1、UDC 311.13(083.5) 中华人民共和回国家标准GB 4086.1 4086. 6-83 统计分布数值表Tables for statistical distributions 1983也12-21发布1984时10-01实搞束桥;他周批准中华人民共和国国家标准UDC 311.13(创3.5)统计分布数值表F分布GB 4086. 4-83 Tables for statistical distributions F-distribution 本标准给出统计学中常用的F分布的一种数值表,其名称、表距和精度如下zP分布分位数表p=0.5(0.05)0.95, 0.975, 0.饨,0.9
2、9,0.995, 45位小数0.9975, 0.999, 0.9995 vh Vz = 1 ( 1 l30( 2 )40( 5 )70(10) 120, 150, 180, 240, = 表中的分位数对应于“F侧概率。虽然表中给出45位小数,但是在使用中常姿取几位,姿囱实际问题决定。在应用巾不能满足要求时,可参考附录的处理方法。国家标准周198312-21发布1984-10“们实施53 GB 4088.488 F分布分位数表_r叫J .,;2 叫,什F,fv1V21 (”2+V川C1叩1dF=p J B 0.469020.46844 12345 句44柿、,与呼,胁4.2252 4.2100
3、4.1960 4.1830 4.1709 2.20036 2.19541 2.19082 2.18657 2.18261 5236? 18781 95297 22211 77777 . 11111 4.1491 4.1300 tm 4.0847 2.86926 2.85922 2.85035 2.M2“ 2.83535 2.17545 2.16917 2.16361 2.15865 2.15420 62721 3110 ;18 tAVAU向n7r776 -w.,. 11111 1.38448 1.38214 1.37997 1.37796 1.37608 1.37269 1.36971 1.3
4、6707 1.36471 1.36259 67161 36163 86:2 11111 11111 . 11111 0.90578 o. 90456 0.90342 0.90236 0.90137 0.73216 0.73126 0 . 73042 0.72964 0.72892 0.58826 0.58760 0.58698 0.58641 0.58587 0.46791 0.46743 0.46697 0.46655 0.46616 67890 :223 72220 87816 p7542 AVAnAUn 11111 . 11111 0.89959 0.89802 0.89663 0.89
5、539 0.89427 0.72761 0.72645 .0.72543 0.72451 o. 72369 0.58490 0.58405 0.58330 0.58262 0.58201 42662 ;?3 54433 ,。,。,。,OAV44444 . ozozuv24680 ;34 4.0566 4.0343 4.0162 4.0012 3. 9886 2.82048 2.80866 2.79904 :79107 .78435 Z.14486 2.13743 2. 13137 2. 12635 2.12211 1.69169 1.68666 1.68256 1.67915 1.67628
6、,UTAU-F,例,附。2 v, = 0.9995 19999”.5000 1999.0000 236.6102 87.4427 49.7820 0.9990 499999.5000 999 .oooo 148.5000 61.2456 37.1223 0.975 79999 .5000 399.0000 79. 9325 38.0000 24.9640 0.9950 19999.5000 199.0000 49.7993 26.2843 18.3138 。.99004999 .5000 99 .0000 30.8165 18.0000 13.2739 0.9800 1249.5000 49.
