二项分布临界值表
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附表1 符号检验界域表附表2 二项分布表()∑=---=≤xk kn k p p k n k n x X P 01)!(!!)(附表3 标准正态分布表[])(1)(21)(22Z z dweZ W ZΦ-=-Φ-Φ-∞-⎰π附表4 威尔科克森带符号的秩和检验临界值(T值)表这里T是最大整数,即P(T≤t/n)≤a累积的单尾概率附表5 秩和检验临界值表括号数值表示样本容量(n1,n2)附表6 曼.怀特尼检验(U的临界值)单尾或双尾单尾或双尾附表7 游程检验的临界值表r下表 (a/2=r上表 (a/2=附表8 关于最长游程检验的临界值表当n1,n2≤25时,Wa的值P(W≥Wa)≤aⅠ a=Ⅱ a=附表9 游程长度平方和检验的临界值表当n=3---15时,使P(W ≥W a )≤a 的W a 的值附表10 X2分布表本表对自由度 n的X2分布给出上侧分位数(X2a)表,P(X2n>X2a)=α附表11 Kolmogorov—Smirnov拟合优度检验临界值D表n附表12 Kolmogorov----Smirnov双样本检验中D的分子KD的临界值表(小样本) n1=n2≤30附表12续 Kolmogorov----Smirnov双样本检验中D的临界值表(大样本: n1+n2>35, 双尾检验)附表13 Spearman检验统计量的临界值近似右尾临界值rs *;P(rs>rs*)≤a;n=4--30注意:r s *的相应左尾临界值为-r s *附表14 Kendall检验统计量的临界值当n>60时,T的近似数可以由下式得到:W p ≌Xp18)52)(1(+-nnn式中Xp的值可以从标准正态分布中得到。
上表中只给出肯达尔统计检验量T的数值Wp,即T的数值的上界,而下界数可由以下关系式得出:Wp =-Wp临界域为:T>Wp 或T<-Wp附表15 Kendall协和系数中S的临界值表a=a=附表16 Cruskall---Wallis检验统计量的临界值附表17 上、下游程分布的数目附表18 多重比较的临界值Z。
二项分布临界值表附表1 二项分布临界值表在p=q=21下,x或n–x(不论何者为大)的临界值n单侧检验(α)双侧检验(α)0.05 0.01 0.05 0.015 5 ———6 6 — 6 —7 7 7 7 —8 7 8 8 —9 8 9 8 910 9 10 9 1011 9 10 10 1112 10 11 10 1113 10 12 11 1214 11 12 12 1315 12 13 12 1316 12 14 13 1417 13 14 13 1518 13 15 14 1519 14 15 15 1620 15 16 15 1721 15 17 16 1722 16 17 17 1823 16 18 17 1924 17 19 18 1925 18 19 18 2026 18 20 19 2027 19 20 20 2128 19 21 20 2229 20 22 21 2230 20 22 21 2312附表2 正态分布概率表()z xx P Z F <-=σ)(ZF (Z )ZF (Z )ZF (Z )ZF (Z )0.00 0.0000 0.35 0.2737 0.70 0.5161 1.05 0.7063 0.01 0.0080 0.36 0.2812 0.71 0.5223 1.06 0.7109 0.02 0.0160 0.37 0.2886 0.72 0.5285 1.07 0.7154 0.03 0.0239 0.38 0.2961 0.73 0.5346 1.08 0.7199 0.040.03190.390.30350.740.54071.090.72430.05 0.0399 0.40 0.3108 0.75 0.5467 1.10 0.7287 0.06 0.0478 0.41 0.3182 0.76 0.5527 1.11 0.7330 0.07 0.0558 0.42 0.3255 0.77 0.5587 1.12 0.7373 0.08 0.0638 0.43 0.3328 0.78 0.5646 1.13 0.7415 0.090.07170.440.34010.790.57051.140.74570.10 0.0797 0.45 0.3473 0.80 0.5763 1.15 0.7499 0.11 0.0876 0.46 0.3545 0.81 0.5821 1.16 0.7540 0.12 0.0955 0.47 0.3616 0.82 0.5878 1.17 0.7580 0.13 0.1034 0.48 0.3688 0.83 0.5935 1.18 0.7620 0.140.11130.490.37590.840.59911.190.76600.15 0.1192 0.50 0.3829 0.85 0.6047 1.20 0.7699 0.16 0.1271 0.51 0.3899 0.86 0.6102 1.21 0.7737 0.17 0.1350 0.52 0.3969 0.87 0.6157 1.22 0.7775 0.18 0.1428 0.53 0.4039 0.88 0.6211 1.23 0.7813 0.190.15070.540.41080.890.62651.240.78500.20 0.1585 0.55 0.4177 0.90 0.6319 1.25 0.7887 0.21 0.1663 0.56 0.4245 0.91 0.6372 1.26 0.7923 0.22 0.1741 0.57 0.4313 0.92 0.6424 1.27 0.7959 0.23 0.1819 0.58 0.4381 0.93 0.6476 1.28 0.7995 0.240.18970.590.44480.940.65281.290.80300.25 0.1974 0.60 0.4515 0.95 0.6579 1.30 0.8064 0.26 0.2051 0.61 0.4581 0.96 0.6629 1.31 0.8098 0.27 0.2128 0.62 0.4647 0.97 0.6680 1.32 0.8132 0.28 0.2205 0.63 0.4713 0.98 0.6729 1.33 0.8165 0.290.22820.640.47780.990.67781.340.81980.30 0.2358 0.65 0.4843 1.00 0.6827 1.35 0.8230 0.31 0.2434 0.66 0.4907 1.01 0.6875 1.36 0.8262 0.32 0.2510 0.67 0.4971 1.02 0.6923 1.37 0.8293 0.33 0.2586 0.68 0.5035 1.03 0.6970 1.38 0.8324 0.34 0.2661 0.69 0.5098 1.04 0.7017 1.39 0.8355Z F(Z) Z F(Z) Z F(Z) Z F(Z) 1.40 0.8385 1.75 0.9199 2.20 0.9722 2.90 0.9962 1.41 0.8415 1.76 0.9216 2.22 0.9736 2.92 0.9965 1.42 0.8444 1.77 0.9233 2.24 0.9749 2.94 0.9967 1.43 0.8473 1.78 0.9249 2.26 0.9762 2.96 0.9969 1.44 0.8501 1.79 0.9265 2.28 0.9774 2.98 0.99711.45 0.8529 1.80 0.92812.30 0.97863.00 0.9973 1.46 0.8557 1.81 