 21 = x 3 − x 1 x n−1 − x 1 13 0.351 0.399 0.467 0.521 0.578 0.615 0.649 14 0.370 0.421 0.492 0.546 0.602 0.641 0.674 15 0.353 0.402 0.472 0.525 0.579 0.616 0.647 16 0.338 0.386 0.454 0.507 0.559 0.595 0.624 17 0.325 0.373 0.438 0.490 0.542 0.577 0.605 18 0.314 0.361 0.424 0.475 0.527 0.561 0.589 r 22 = x 3 − x 1 x n−2 − x 1 19 0.304 0.350 0.412 0.462 0.514 0.547 0.575 20 0.295 0.340 0.401 0.450 0.502 0.535 0.562 21 0.287 0.331 0.391 0.440 0.491 0.524 0.551 22 0.280 0.323 0.382 0.430 0.481 0.514 0.541 23 0.274 0.316 0.374 0.421 0.472 0.505 0.532 24 0.268 0.310 0.367 0.413 0.464 0.497 0.524 25 0.262 0.304 0.360 0.406 0.457 0.489 0.516 Source: Dixon and Massey, 1957 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 199 — #15 TABLES 199 Table 9 Critical values of the Studentized range for multiple comparison Level of significance α = 0.05 K ν 2 234567891011121314151617181920 1 17.969 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07 50.59 51.96 53.20 54.33 55.36 56.32 57.22 58.04 58.83 59.56 2 6.085 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99 14.39 14.75 15.08 15.38 15.65 15.91 16.14 16.37 16.57 16.77 3 4.501 5.91 6.82 7.50 8.04 8.48 8.85 9.18 9.46 9.72 9.95 10.15 10.35 10.52 10.69 10.84 10.98 11.11 11.24 4 3.926 5.04 5.76 6.29 6.71 7.05 7.35 7.60 7.83 8.03 8.21 8.37 8.52 8.66 8.79 8.91 9.03 9.13 9.23 5 3.635 4.60 5.22 5.67 6.03 6.33 6.58 6.80 6.99 7.17 7.32 7.47 7.60 7.72 7.83 7.93 8.03 8.12 8.21 6 3.460 4.34 4.90 5.30 5.63 5.90 6.12 6.32 6.49 6.65 6.79 6.92 7.03 7.14 7.24 7.34 7.43 7.51 7.59 7 3.344 4.16 4.68 5.06 5.36 5.61 5.82 6.00 6.16 6.30 6.43 6.55 6.66 6.76 6.85 6.94 7.02 7.10 7.17 8 3.261 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92 6.05 6.18 6.29 6.39 6.48 6.57 6.65 6.73 6.80 6.87 9 3.199 3.95 4.41 4.76 5.02 5.24 5.43 5.59 5.74 5.87 5.98 6.09 6.19 6.28 6.36 6.44 6.51 6.58 6.64 10 3.151 3.88 4.33 4.65 4.91 5.12 5.30 5.46 5.60 5.72 5.83 5.93 6.03 6.11 6.19 6.27 6.34 6.40 6.47 11 3.113 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49 5.61 5.71 5.81 5.90 5.98 6.06 6.13 6.20 6.27 6.33 12 3.081 3.77 4.20 4.51 4.75 4.95 5.12 5.27 5.39 5.51 5.61 5.71 5.80 5.88 5.95 6.02 6.09 6.15 6.21 13 3.055 3.73 4.15 4.45 4.69 