7、0000 18.8581 12.1421 9.4544 0.9750 799.5000 39.0000 16.0441 10.6491 8.433品12345 34.7976 27.2057 nm 17 .8653 27.0000 21.6890 18.4937 16.3871 14.9054 19.1042 15.8871 13.8885 12.5392 11.5723 14.5441 12.4040 11.V424 10.1067 队427010.9248 9.5466 8.6491 8.0215 7.55” 8.0521 7 .2026 6.6366 6.2340 5.9336 7.25
8、99 6.5415 6.0595 5.7147 5.4564 67890 1 16.4053 15.2972 14.4298 13.7336 13.1632 13.8116 12.9737 1Dm 11.3391 10.8480 10.2865 9.8392 9.4748 9.1726 8.9122 8.5096 队18657.9216 7.7008 7.2057 6.9266 6.7010 6.5149 6.3589 ri 5.2559 5.0959 4.9653 4.8567 4.7650 12345 11111 12.6880 12.2862 1Hm 10.9710 10.6584 10
9、.3899 10.1568 9 .9526 8.9179 8.7006 8.5130 8.3494 8.2056 7 .5138 7.3536 7.2148 7.0935 6.9865 6.2262 6.1121 6.0129 5.9259 5.由俑S.0455 j 4.686? 4.6189 4.5597 4.5075 4.4613 67890 11112 11.1557 10.9526 10.7712 10.6083 10.4611 9.7723 9.6120 9.4685 9.3394 9.2225 .0782 .9646 7.8626 7.7706 7.6871 6.8914 6.80
10、64 6.7300 6.6609 6.5982 5.7804 5.7190 5.6637 5.6136 S.5680 4. 7404 4.6980 4.6597 4.6250 4.5934 4.4199 4.3828 4.3492 4.3187 4.2909 12345 22:2 10.3275 l0.2058 10.0944 孔9219.8977 .1163 9.014 8. 9305 8;8488 8.7734 7.6111 川.4778 7.4190 7.3646 9. 7297 9 .5844 9 .4576 9.3460 9.2470 8.6388 8.5223 自.42048.33
11、05 8.2508 7.2品747.1831 7 .1091 7 .0438 6. 9857 6.5409 6.4885 6.4403 6.3958 6.3547 6.2810 6.2169 6.1606 6.1108 6.0664 5.5263 5.4881 5.4529 4肌.3903 4.5644 4 .5378 4.5133 4.49.06 4.4696 4.2655 4.2421 4.2205 4.2006 4.1821 ,。,raonyAU,?骂,吨$3:3咆.289 5.2479 5.2112 5.1785 4.4318 4.3987 4.3697 4.3439 4.3208 4
12、.1488 4.1197 4.。9414.0713 4.0510 24680 33334 flm 8.0855 7. 9564 7 .8528 7.7678 7 .6968 04273 5041, 6791 161 . 66666 5.9741 S.9016 5.8431 5.7950 5.7547 5.1103 5.0566 5.。1324.9774 4.9474 4.2727 4.2347 4.2040 4. 1785 4.1572 4.0085 3.9749 3.9477 3.9253 3.9064 5051 4ii 8.4自948.3711 8.2806 8.2091 队15127.6
13、366 7 .5401 7.4661 7 .4077 7.3603 6.5348 6.4635 6.4086 6.3652 6.3300 5. 7204 5.6652 5.6228 5.5892 5.5619 4.9219 4.8807 4.8491 4.8239 4.8035 4.1390 4.1097 4.0871 4.0691 4.0545 .8903 .8643 :8443 .8284 3.8154 70 80 90 100 110 8.1033 7.9994 7.9311 7.8468 7.6009 nm 6.3008 6.2373 6.1954 6.1436 5.9915 5.53
14、93 5.的005.4574 5.4170 5.2983 4.7865 4.7495 4. 7250 4.6947 4.6052 4:m t9120 3.8046 3.7811 3. 7655 .7462 .6889 120 150 180 Z40 57 当p 1凤”(2,120) = 1/4.7865=0.2089. GB 40” F分布分位数褒】2叫2r;o 1/2 -I F, (V州11: V1 ;.2 In J、(均v1F叫,川,12dF叩F,例,旧 3 v, = 呻翩翩翩 P v, 0.9500 3.96324 1呼9.6 42 1.46714 1.38168 215.7073 1队
15、16439 .2766 6.5914 5.4095 。.9000!JH 0.8500 23.57180 5.82581 5.8087 .1 360 2.77640 0.8000 13.06393 4.15635 2.3594 2.48474 2.25302 o.1soo 8.19986 3. 15337 2.35555 2.046品71.88427 0.7000 .55719 .48354 1. 93984 1.72150 1.60453 0.6500 0.6000 12345 2.92816 1.64316 1喻374551.26059 1.19780 0.5500 2.21792 1.36