0.9297 2.32 0.9797 3.20 0.9986 1.47 0.8584 1.82 0.9312 2.34 0.9807 3.40 0.9993 1.48 0.8611 1.83 0.9328 2.36 0.9817 3.60 0.99968 1.49 0.8638 1.84 0.9342 2.38 0.9827 3.80 0.99986 1.50 0.8664 1.85 0.9357 2.40 0.98364.00 0.99994 1.51 0.8690 1.86 0.9371 2.42 0.9845 4.50 0.999994 1.52 0.8715 1.87 0.9385 2.44 0.98535.00 0.999999 1.53 0.8740 1.88 0.9399 2.46 0.98611.54 0.8764 1.89 0.94122.48 0.98691.55 0.8789 1.90 0.94262.50 0.98761.56 0.8812 1.91 0.94392.52 0.98831.57 0.8836 1.92 0.94512.54 0.98891.58 0.8859 1.93 0.94642.56 0.98951.59 0.8882 1.94 0.94762.58 0.99011.60 0.8904 1.95 0.94882.60 0.99071.61 0.8926 1.96 0.95002.62 0.99121.62 0.8948 1.97 0.95122.64 0.99171.63 0.8969 1.98 0.95232.66 0.99221.64 0.8990 1.99 0.95342.68 0.99261.65 0.90112.00 0.9545 2.70 0.99311.66 0.90312.02 0.9566 2.72 0.99351.67 0.90512.04 0.9587 2.74 0.99391.68 0.90702.06 0.9606 2.76 0.99421.69 0.90902.08 0.9625 2.78 0.99461.70 0.91092.10 0.9643 2.80 0.99491.71 0.91272.12 0.9660 2.82 0.99521.72 0.91462.14 0.9676 2.84 0.99551.73 0.91642.16 0.9692 2.86 0.99581.74 0.91812.18 0.9707 2.88 0.996034附表3 t 分布临界值表αα=>)]()([v t v t P单侧 双侧 α=0.10 α=0.20 0.05 0.10 0.025 0.05 0.01 0.02 0.005 0.01 ν= 1 3.078 6.314 12.706 31.821 63.657 2 1.886 2.920 4.303 6.965 9.925 3 1.638 2.353 3.182 4.541 5.841 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 2.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 22 1.321 1.717 2.074 2.508 2.819 23 1.319 1.714 2.069 2.500 2.807 24 1.318 1.711 2.064 2.492 2.797 25 1.316 1.708 2.060 2.485 2.787 26 1.315 1.706 2.056 2.479 2.779 27 1.314 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 2.763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 40 1.303 1.684 2.021 2.423 2.704 50 1.299 1.676 2.009 2.403 2.678 60 1.296 1.671 2.000 2.390 2.660 70 1.294 1.667 1.994 2.381 2.648 80 1.292 1.664 1.990 2.374 2.639 90 1.291 1.662 1.987 2.368 2.632 100 1.290 1.660 1.984 2.364 2.626 125 1.288 1.657 1.979 2.357 2.616 150 1.287 1.655 1.976 2.351 2.609 200 1.286 1.653 1.972 2.345 2.601 ∞1.2821.645 1.9602.326 2.5765附表4 2χ分布临界值表ανχνχ=>)]()([22P ν显 著 性 水 平(α)0.99 0.98 0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.02 0.01 1 0.0002 0.0006 0.0039 0.0158 0.0642 0.148 0.455 1.074 1.642 2.706 3.841 5.412 6.635 2 0.0201 0.0404 0.103 0.211 0.446 0.713 1.386 2.403 3.219 4.605 5.991 7.824 9.210 3 0.115 0.185 0.352 0.584 1.005 1.424 2.366 3.665 4.642 6.251 7.815 9.837 11.341 4 0.297 0.429 0.711 1.064 1.649 2.195 3.357 4.878 5.989 7.779 9.488 11.668 13.277 5 0.554 0.752 1.145 1.610 2.343 3.000 4.351 6.064 7.289 9.236 11.070 13.388 15.068 6 0.872 1.134 1.635 2.204 3.070 3.828 5.348 7.231 8.558 10.645 13.592 15.033 16.812 7 1.239 1.564 2.167 2.833 3.822 4.671 6.346 8.383 9.803 12.017 14.067 16.622 18.475 8 1.646 2.032 2.733 3.490 4.594 5.527 7.344 9.524 11.030 13.362 15.507 18.168 20.090 9 2.088 2.532 3.325 4.168 5.380 6.393 8.343 10.656 12.242 14.684 16.919 19.679 21.666 10 2.558 3.059 3.940 4.865 6.179 7.267 9.342 11.781 13.442 15.987 18.307 21.161 23.209 11 3.053 3.609 4.575 5.578 6.989 8.148 10.341 12.899 14.631 17.275 19.675 22.618 24.725 12 3.571 4.178 5.226 6.304 7.807 9.304 11.340 14.011 15.812 18.549 21.026 24.054 26.217 13 4.107 4.765 5.892 7.042 8.634 9.926 12.340 15.119 16.985 19.812 22.362 25.472 27.688 14 4.660 5.368 6.571 7.790 9.467 10.821 13.339 16.222 18.151 21.064 23.685 26.873 29.141 15 5.229 5.985 7.261 