4.88 5.05 5.19 5.32 5.43 5.53 5.63 5.71 5.79 5.85 5.93 5.99 6.05 6.11 14 3.033 3.70 4.11 4.41 4.64 4.83 4.99 5.13 5.25 5.36 5.46 5.55 5.64 5.71 5.79 5.85 5.91 5.97 6.03 15 3.014 3.67 4.08 4.37 4.59 4.78 4.94 5.08 5.20 5.31 5.40 5.49 5.57 5.65 5.72 5.78 5.85 5.90 5.96 16 2.998 3.65 4.05 4.33 4.56 4.74 4.90 5.03 5.15 5.26 5.35 5.44 5.52 5.59 5.66 5.73 5.79 5.84 5.90 17 2.984 3.63 4.02 4.30 4.52 4.70 4.86 4.99 5.11 5.21 5.31 5.39 5.47 5.54 5.61 5.67 5.73 5.79 5.84 18 2.971 3.61 4.00 4.28 4.49 4.67 4.82 4.96 5.07 5.17 5.27 5.35 5.43 5.50 5.57 5.63 5.69 5.74 5.79 19 2.960 3.59 3.98 4.25 4.47 4.65 4.79 4.92 5.04 5.14 5.23 5.31 5.39 5.46 5.53 5.59 5.65 5.70 5.75 20 2.950 3.58 3.96 4.23 4.45 4.62 4.77 4.90 5.01 5.11 5.20 5.28 5.36 5.43 5.49 5.55 5.61 5.66 5.71 21 2.941 3.56 3.94 4.21 4.43 4.60 4.74 4.87 4.98 5.08 5.17 5.25 5.33 5.40 5.46 5.52 5.58 5.62 5.67 22 2.933 3.55 3.93 4.20 4.41 4.58 4.72 4.85 4.96 5.05 5.15 5.23 5.30 5.37 5.43 5.49 5.55 5.59 5.64 23 2.926 3.54 3.91 4.18 4.39 4.56 4.70 4.83 4.94 5.03 5.12 5.20 5.27 5.34 5.40 5.46 5.52 5.57 5.62 24 2.919 3.53 3.90 4.17 4.37 4.54 4.68 4.81 4.92 5.01 5.10 5.18 5.25 5.32 5.38 5.44 5.49 5.55 5.59 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 200 — #16 200 100 STATISTICAL TESTS Table 9 continued K ν 2 234567891011121314151617181920 25 2.913 3.52 3.89 4.16 4.36 4.52 4.66 4.79 4.90 4.99 5.08 5.16 5.23 5.30 5.36 5.42 5.48 5.52 5.57 26 2.907 3.51 3.88 4.14 4.34 4.51 4.65 4.78 4.89 4.97 5.06 5.14 5.21 5.28 5.34 5.40 5.46 5.50 5.55 27 2.902 3.51 3.87 4.13 4.33 4.50 4.63 4.76 4.87 4.96 5.04 5.12 5.19 5.26 5.32 5.38 5.43 5.48 5.53 28 2.897 3.50 3.86 4.12 4.32 4.48 4.62 4.75 4.86 4.94 5.03 5.11 5.18 5.24 5.30 5.36 5.42 5.46 5.51 29 2.892 3.49 3.85 4.11 4.31 4.47 4.61 4.73 4.84 4.93 5.01 5.09 5.16 5.23 5.29 5.35 5.40 5.44 5.49 30 2.888 3.49 3.85 4.10 4.30 4.46 4.60 4.72 4.82 4.92 5.00 5.08 5.15 5.21 5.27 5.33 5.38 5.43 5.47 31 2.884 3.48 3.83 4.09 4.29 4.45 4.59 4.71 4.82 4.91 4.99 5.07 5.14 5.20 5.26 5.32 5.37 5.41 5.46 32 2.881 3.48 3.83 4.09 4.28 4.44 4.58 4.70 4.81 4.89 4.98 5.06 5.13 5.19 5.24 5.30 5.35 5.40 5.45 33 2.877 3.47 3.82 4.08 4.27 4.44 4.57 4.69 4.80 4.88 4.97 5.04 5.11 5.17 5.23 5.29 5.34 5.39 