16、145 1.17066 1.08801 1.04200 0.5000 1.70923 1.13494 1.00000 0.94053 0.90715 3.28876 3.07407 2.2380 .81刷.72767 .56992 .43342 2.33660 2.26442 2.20855 2.11259 2.01856 1.95125 1. 90072 1;86140 3755 ,句内鸣,俨2046812 8110 7rid . 11111 。7甸、rhay,句82307 12697 3841p 54”43 . 11111 1.32803 1.29125 1.26446 1.24409 1
17、.22807 p2142 07744 80053 e23l向w”。1,IAUA . 11111 1.01271 0.99243 0.97756 0.96619 o. 95722 0.88578 0,87094 0.86004 0.85168 0.84508 47890 1 3.5874 3.4903 3.4105 3.3439 3.2874 :m i:虽2.16404 2.12776 .09761 .07218 2.05号42:13 91750 94249 20864 il7 . 11111 ,喻,、,3,句89172 9051 76432 55555 . 11111 1.38056 1.36
18、643 1.35460 1.34456 1.33593 1.21515 1.20450 1. 19558 1.18800 1.18147 1.07369 1.06568 1.05895 1.05322 1.04829 0.94996 0.94396 o. 93892 o. 93463 o.字30930.83973 0.83531 0.83159 0.82842 亿82568,、,3UTK,11111 3.2389 3.1968 f i99 .1 7码3.0984 :! :mt Jn F、70,、11骂d57318 53345 32109 77776 . 11111 zd句,胁怠J?$2。内av
19、AV2JOAHW -oq88 55444 . 11111 !:!?;: nyAUoe,。78449 50628 77665 11111 . 11111 p2914 928p2 30631 44333 AUAAVAUAU . 11111 0.92770 o.2487 0.92237 0.92013 0.91812 0.82330 0.82121 日mfi0.81621 67890 tIv吨,3.0725 3.0491 .0280 .0088 2.9”Z 2.36489 2.35117 z,33s73 2.32739 2.31702 1. 96605 1. 95672 1.94825 1.4052
20、 1.93344 95342 365?8 81594 8!; 66666 . 11111 76042 22757 50517 ,吻t,。,。,、,4444 . 11111 56278 02867 、Jhae句,eoppqa 39骂,?只,也. 11111 1. 15578 1.15290 1.15028 1.14789 1.14569 1.02883 1.02665 1.02466 1.02284 1.02117 0.91631 0.91467 0.91317 0.91180 0.91055 0.81487 0.81365 0.81255 0.81153 0.81060 ;345 吨kr饵,、
21、,去42. 9752 2. 9604 2.9467 .9340 .9223 2.30749 2.29871 2.29060 2.28307 2.27607 1.9264 1. 92094 1. 91538 1.91023 1.90544 ,AW啕JAHW吨,17705 05184 65544 66666 . 11111 aAZ2,。,。2p915 40752 55446 444左”. 11111 1.28612 1.28366 1.28138 1.27927 1.27730 1.01964 1.14367 1.01821 1.14179 1.0160 1.14006 1.01567 1.138
22、45 1.01453 1. 13695 。.909390.90832 0.90732 o. 90640 o. 90554 0.80974 0.80895 0.80821 0.80753 0.80689 678,。吨,、,也、,h、62d2.9011 .8826 .8663 2.8517 2.8387 2.26345 ps39 .2 61 2.23390 .2.22609 1.89678 1.88918 1.88246 1.87647 1.87109 31154 27845 8139 33221 66666 . 11111 6370r 87088 73063 33322 44444 . 1111
23、1 30zt,a1 76831 写,乓4377666 龟,?巧,?td. 11111 3432 州. 。,f。,410776 3写,吨,也?2411111 . 11111 643?p 46052 20976 11000 00000 . 嘈11111 0.90398 0.90261 0.90139 0.90030 0.8933 : 24680 3333 2.8115 2. 7900 fl725 581 2.7459 2.20972 2.19673 2.18617 177 .17003 1448r 88543 ;12 55433 88B88 . 11111 1.61131 1.60476 1.59
24、943 1.59500 1.59126 命。,abaov377746 72852 11000 4444” ., . 11111 1.25842 1.25468 1.25163 1.24910 1.24696 aa吨。,。?RV56347 i753 、,也1Jlt,11111 . L11,1.00356 1.0013 0.99961 0.99814 0.99689 0.89727 0.89562 0.89428 0.89317 0.89222 0.80075 日,799530.79853 0.79770 0.79700 505! 45566 nm 45685 75632 31: 65433 11
25、111 . 22i2 1.82800 1.82094 1.815帖1.81110 1.80753 7qi7 08860 828: 88777 55555 . 11111 55326 3399 06308 09998 ,句写茎333. 11111 1.24513 1.24217 1.23986 1.23803 1.23652 1550 31398 20865 嘈IAAUAU11111 . 11111 0.99582 0.99409 0.99274 0.99167 o.907 0.89142 0.89011 0.88909 0.88828 0.88761 o. 79640 0.79543 0.79