8.547 10.307 11.721 14.339 17.322 19.311 22.307 24.996 28.259 30.578 16 5.812 6.614 7.962 9.312 11.152 12.624 15.338 18.413 20.465 23.542 26.296 29.633 32.000 17 6.408 7.255 8.672 10.035 12.002 13.531 16.338 19.511 21.615 24.769 27.587 30.995 33.409 18 7.015 7.906 9.390 10.865 12.857 14.440 17.338 20.601 22.760 25.989 28.869 32.346 34.805 19 7.633 8.567 10.117 11.651 13.716 15.352 18.338 21.689 23.900 27.204 30.144 33.687 36.191 20 8.260 9.237 10.851 12.443 14.578 16.266 19.337 22.775 25.038 28.412 31.410 35.020 37.566 21 8.897 9.915 11.591 13.240 15.445 17.182 20.337 23.858 26.171 29.615 32.671 36.343 38.932 22 9.542 10.600 12.338 14.041 16.314 18.101 21.337 24.939 27.301 30.813 33.924 37.659 40.289 23 10.196 11.293 13.091 14.848 17.187 19.021 22.337 26.018 28.429 32.007 35.172 37.968 41.638 24 10.856 11.992 13.848 15.659 18.062 19.943 23.337 27.096 29.553 33.196 36.415 40.270 42.980 25 11.524 12.697 14.611 16.473 18.940 20.867 24.337 28.172 30.675 34.382 37.652 41.566 44.314 26 12.198 13.409 15.379 17.292 19.820 21.792 25.336 29.246 31.795 35.563 38.885 42.856 45.642 27 12.897 14.125 16.151 18.114 20.703 22.719 26.336 30.319 32.912 36.741 40.113 44.140 46.963 28 13.565 14.847 16.928 18.930 21.588 23.647 27.336 31.391 34.027 37.916 41.337 45.419 48.278 29 14.256 15.574 17.708 19.768 22.475 24.577 28.336 32.461 35.139 39.087 42.557 46.693 49.588 3014.59316.30618.49320.59923.36425.50829.33633.53036.25040.25643.77347.96250.8926附表5 F 分布临界值表(α=0.05)ανννν=>)],(),([F F P 1ν2ν 1 2 3 4 5 6 8 10 15 1 161.4 199.5 215.7 224.6 230.2 234.0 238.9 241.9 245.9 2 18.51 19.00 19.16 19.25 19.30 19.33 19.37 19.40 19.43 3 10.13 9.55 9.28 9.12 9.01 8.94 8.85 8.79 8.70 4 7.71 6.94 6.59 6.39 6.26 6.16 6.04 5.96 5.86 5 6.61 5.79 5.41 5.19 5.05 4.95 4.82 4.74 4.62 6 5.99 5.14 4.76 4.53 4.39 4.28 4.15 4.06 3.94 7 5.59 4.74 4.35 4.12 3.97 3.87 3.73 3.64 3.51 8 5.32 4.46 4.07 3.84 3.69 3.58 3.44 3.35 3.22 9 5.12 4.26 3.86 3.63 3.48 3.37 3.23 3.14 3.01 10 4.96 4.10 3.71 3.48 3.33 3.22 3.07 2.98 2.85 11 4.84 3.98 3.59 3.36 3.20 3.09 2.95 2.85 2.72 12 4.75 3.89 3.49 3.26 3.11 3.00 2.85 2.75 2.62 13 4.67 3.81 3.41 3.18 3.03 2.92 2.77 2.67 2.53 14 4.60 3.74 3.34 3.11 2.96 2.85 2.70 2.60 2.46 15 4.54 3.68 3.29 3.06 2.90 2.79 2.64 2.54 2.40 16 4.49 3.63 3.24 3.01 2.85 2.74 2.59 2.49 2.35 17 4.45 3.59 3.20 2.96 2.81 2.70 2.55 2.45 2.31 18 4.41 3.55 3.16 2.93 2.77 2.66 2.51 2.41 2.27 19 4.38 3.52 3.13 2.90 2.74 2.63 2.48 2.38 2.23 20 4.35 3.49 3.10 2.87 2.71 2.60 2.45 2.35 2.20 21 4.32 3.47 3.07 2.84 2.68 2.57 2.42 2.32 2.18 22 4.30 3.44 3.05 2.82 2.66 2.55 2.40 2.30 2.15 23 4.28 3.42 3.03 2.80 2.64 2.53 2.37 2.27 2.13 24 4.26 3.40 3.01 2.78 2.62 2.51 2.36 2.25 2.11 25 4.24 3.39 2.99 2.76 2.60 2.49 2.34 2.24 2.09 26 4.23 3.37 2.98 2.74 2.59 2.47 2.32 2.22 2.07 27 4.21 3.35 2.96 2.73 2.57 2.46 2.31 2.20 2.06 28 4.20 3.34 2.95 2.71 2.56 2.45 2.29 2.19 2.04 29 4.18 3.33 2.93 2.70 2.55 2.43 2.28 2.18 2.03 30 4.17 3.32 2.92 2.69 2.53 2.42 2.27 2.16 2.01 40 4.08 3.23 2.84 2.61 2.45 2.34 2.18 2.08 1.92 50 4.03 3.18 2.79 2.56 2.40 2.29 2.13 2.03 1.87 60 4.00 3.15 2.76 2.53 2.37 2.25 2.10 1.99 1.84 70 3.98 3.13 2.74 2.50 2.35 2.23 2.07 1.97 1.81 80 3.96 3.11 2.72 2.49 2.33 2.21 2.06 1.95 1.79 90 3.95 3.10 2.71 2.47 2.32 2.20 2.04 1.94 1.78 100 3.94 3.09 2.70 2.46 2.31 2.19 2.03 1.93 1.77 125 3.92 3.07 2.68 2.44 2.29 2.17 2.01 1.91 1.75 150 3.90 3.06 