5.44 34 2.874 3.47 3.82 4.07 4.27 4.43 4.56 4.68 4.79 4.87 4.96 5.03 5.10 5.16 5.22 5.28 5.33 5.37 5.42 35 2.871 3.46 3.81 4.07 4.26 4.42 4.55 4.67 4.78 4.86 4.95 5.02 5.09 5.15 5.21 5.27 5.32 5.36 5.41 36 2.868 3.46 3.81 4.06 4.25 4.41 4.55 4.66 4.77 4.85 4.94 5.01 5.08 5.14 5.20 5.26 5.31 5.35 5.40 37 2.865 3.45 3.80 4.05 5.25 4.41 4.54 4.65 4.76 4.84 4.93 5.00 5.08 5.14 5.19 5.25 5.30 5.34 5.39 38 2.863 3.45 3.80 4.05 4.24 4.40 4.53 4.64 4.75 4.84 4.92 5.00 5.07 5.13 5.18 5.24 5.29 5.33 5.38 39 2.861 3.44 3.79 4.04 4.24 4.40 4.53 4.64 4.75 4.83 4.92 4.99 5.06 5.12 5.17 5.23 5.28 5.32 5.37 40 2.858 3.44 3.79 4.04 4.23 4.39 4.52 4.63 4.73 4.82 4.90 4.98 5.04 5.11 5.16 5.22 5.27 5.22 5.36 50 2.841 3.41 3.76 4.00 4.19 4.34 4.47 4.58 4.69 4.76 4.85 4.92 4.99 5.05 5.10 5.15 5.20 5.24 5.29 60 2.829 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65 4.73 4.81 4.88 4.94 5.00 5.06 5.11 5.15 5.20 5.24 120 2.800 3.36 3.68 3.92 4.10 4.24 4.36 4.47 4.56 4.64 4.71 4.78 4.84 4.90 4.95 5.00 5.04 5.09 5.13 ∞ 2.772 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47 4.55 4.62 4.68 4.74 4.80 4.85 4.89 4.93 4.97 5.01 GOKA: “CHAP06A” — 2006/6/10 — 17:23 — PAGE 201 — #17 TABLES 201 Table 9 continued Level of significance α = 0.01 K ν 2 234567891011121314151617181920 1 90.025 135.0 164.3 185.6 202.2 215.8 227.2 237.0 245.6 253.2 260.0 266.2 271.8 277.0 281.8 286.3 290.4 294.3 298.0 2 14.036 19.02 22.29 24.72 26.63 28.20 29.53 30.68 31.69 32.59 33.40 34.13 34.81 35.43 36.00 36.53 37.03 37.50 37.95 3 8.260 10.62 12.17 13.33 14.24 15.00 15.64 16.20 16.69 17.13 17.53 17.89 18.22 18.52 18.81 19.07 19.32 19.55 19.77 4 6.511 8.12 9.17 9.96 10.58 11.10 11.55 11.93 12.27 12.57 12.84 13.09 13.32 13.53 13.73 13.91 14.08 14.24 14.40 5 5.702 6.98 7.80 8.42 8.91 9.32 9.67 9.97 10.24 10.48 10.70 10.89 11.08 11.24 11.40 11.55 11.68 11.81 11.93 6 5.243 6.33 7.08 7.56 7.97 8.32 8.61 8.87 9.10 9.30 9.48 9.65 9.81 9.95 10.08 10.21 10.32 10.43 10.54 7 4.949 5.92 6.54 7.01 7.37 7.68 7.94 8.17 8.37 8.55 8.71 8.86 9.00 9.12 9.24 9.35 9.46 9.55 9.65 8 4.745 5.64 6.20 6.62 6.96 7.24 7.47 7.68 7.86 8.03 8.18 8.31 8.44 8.55 8.66 8.76 8.85 8.94 9.03 9 4.596 5.43 5.96 6.35 6.66 6.91 7.13 7.33 