26、467 0.79407 0.79357 70 80 90 100 110 2.6802 2.6649 .6时.6422 2.6049 1附.1 066 2.11446 2.10674 2.08380 7775 6998阳“7?23A1 81902 06i7 76654 :555 . 11111 鸣,胁、JL”,aw萨、JF、d3,33饨,t吩3,向6nvg自Bran,、等3323写d. 11111 lgu 44497 $7353 421674 900p9 4EA. . 5mHWAHV . 11111 0.99006 0.98845 0.98738 0.98605 0.98206 0.88706
27、 0.88584 0.88503 0.88402 0.88100 0.79316 0.79226 0.79166 0.79091 0.78866 120 150 180 240 00 斗1:!ll!对于自由度(叫,v,和“F侧概事P给出F分帘的分位数F,叫,)。例g对于(町,v,川(3,70)和p衍。.9,几(川,Vz)怨2.16374,58 GB 4088 i一”F分布分1tL徽表”机2町!r:叫1,叶几(Vi.V2) I f:飞2,工,:、(v1F,.,. ,12dF= p F,/2 /2叫I-1 F. (v, v. I rF v,f V2 I F 2 (Va刊1F叫州州12dF=p, z
28、 J, B 4 。.950012345 224.5832 19 .2468 9. 1172 6.3882 5.1922 4.5337 4.1203 3.8379 3.6331 3.4780 0.9000 55.83296 9.24342 5.34264 10725 J.52020 Pi: 18阳.96053 俨俨3.6 68 Z.60534 0.8500 258249 5; 90651 3.81658 3.。91612.73090 。.800013.6443司flm 。.75-00 8.58094 3.23205 2.39011 .06418 .89268 0.7000 5.82984 2.5
29、6110 1. 98453 1. 75287 1.62863 。.65002:m Hm 0.6000 阳1.71825 t.43153 1.30984 1.24275 0.5500 2.35275 1.43513 1.23132 t,14308 1.09397 o.sooo t.82271 1.20711 1.06323 1.00000 o.6456 (fm :m! i:m EJ,?”AU啡,. . ,722075454 81629 唱,、,。,。电,. 11111 P3623 、rt鞠,、d吨J幡啕,a18018 59i0 54aa句4. 11111 46to3 i343 AUhu句,AU3
30、62?75 33222 . 11111 7731 29512 00?30 0732 21111 . 11111 04612 70104 21:3 ifo huhAUOZU . 11111 0.9411 0.92619 o.91465 o.0580 0.89882 67890 1 ;圳9.4sg10 .43 71 2.3969 2.36143 2.09454 2.0567 2.02542 1. 99894 1.97629 23434 54873 58560 96421 F7777 . 11111 1.57042 1.55035 1.53358 .51936 1 .50714 88406 0936
31、3 04212 9r654 2霄3,33. 11111 1.23947 1.22805 1 .21847 1 .21033 1.2由3321. 10984 1.10123 1.09401 1.08785 1.08255 o. 99566 0.98924 0.98385 0.97926 Q.97530 0.89316 o.88848 0.88455 g.88119 .87830 12345 11111 .0069 .9647 2.9277 2.8951 2.8661 :m 08015 75511 69419 ;219 “vnyny。,。. 11111 414p6 17792 ,。,3吨,?”,9
32、$765 ,。,。,。ab70. 11111 45: 52071 679; 98776 44444 . 11111 497: 320; 47150 2J吻、4t唱,3写32,、4. 11111 26281 ?t,向71729 90887 11111 . 11111 48?92 98202 73074 77766 AUAUAUAONV . 11111 0.97185 0.96882 0.96614 0.96374 0.96159 o.87579 0.87357 0.87161 8:m 47890 4lt1 2.8401 2.8167 r.n 2.7587 2.23334 nim .19488 .
33、18424 074?1 46874 88?14 87665 88888 . 11111 ,1,、豆、,句43B95 69261 4i22 66666 . 11111 1.45930 1.45396 1.44910 1.44467 1.44060 1.30607 1.30201 1.29831 1.29494 1.29183 的ynuazu3,。,。,吨,. r2?-zv, 77466 11111 . 11111 3a凰”馆、币。62113 1?73 655; 向UOZUau. 11111 0.95965 0.95789 0.95629 o. 95482 0.95348 0.86688 0.86
34、559 0.86442 o.86335 0.86236 12345 匀,骂kr髦,髦”2.7426 2.7278 2.7141 .7014 .6896 76413 44142 45rq2 74544 11111 . 吨,也句?24吨,um i:m 77270 59771 ,。173AU11000 66666 . 11111 u 8&031 93965 84319 88$1 22222 . 11111 ,、,2AZJEF66104 20875 ,的76RJRZ311111 . 11111 1.05172 1.05019 1.04877 1.04745 1.04622 &:m 0.86145 0.