2.66 2.43 2.27 2.16 2.00 1.89 1.73 200 3.89 3.04 2.65 2.42 2.26 2.14 1.98 1.88 1.72 ∞3.843.002.602.372.212.101.941.831.6771ν2ν 1 2 3 4 5 6 8 10 15 1 4052 4999 5403 5625 5764 5859 5981 6065 6157 2 98.50 99.00 99.17 99.25 99.30 99.33 99.37 99.40 99.43 3 34.12 30.82 29.46 28.71 28.24 27.91 27.49 27.23 26.87 4 21.20 18.00 16.69 15.98 15.52 15.21 14.80 14.55 14.20 5 16.26 13.27 12.06 11.39 10.97 10.67 10.29 10.05 9.72 6 13.75 10.92 9.78 9.15 8.75 8.47 8.10 7.87 7.56 7 12.25 9.55 8.45 7.85 7.46 7.19 6.84 6.62 6.31 8 11.26 8.65 7.59 7.01 6.63 6.37 6.03 5.81 5.52 9 10.56 8.02 6.99 6.42 6.06 5.80 5.47 5.26 4.96 10 10.04 7.56 6.55 5.99 5.64 5.39 5.06 4.85 4.56 11 9.65 7.21 6.22 5.67 5.32 5.07 4.74 4.54 4.25 12 9.33 6.93 5.95 5.41 5.06 4.82 4.50 4.30 4.01 13 9.07 6.70 5.74 5.21 4.86 4.62 4.30 4.10 3.82 14 8.86 6.51 5.56 5.04 4.69 4.46 4.14 3.94 3.66 15 8.86 6.36 5.42 4.89 4.56 4.32 4.00 3.80 3.52 16 8.53 6.23 5.29 4.77 4.44 4.20 3.89 3.69 3.41 17 8.40 6.11 5.19 4.67 4.34 4.10 3.79 3.59 3.31 18 8.29 6.01 5.09 4.58 4.25 4.01 3.71 3.51 3.23 19 8.18 5.93 5.01 4.50 4.17 3.94 3.63 3.43 3.15 20 8.10 5.85 4.94 4.43 4.10 3.87 3.56 3.37 3.09 21 8.02 5.78 4.87 4.37 4.04 3.81 3.51 3.31 3.03 22 7.95 5.72 4.82 4.31 3.99 3.76 3.45 3.26 2.98 23 7.88 5.66 4.76 4.26 3.94 3.71 3.41 3.21 2.93 24 7.82 5.61 4.72 4.22 3.90 3.67 3.36 3.17 2.89 25 7.77 5.57 4.68 4.18 3.85 3.63 3.32 3.13 2.85 26 7.72 5.53 4.64 1.14 3.82 3.59 3.29 3.09 2.81 27 7.68 5.49 4.60 4.11 3.78 3.56 3.26 3.06 2.78 28 7.64 5.45 4.57 4.07 3.75 3.53 3.23 3.03 2.75 29 7.60 5.42 4.54 4.04 3.73 3.50 3.20 3.00 2.73 30 7.56 5.39 4.51 4.02 3.70 3.47 3.17 2.98 2.70 40 7.31 5.18 4.31 3.83 3.51 3.29 2.99 2.80 2.52 50 7.17 5.06 4.20 3.72 3.41 3.19 2.89 2.70 2.42 60 7.08 4.98 4.13 3.65 3.34 3.12 2.82 2.63 2.35 70 7.01 4.92 4.07 3.60 3.29 3.07 2.78 2.59 2.31 80 6.96 4.88 4.04 3.56 3.26 3.04 2.74 2.55 2.27 90 6.93 4.85 4.01 3.53 3.23 3.01 2.72 2.52 2.42 100 6.90 4.82 3.98 3.51 3.21 2.99 2.69 2.50 2.22 125 6.84 4.78 3.94 3.47 3.17 2.95 2.66 2.47 2.19 150 6.81 4.75 3.91 3.45 3.14 2.92 2.63 2.44 2.16 200 6.76 4.71 3.88 3.41 3.11 2.89 2.60 2.41 2.13 ∞6.634.613.783.323.022.802.512.232.048附表6 秩和检验表表中列出了秩和下限)(αT 及秩和上限)(αT 的值α=0.05α=0.0251n2n)(1αT )(2αT 1n2n)(1αT )(2αT1n2n)(1αT )(2αT 1n2n)(1αT )(2αT2 43 11 5 5 19 36 2 6 3 15 5 6 19 41 2 5 3 13 5 6 20 40 2 7 3 17 5 7 20 45 2 64 145 7 22 43 2 8 3 19 5 8 21 49 2 7 4 16 5 8 23 47 2 9 3 21 5 9 22 53 28 4 18 59 25 50 2 10 4 22 5 10 24 56 2 9 4 20 5 10 26 54 3 4 6 18 6 6 26 52 2 10 5 21 6 6 28 50 3 5 6 21 6 7 28 56 3 3 6 15 6 7 30 54 3 6 7 23 6 8 29 61 3 4 7 17 6 8 32 58 3 7 8 25 6 9 31 65 3 5 7 20 6 9 33 63 3 8 8 28 6 10 33 69 3 6 8 22 6 10 35 67 3 9 9 30 7 7 37 68 3 7 9 24 7 7 39 66 3 10 9 33 7 8 39 73 3 8 9 27 7 8 41 71 4 4 11 25 7 10 43 83 3 9 10 29 7 9 43 76 4 5 12 28 8 8 49 87 3 10 11 31 7 10 46 80 4 6 12 32 8 9 51 93 4 4 12 24 8 8 52 84 4 7 13 35 8 10 54 98 4 5 13 27 8 9 54 90 4 8 14 38 9 9 63 108 4 6 14 30 8 10 57 95 4 9 15 41 9 10 66 114 4 7 15 33 9 9 66 105 4 10 16 44 10 10 79 131 4 8 16 36 9 10 69 111 5 5 18 37 4 9 17 39 10 10 93 127 4101842附表7 游程检验R临界值表表中对应于n1与n2的有两行数值。