7.49 7.65 7.78 7.91 8.03 8.13 8.23 8.33 8.41 8.49 8.57 10 4.482 5.27 5.77 6.14 6.43 6.67 6.87 7.05 7.21 7.36 7.49 7.60 7.71 7.81 7.91 7.99 8.08 8.15 8.23 11 4.392 5.15 5.62 5.97 6.25 6.48 6.67 6.84 6.99 7.13 7.25 7.36 7.46 7.56 7.65 7.73 7.81 7.88 7.95 12 4.320 5.05 5.50 5.84 6.10 6.32 6.51 6.67 6.81 6.94 7.06 7.17 7.26 7.36 7.44 7.52 7.59 7.66 7.73 13 4.260 4.96 5.40 5.73 5.98 6.19 6.37 6.53 6.67 6.79 6.90 7.01 7.10 7.19 7.27 7.35 7.42 7.48 7.55 14 4.210 4.89 5.32 5.63 5.88 6.08 6.26 6.41 6.54 6.66 6.77 6.87 6.96 7.05 7.13 7.20 7.27 7.33 7.39 15 4.167 4.84 5.25 5.56 5.80 5.99 6.16 6.31 6.44 6.55 6.66 6.76 6.84 6.93 7.00 7.07 7.14 7.20 7.26 16 4.131 4.79 5.19 5.49 5.72 5.92 6.08 6.22 6.35 6.46 6.56 6.66 6.74 6.82 6.90 6.97 7.03 7.09 7.15 17 4.099 4.74 5.14 5.43 5.66 5.85 6.01 6.15 6.27 6.38 6.48 6.57 6.66 6.73 6.81 6.87 6.94 7.00 7.05 18 4.071 4.70 5.09 5.38 5.60 5.79 5.94 6.08 6.20 6.31 6.41 6.50 6.58 6.65 6.73 6.79 6.85 6.91 6.97 19 4.045 4.67 5.05 5.33 5.55 5.73 5.89 6.02 6.14 6.25 6.34 6.43 6.51 6.58 6.65 6.72 6.78 6.84 6.89 20 4.024 4.64 5.02 5.29 5.51 5.69 5.84 5.97 6.09 6.19 6.28 6.37 6.45 6.52 6.59 6.65 6.71 6.77 6.82 21 4.004 4.61 4.99 5.26 5.47 5.65 5.80 5.92 6.04 6.14 6.24 6.32 6.39 6.47 6.53 6.59 6.65 6.70 6.76 22 3.986 4.58 4.96 5.22 5.43 5.61 5.76 5.88 6.00 6.10 6.19 6.27 6.35 6.42 6.48 6.54 6.60 6.65 6.70 23 3.970 4.56 4.93 5.20 5.40 5.57 5.72 5.84 5.96 6.06 6.15 6.23 6.30 6.37 6.43 6.49 6.55 6.60 6.65 24 3.955 4.55 4.91 5.17 5.37 5.54 5.69 5.81 5.92 6.02 6.11 6.19 6.26 6.33 6.39 6.45 6.51 6.56 6.61 [...]... significance α = 0.01 νx 2 3 4 5 6 7 8 9 10 16 36 144 ∞ 2 3 4 5 0 .99 99 0 .99 33 0 .96 76 0 .92 79 0 .99 50 0 .94 23 0.8643 0.7885 0 .97 94 0.8831 0.7814 0. 695 7 0 .95 86 0.8335 0.7212 0.63 29 0 .93 73 0. 793 3 0.6761 0.5875 0 .91 72 0.7606 0.6410 0.5531 0. 898 8 0.7335 0.61 29 0.52 59 0.8823 0.7107 0.5 897 0.5037 0.8674 0. 691 2 0.5702 0.4854 0.85 39 0.6743 0.5536 0.4 697 0. 794 9 0.60 59 0.4884 0.4 094 0.7067 0.5153 0.4057 0.3351 0.6062... 4.40 5.46 5.51 5.56 5.60 5.64 100 150 200 500 1000 1 .99 0 1 .99 3 1 .99 5 1 .99 8 1 .99 9 14.07 17.26 19. 95 31. 59 44.70 4.03 4.32 4.53 5.06 5.50 6.53 6.82 7.01 7.60 7 .99 4.10 4.38 4. 