目录附表一:随机数表______________________________________________________________ 附表二:标准正态分布表________________________________________________________ 附表三:t分布临界值表_________________________________________________________附表四:2 分布临界值表 _______________________________________________________ 附表五:F分布临界值表(α=0.05)______________________________________________ 附表六:单样本K-S检验统计量表 ________________________________________________ 附表七:符号检验界域表________________________________________________________ 附表八:游程检验临界值表______________________________________________________ 附表九:相关系数临界值表______________________________________________________ 附表十:Spearman等级相关系数临界值表__________________________________________ 附表十一:Kendall等级相关系数临界值表_________________________________________附表十二:控制图系数表________________________________________________________附表一:随机数表(查表时注意:v是指自由度,并分单侧和双侧两种类型)(左侧的示意图是单侧检验的情形)2附表四:分布临界值表附表五:F分布临界值表(α=0.05)F分布临界值表(α=0.01)附表六:单样本K-S检验统计量表附表十:Spearman等级相关系数临界值表附表十一:Kendall 等级相关系数临界值表附表十二:控制图系数表。
附表1 符号检验界域表附表2 二项分布表()∑=---=≤xk kn k p p k n k n x X P 01)!(!!)(附表3 标准正态分布表[])(1)(21)(22Z z dweZ W ZΦ-=-Φ-Φ-∞-⎰π附表4 威尔科克森带符号的秩和检验临界值(T值)表这里T是最大整数,即P(T≤t/n)≤a累积的单尾概率附表5 秩和检验临界值表括号数值表示样本容量(n1,n2)附表6 曼.怀特尼检验(U的临界值)单尾0.025或双尾0.05单尾0.05或双尾0.1附表7 游程检验的临界值表附表8 关于最长游程检验的临界值表当n1,n2≤25时,W a的值P(W≥W a)≤a Ⅰa=0.01Ⅱa=0.05附表9 游程长度平方和检验的临界值表附表10 X2分布表本表对自由度n的X2分布给出上侧分位数(X2a)表,P(X2n>X2a)=α附表11 Kolmogorov—Smirnov拟合优度检验临界值D n表附表12 Kolmogorov----Smirnov双样本检验中D的分子K D的临界值表(小样本) n1=n2≤30附表12续 Kolmogorov----Smirnov双样本检验中D的临界值表附表13 Spearman检验统计量的临界值近似右尾临界值r s*;P(r s>r s*)≤a;n=4--30注意:r s*的相应左尾临界值为-r s*附表14 Kendall检验统计量的临界值当n>60时,T的近似数可以由下式得到:W p≌X p18)52)(1(+-nnn式中X p的值可以从标准正态分布中得到。
上表中只给出肯达尔统计检验量T的数值W p,即T的数值的上界,而下界数可由以下关系式得出:W p=-W p临界域为:T>W p或T<-W p附表15 Kendall协和系数中S的临界值表附表16 Cruskall---Wallis检验统计量的临界值附表17 上、下游程分布的数目附表18 多重比较的临界值Z。
附录附表一:随机数表 _________________________________________________________________________ 2附表二:标准正态分布表 ___________________________________________________________________ 3附表三:t分布临界值表____________________________________________________________________ 4附表四:2分布临界值表__________________________________________________________________ 5附表五:F分布临界值表(α=0。
05) _______________________________________________________ 7附表六:单样本K—S检验统计量表_________________________________________________________ 9附表七:符号检验界域表 __________________________________________________________________ 10附表八:游程检验临界值表 _________________________________________________________________ 11附表九:相关系数临界值表 ________________________________________________________________ 12附表十:Spearman等级相关系数临界值表____________________________________________________ 13附表十一:Kendall等级相关系数临界值表____________________________________________________ 14附表十二:控制图系数表 __________________________________________________________________ 15附表一:随机数表(查表时注意:v是指自由度,并分单侧和双侧两种类型)(左侧的示意图是单侧检验的情形)2附表四:分布临界值表附表五:F分布临界值表(α=0。
附表1 二项分布临界值表在p=q=下,x或n–x(不论何者为大)的临界值n 单侧检验()双侧检验()0.050.010.050.0155———66—6—7777—8788—98989 10910910 119101011 1210111011 1310121112 1411121213 1512131213 1612141314 1713141315 1813151415 1914151516 2015161517 2115171617 2216171718 2316181719 24171918192518191820 2618201920 2719202021 2819212022 2920222122 3020222123附表2 正态分布概率表Z F(Z)Z F(Z)Z F(Z)Z F(Z)0.000.00000.350.27370.700.5161 1.050.7063 0.010.00800.360.28120.710.5223 1.060.7109 0.020.01600.370.28860.720.5285 1.070.7154 0.030.02390.380.29610.730.5346 1.080.7199 0.040.03190.390.30350.740.5407 1.090.72430.050.03990.400.31080.750.5467 1.100.7287 0.060.04780.410.31820.760.5527 1.110.7330 0.070.05580.420.32550.770.5587 1.120.7373 0.080.06380.430.33280.780.5646 1.130.7415 0.090.07170.440.34010.790.5705 1.140.74570.100.07970.450.34730.800.5763 1.150.7499 0.110.08760.460.35450.810.5821 1.160.7540 0.120.09550.470.36160.820.5878 1.170.7580 0.130.10340.480.36880.830.5935 1.180.7620 0.140.11130.490.37590.840.5991 1.190.76600.150.11920.500.38290.850.6047 1.200.7699 0.160.12710.510.38990.860.6102 1.210.7737 0.170.13500.520.39690.870.6157 1.220.7775 0.180.14280.530.40390.880.6211 1.230.7813 0.190.15070.540.41080.890.6265 1.240.78500.200.15850.550.41770.900.6319 1.250.78870.210.16630.560.42450.910.6372 1.260.79230.220.17410.570.43130.920.6424 1.270.79590.230.18190.580.43810.930.6476 1.280.79950.240.18970.590.44480.940.6528 1.290.80300.250.19740.600.45150.950.6579 1.300.80640.260.20510.610.45810.960.6629 1.310.80980.270.21280.620.46470.970.6680 1.320.81320.280.22050.630.47130.980.6729 1.330.81650.290.22820.640.47780.990.6778 1.340.81980.300.23580.650.4843 1.000.6827 1.350.82300.310.24340.660.4907 1.010.6875 1.360.82620.320.25100.670.4971 1.020.6923 1.370.82930.330.25860.680.5035 1.030.6970 1.380.83240.340.26610.690.5098 1.040.7017 1.390.8355附表2(续)Z F(Z)Z F(Z)Z F(Z)Z F(Z)1.400.83851.750.91992.200.97222.900.99621.410.84151.760.92162.220.97362.920.99651.420.84441.770.92332.240.97492.940.99671.430.84731.780.92492.260.97622.960.99691.440.85011.790.92652.280.97742.980.99711.450.85291.800.92812.300.97863.000.99731.460.85571.810.92972.320.97973.200.9986 1.470.85841.820.93122.340.98073.400.9993 1.480.86111.830.93282.360.98173.600.99968 1.490.86381.840.93422.380.98273.800.999861.500.86641.850.93572.400.98364.000.99994 1.510.86901.860.93712.420.98454.500.999994 1.520.87151.870.93852.440.98535.000.999999 1.530.87401.880.93992.460.98611.540.87641.890.94122.480.98691.550.87891.900.94262.500.98761.560.88121.910.94392.520.98831.570.88361.920.94512.540.98891.580.88591.930.94642.560.98951.590.88821.940.94762.580.99011.600.89041.950.94882.600.99071.610.89261.960.95002.620.99121.620.89481.970.95122.640.99171.630.89691.980.95232.660.99221.640.89901.990.95342.680.99261.650.90112.000.95452.700.99311.660.90312.020.95662.720.99351.670.90512.040.95872.740.9939 1.680.90702.060.96062.760.9942 1.690.90902.080.96252.780.99461.700.91092.100.96432.800.9949 1.710.91272.120.96602.820.9952 1.720.91462.140.96762.840.9955 1.730.91642.160.96922.860.9958 1.740.91812.180.97072.880.9960附表3 t分布临界值表单侧双侧=0.10=0.200.050.100.0250.050.010.020.0050.01= 1 3.078 6.31412.70631.82163.6572 1.886 2.920 4.303 6.9659.9253 1.638 2.353 3.182 4.541 5.8414 1.533 2.132 2.776 3.747 4.6045 1.476 2.015 2.571 3.365 4.0326 1.440 1.943 2.447 3.143 3.7077 1.415 1.895 2.365 2.998 3.4998 1.397 1.860 2.306 2.896 2.3559 1.383 1.833 2.262 2.821 3.25010 1.372 1.812 2.228 2.764 3.16911 1.363 1.796 2.201 2.718 3.10612 1.356 1.782 2.179 2.681 3.05513 1.350 1.771 2.160 2.650 3.01214 1.345 1.761 2.145 2.624 2.97715 1.341 1.753 2.131 2.602 2.94716 1.337 1.746 2.120 2.583 2.92117 1.333 1.740 2.110 2.567 2.89818 1.330 1.734 2.101 2.552 2.87819 1.328 1.729 2.093 2.539 2.86120 1.325 1.725 2.086 2.528 2.84521 1.323 1.721 2.080 2.518 2.83122 1.321 1.717 2.074 2.508 2.81923 1.319 1.714 2.069 2.500 2.80724 1.318 1.711 2.064 2.492 2.79725 1.316 1.708 2.060 2.485 2.78726 1.315 1.706 2.056 2.479 2.77927 1.314 1.703 2.052 2.473 2.77128 1.313 1.701 2.048 2.467 2.76329 1.311 1.699 2.045 2.462 2.75630 1.310 1.697 2.042 2.457 2.750 40 1.303 1.684 2.021 2.423 2.704 50 1.299 1.676 2.009 2.403 2.678 60 1.296 1.671 2.000 2.390 2.660 70 1.294 