59 5.13 5.57 6.36 6.64 6.84 7.42 7.80 4.21 4.48 4.68 5.25 5.68 6.11 6. 39 6.60 7.15 7.54 4.31 4. 59 4.78 5.47 5. 79 5 .90 6.18 6. 39 6 .94 7.33 4.44 4.72 4 .90 5. 49 5 .92 5.68 5 .96 6.15 6.72 7.11 Source: Sachs, 197 2 Table 15 Critical values... 17 18 19 20 1 .93 6 1 .94 4 1 .94 4 1 .94 9 1 .94 9 5.477 5.657 5.831 6.000 6.164 2. 79 2.83 2.87 2 .90 2 .94 4.62 4.70 4.78 4.85 4 .91 2.84 2.88 2 .92 2 .96 2 .99 4.52 4.60 4.67 4.74 4.80 2 .93 2 .97 3.01 3.05 3. 09 4.37 4.44 4.51 4.56 4.63 3.01 3.06 3.10 3.14 3.18 4.24 4.31 4.37 4.43 4. 49 3.12 3.17 3.21 3.25 3. 29 4. 09 4.15 4.21 4.27 4.32 25 30 35 40 45 1 .96 1 1 .96 6 1 .97 2 1 .97 5 1 .97 8 6 .93 7.62 8.25 8.83 9. 38 3. 09 3.21... 3. 399 3.552 3.685 2.37 2. 49 2. 59 2.68 2.76 2 .94 9 3.143 3.308 3.4 49 3.57 11 12 13 14 15 1 .91 5 1 .91 5 1 .92 7 1 .92 7 1 .93 6 4.472 4. 690 4. 899 5. 099 5. 292 2.53 2. 59 2.64 2.70 2.74 4.0 79 4.208 4.325 4.431 4.53 2.58 2.64 2.70 2.75 2.80 4.012 4.134 4.244 4.34 4.44 2.66 2.72 2.78 2.83 2.88 3 .90 3 4.02 4.12 4.21 4. 29 2.74 2.80 2.86 2 .92 2 .97 3.80 3 .91 4.00 4. 09 4.17 2.84 2 .90 2 .96 3.02 3.07 3.68 3.78 3.87 3 .95 4.02... 5 .94 6.01 6.07 3.73 3.80 3.86 3 .91 3 .96 5.54 5.63 5.70 5.77 5.83 3.83 3 .90 3 .96 4.01 4.06 5.35 5.43 5.51 5.57 5.63 3 .95 4.02 4.08 4.14 4. 19 5.14 5.22 5. 29 5.35 5.41 75 80 85 90 95 1 .98 7 1 .98 7 1 .98 8 1 .98 9 1 .99 0 12.17 12.57 12 .96 13.34 13.71 3.83 3.88 3 .92 3 .96 3 .99 6.30 6.35 6.40 6.45 6. 49 3 .90 3 .94 3 .99 4.02 4.06 6.13 6.18 6.23 6.27 6.32 4.01 4.05 4. 09 4.13 4.17 5.88 5 .93 5 .98 6.03 6.07 4.11 4.16 4.20... 7 29 120 49 28 19. 1 5 6 7 8 9 10 11 12 1036 151 59 33 22 1362 184 69 38 25 1705 216∗ 79 42 27 2063 2 49 89 46 30 2432 281∗ 97 50 32 2813 310∗ 106 54 34 3204 337∗ 113 57 36 3605 361∗ 120 60 37 7 8 9 10 12 8. 89 7.50 6.54 5.85 4 .91 12.1 9. 9 8.5 7.4 6.1 14.5 11.7 9. 9 8.6 6 .9 16.5 13.2 11.1 9. 6 7.6 18.4 14.5 12.1 10.4 8.2 20 15.8 13.1 11.1 8.7 22 16 .9 13 .9 11.8 9. 1 23 17 .9 14.7 12.4 9. 5 24 18 .9 15.3 12 .9 9 .9. .. 28.54 29. 98 31.40 28.81 30.26 31.68 29. 07 30.52 31 .95 29. 30 30.77 32.20 29. 70 31. 19 32.66 29. 99 31.53 33.03 30.16 31.77 33.32 30. 19 31. 89 33.51 30.06 31.88 33. 