1.667 1.994 2.381 2.648 80 1.292 1.664 1.990 2.374 2.639 90 1.291 1.662 1.987 2.368 2.632 100 1.290 1.660 1.984 2.364 2.626 125 1.288 1.657 1.979 2.357 2.616 150 1.287 1.655 1.976 2.351 2.609 200 1.286 1.653 1.972 2.345 2.6011.282 1.645 1.9602.326 2.576附表4 分布临界值表显著性水平()0.990.980.950.900.800.700.500.300.200.1010.00020.00060.00390.01580.06420.1480.455 1.074 1.642 2.706 3.841 20.02010.04040.1030.2110.4460.713 1.386 2.403 3.219 4.605 5.991 30.1150.1850.3520.584 1.005 1.424 2.366 3.665 4.642 6.2517.815 40.2970.4290.711 1.064 1.649 2.195 3.357 4.878 5.9897.7799.488 50.5540.752 1.145 1.610 2.343 3.000 4.351 6.0647.2899.23611.070 60.872 1.134 1.635 2.204 3.070 3.828 5.3487.2318.55810.64513.5927 1.239 1.564 2.167 2.833 3.822 4.671 6.3468.3839.80312.01714.0678 1.646 2.032 2.733 3.490 4.594 5.5277.3449.52411.03013.36215.5079 2.088 2.532 3.325 4.168 5.380 6.3938.34310.65612.24214.68416.91910 2.558 3.059 3.940 4.865 6.1797.2679.34211.78113.44215.98718.30711 3.053 3.609 4.575 5.578 6.9898.14810.34112.89914.63117.27519.67512 3.571 4.178 5.226 6.3047.8079.30411.34014.01115.81218.54921.02613 4.107 4.765 5.8927.0428.6349.92612.34015.11916.98519.81222.36214 4.660 5.368 6.5717.7909.46710.82113.33916.22218.15121.06423.68515 5.229 5.9857.2618.54710.30711.72114.33917.32219.31122.30724.99616 5.812 6.6147.9629.31211.15212.62415.33818.41320.46523.54226.29617 6.4087.2558.67210.03512.00213.53116.33819.51121.61524.76927.587 187.0157.9069.39010.86512.85714.44017.33820.60122.76025.98928.869 197.6338.56710.11711.65113.71615.35218.33821.68923.90027.20430.144 208.2609.23710.85112.44314.57816.26619.33722.77525.03828.41231.410 218.8979.91511.59113.24015.44517.18220.33723.85826.17129.61532.671 229.54210.60012.33814.04116.31418.10121.33724.93927.30130.81333.924 2310.19611.29313.09114.84817.18719.02122.33726.01828.42932.00735.172 2410.85611.99213.84815.65918.06219.94323.33727.09629.55333.19636.415 2511.52412.69714.61116.47318.94020.86724.33728.17230.67534.38237.652 2612.19813.40915.37917.29219.82021.79225.33629.24631.79535.56338.885 2712.89714.12516.15118.11420.70322.71926.33630.31932.91236.74140.113 2813.56514.84716.92818.93021.58823.64727.33631.39134.02737.91641.337 2914.25615.57417.70819.76822.47524.57728.33632.46135.13939.08742.5573014.59316.30618.49320.59923.36425.50829.33633.53036.25040.25643.773附表5 F分布临界值表(=0.05)12345681015 1161.4199.5215.7224.6230.2234.0238.9241.9245.9 218.5119.0019.1619.2519.3019.3319.3719.4019.43 310.139.559.289.129.018.948.858.798.70 47.71 6.94 6.59 6.39 6.26 6.16 6.04 5.96 5.865 6.61 5.79 5.41 5.19 5.05 4.95 4.82 4.74 4.626 5.99 5.14 4.76 4.53 4.39 4.28 4.15 4.06 3.947 5.59 4.74 4.35 4.12 3.97 3.87 3.73 3.64 3.518 5.32 4.46 4.07 3.84 3.69 3.58 3.44 3.35 3.229 5.12 4.26 3.86 3.63 3.48 3.37 3.23 3.14 3.0110 4.96 4.10 3.71 3.48 3.33 3.22 3.07 2.98 2.8511 4.84 3.98 3.59 3.36 3.20 3.09 2.95 2.85 2.7212 4.75 3.89 3.49 3.26 3.11 3.00 2.85 2.75 2.6213 4.67 3.81 3.41 3.18 3.03 2.92 2.77 2.67 2.5314 4.60 3.74 3.34 3.11 2.96 2.85 2.70 2.60 2.4615 4.54 3.68 3.29 3.06 2.90 2.79 2.64 2.54 2.4016 4.49 3.63 3.24 3.01 2.85 2.74 2.59 2.49 2.3517 4.45 3.59 3.20 2.96 2.81 2.70 2.55 2.45 2.3118 4.41 3.55 3.16 2.93 2.77 2.66 2.51 2.41 2.2719 4.38 3.52 3.13 2.90 2.74 2.63 2.48 2.38 2.2320 4.35 3.49 3.10 2.87 2.71 2.60 2.45 2.35 2.2021 4.32 3.47 3.07 2.84 2.68 2.57 2.42 2.32 2.1822 4.30 3.44 3.05 2.82 2.66 2.55 2.40 2.30 2.1523 4.28 3.42 3.03 2.80 2.64 2.53 2.37 2.27 2.1324 4.26 3.40 3.01 2.78 2.62 2.51 2.36 2.25 2.1125 4.24 3.39 2.99 2.76 2.60 2.49 2.34 2.24 2.0926 4.23 3.37 2.98 2.74 2.59 2.47 2.32 2.22 2.0727 4.21 3.35 2.96 2.73 2.57 2.46 2.31 2.20 2.0628 4.20 3.34 2.95 2.71 2.56 2.45 2.29 2.19 2.0429 4.18 3.33 2.93 2.70 2.55 2.43 2.28 2.18 2.0330 4.17 3.32 2.92 2.69 2.53 2.42 2.27 2.16 2.01 40 4.08 3.23 2.84 2.61 2.45 2.34 2.18 2.08 1.92 50 4.03 3.18 2.79 2.56 2.40 2.29 2.13 2.03 1.87 60 4.00 3.15 2.76 2.53 2.37 2.25 2.10 1.99 1.84 70 3.98 3.13 2.74 2.50 2.35 2.23 2.07 1.97 1.81 80 3.96 3.11 2.72 2.49 2.33 2.21 2.06 1.95 1.79 90 3.95 3.10 2.71 2.47 2.32 2.20 2.04 1.94 1.78 100 3.94 3.09 2.70 2.46 2.31 2.19 2.03 1.93 1.77 125 3.92 3.07 2.68 2.44 2.29 2.17 2.01 1.91 1.75 150 3.90 3.06 2.66 2.43 2.27 2.16 2.00 1.89 1.73 200 3.89 3.04 2.65 2.42 2.26 2.14 1.98 1.88 1.72∞ 3.84 3.00 2.60 2.37 2.21 2.10 1.94 1.83 1.67附表5(续)12345681015 1405249995403562557645859598160656157 298.5099.0099.1799.2599.3099.3399.3799.4099.43 334.1230.8229.4628.7128.2427.9127.4927.2326.87 421.2018.0016.6915.9815.5215.2114.8014.5514.20 516.2613.2712.0611.3910.9710.6710.2910.059.72 613.7510.929.789.158.758.478.107.877.56 712.259.558.457.857.467.19 6.84 6.62 6.31811.268.657.597.01 6.63 6.37 6.03 5.81 5.52 910.568.02 6.99 6.42 6.06 5.80 5.47 5.26 4.96 1010.047.56 6.55 5.99 5.64 5.39 5.06 4.85 4.56 119.657.21 6.22 5.67 5.32 5.07 4.74 4.54 4.25 129.33 6.93 5.95 5.41 5.06 4.82 4.50 4.30 4.01 139.07 6.70 5.74 5.21 4.86 4.62 4.30 4.10 3.82 148.86 6.51 5.56 5.04 4.69 4.46 4.14 3.94 3.66 158.86 6.36 5.42 4.89 4.56 4.32 4.00 3.80 3.52 168.53 6.23 5.29 4.77 4.44 4.20 3.89 3.69 3.41 178.40 6.11 5.19 4.67 4.34 4.10 3.79 3.59 3.31 188.29 6.01 5.09 4.58 4.25 4.01 3.71 3.51 3.23 198.18 5.93 5.01 4.50 4.17 3.94 3.63 3.43 3.15 208.10 5.85 4.94 4.43 4.10 3.87 3.56 3.37 3.09 218.02 5.78 4.87 4.37 4.04 3.81 3.51 3.31 3.03 227.95 5.72 4.82 4.31 3.99 3.76 3.45 3.26 2.98 237.88 5.66 4.76 4.26 3.94 3.71 3.41 3.21 2.93 247.82 5.61 4.72 4.22 3.90 3.67 3.36 3.17 2.89 257.77 5.57 4.68 4.18 3.85 3.63 3.32 3.13 2.85 267.72 5.53 4.64 1.14 3.82 3.59 3.29 3.09 2.81 277.68 5.49 4.60 4.11 3.78 3.56 3.26 3.06 2.78 287.64 5.45 4.57 4.07 3.75 3.53 3.23 3.03 2.75 297.60 5.42 4.54 4.04 3.73 3.50 3.20 3.00 2.73 307.56 5.39 4.51 4.02 3.70 3.47 3.17 2.98 2.70 407.31 5.18 4.31 3.83 3.51 3.29 2.99 2.80 2.52 507.17 5.06 4.20 3.72 3.41 3.19 2.89 2.70 2.42 607.08 4.98 4.13 3.65 3.34 3.12 2.82 2.63 2.35 707.01 4.92 4.07 3.60 3.29 3.07 2.78 2.59 2.3180 6.96 4.88 4.04 3.56 3.26 3.04 2.74 2.55 2.27 90 6.93 4.85 4.01 3.53 3.23 3.01 2.72 2.52 2.42 100 6.90 4.82 3.98 3.51 3.21 2.99 2.69 2.50 2.22 125 6.84 4.78 3.94 3.47 3.17 2.95 2.66 2.47 2.19 150 6.81 4.75 3.91 3.45 3.14 2.92 2.63 2.44 2.16 200 6.76 4.71 3.88 3.41 3.11 2.89 2.60 2.41 2.13∞ 6.63 4.61 3.78 3.32 3.02 2.80 2.51 2.23 2.04附表6 秩和检验表表中列出了秩和下限及秩和上限的值=0.05=0.025 24311551936263155619 25313562040273175720 26414572243283195821 27416582347293215922 2841859255021042251024 294205102654346186626 210521662850356216728 33615673054367236829 34717683258378256931 357206933633882861033 368226103567399307737 379247739663109337839 3892778417144112571043 3910297943764512288849 310113171046804612328951 44122488528447133581054 4513278954904814389963 461430810579549154191066 47153399661054101644101079 48163691069111551837 4917391010931274101842附表7 游程检验R临界值表表中对应于n1与n2的有两行数值。