59 K 100 STATISTICAL TESTS Level of significance α = 0.01 Table 12 continued K Ci Level of significance α = 0.05 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9. 0 10.0 3 4 5 6 7 5 .99 7.81 9. 49 11.07 12. 59 6.47 8.24 9. 88 11.43 12 .94 5. 89 8.63... 25.31 26. 79 20 .90 22.52 24.08 25. 59 27.08 21.08 22.74 24.32 25.85 27.35 21.20 22 .91 24.52 26.08 27. 59 21.35 23.03 24. 69 26.28 27.81 21.13 23.10 24 .90 26.57 28.16 20.64 22 .91 24 .90 26.70 28. 39 19. 76 22.41 24.66 26.65 28.46 – 21.56 24.15 26.38 28.37 – – 23.33 25.86 28.07 13 14 15 26.22 27. 69 29. 14 26.58 28.04 29. 39 26 .93 28. 39 29. 83 27.28 28.73 30.16 27.62 29. 06 30. 49 27 .94 29. 38 30.80 28.25 29. 69 30.11... 18.12 19. 48 20.83 15.60 17.01 18. 39 19. 76 21.10 15.84 17.26 18.65 20.02 21.36 16.06 17. 49 18. 89 20.26 21.61 16.25 17.70 19. 11 20. 49 21.84 16.40 17.88 19. 31 20.70 22.06 16.51 18.03 19. 48 20. 89 22.27 16.60 16.22 19. 75 21.21 22.62 16. 49 18.26 19. 89 21.42 22.88 16.16 18.12 19. 89 21.52 23.06 – 17. 79 19. 73 21. 49 23.12 – – 19. 40 21.32 23.07 13 14 15 21.03 22.36 23.68 21.32 22.65 23 .97 21.60 22 .93 24.24 21. 89 23.21... 0.2 494 0.2214 0. 199 2 0.1811 0.22 29 0. 192 9 0.1700 0.1521 0.1376 0.1667 0.14 29 0.1250 0.1111 0 .1000 12 15 20 24 30 0.6528 0.5747 0.4 799 0.4247 0.3632 0.4751 0.40 69 0.3 297 0.2871 0.2412 0. 391 9 0.3317 0.2654 0.2 295 0. 191 3 0.3428 0.2882 0.2288 0. 197 0 0.1635 0.3 099 0.2 593 0.2048 0.17 59 0.1454 0.2861 0.2386 0.1877 0.1608 0.1327 0.2680 0.2228 0.1748 0.1 495 0.1232 0.2535 0.2104 0.1646 0.1406 0.1157 0.24 19 0.2002 . 0 .98 8 0 .99 7 0 .99 95 0 .99 99 1.000 2 0 .90 0 0 .95 0 0 .98 0 0 .99 0 0 .99 9 3 0.805 0.878 0 .93 4 0 .95 9 0 .99 1 4 0.7 29 0.811 0.882 0 .91 7 0 .97 4 5 0.6 69 0.754 0.833 0.874 0 .95 1 6 0.622 0.707 0.7 89 0.834 0 .92 5 7 0.582. PAGE 192 — #8 192 100 STATISTICAL TESTS Table 3 continued Level of significance α = 0.01 ν 1 ν 2 1234567 89 1 4052 499 9 5403 5625 5764 58 59 592 8 598 1 6022 2 98 .50 99 .00 99 .17 99 .25 99 .30 99 .33 99 .36. 1.7828 1. 792 3 1.80 19 1.8117 1.8216 0 .95 1.8318 1.8421 1.8527 1.8635 1.8745 1.8857 1. 897 2 1 .90 90 1 .92 10 1 .93 33 0 .96 1 .94 59 1 .95 88 1 .97 21 1 .98 57 1 .99 96 2.01 39 2.0287 2.04 39 2.0 595 2.0756 0 .97 2. 092 3