35、$6061 0.85984 0.8511 0.858制,。,. 。内AUi23 2.6684 2.6499 2.6335 2.6190 2.6060 2.12929 2.11793 2.10790 2.09896 2.09095 1.81617 1.80825 t.80123 1.79”8 1.78937 :;!; um 2.07415 2.06082 2.04997 2.04099 2 03341 ?3084 526zq 78048 76654 77777 . 伞. 11111 1.59346 1.58762 1.58245 1.57784 1.57371 l :1 1.5524 1.547
36、76 1.54380 1.41942 1.41501 1.41111 1.m62 1.40449 81367 4ii 5ii 77666 22222 . 11111 80173 4吨P65729753 3句,句,句hT11111 . 11111 1 04399 1.04203 1.04029 1.03873 1.03734 o. 94644 0.947 o. 94366 o. 94250 0.94145 。.85722o.asm 0.85519 0.85433 0.85357 24680 33334 16!3 96388 72841 99888 33333 . 11111 31310 吨kd们
37、吨,的VZP5196 55544 、,949匀,. 11111 79782 ?214 96420 33333 95339 30151 420! 33322 00000 . 11111 :im 0.85195 0.85066 0.84961 Q.84873 0.84799 50505 45566 2.5027 2.4859 2.4729 2.4626 2.4542 2.02695 2.01649 :阳?.00194 1.99668 80820 302r0 47163 43322 77777 . 11111 、J也,、dowt,、449735 04074 43322 55555 . 11111 ,
38、。n荡,EAHZVJ,amuw,、JW. , ?5197 77766 33:3 . 11111 1.24493 1.24174 1.23926 1.23728 1.235品11.12890 1.12645 1.12455 1. 12302 1.12178 36150 01756 64210 22222 向UAUAUAU. . 11111 0.93297 0.93156 o. 93047 0.92960 0.92888 0.84736 0.84633 0.84553 0.84489 0.84437 70 80 90 100 11自2.4472 2.4320 2.4218 2.4093 2.371
39、9 oii 37348 :1吗?8764 999? . 11111 nvlnu?吨,也?16?2 ?3826 11008 77776 . 11111 407355 ?861 27391 吨tl嘈lAA55554 . 11111 49432 45083 51?56 66554 33333 . 11111 26041 3340,6 41?69 33221 、4吨,、4吨,伽匀,. 11111 712 749白408659 句,. , . 4EAHV 11111 . 11111 1.01981 1 . 01807 1.01692 1.01547 1.01116 0.92829 0禽926980.92
40、611 仇925030.92178 0.84393 0.84298 0.84234 ().84155 0.83917 120 150 180 240 = 本司是对于自由度(町,内)和下侧栅模P给出F分布的分位数几(叭,v,)。例z对于(町,叫)= ( 4, 13)和p忌。.9,F,(v,.”,2.43371, 60 GB 4018.4M F分布分位数表p叫2叫11.,1!2-l F. (V V2) r Vi v2 I (Vz+V1F叩川dF叩 i. Jo B.伊tl:对于(叫,)= (5, !00)和P=0.9,F,叫,Vz)=1.90574。62 GB 40”. 4” F分布分位敛E P削叫
41、Z”叫Zi;- 112 -1 , ,. F,(v1 v2) f I Z (均v1F-,., ,dF= p P Jo B (Vi/2, v2/2l JI,h3。5 0.9995 2305619.4233 19”.3000 214.1973 73.6307 39.71” o. 9990 576404.5558 ”9.2999 134.5800 51. 7116 29.7524 0.9975 92224.3929 399.2998 72.6212 32.2609 20.1783 o.950 23055.7982 199.2996 45.3916 22.4564 14.于3960.9900 5763.
42、6496 队299328.2371 15.5219 10.9670 。.98001440.6124 49.2986 17.4288 10.6157 7.9529 。.97502854 7844d 4qa64 82831 . l内,。AV句34l ,理JA咱这J26.6452 20.1726 16.4403 14.0583 12.4251 20.8027 16.2058 13.4847 1Ll137 1004807 14.8842 12.0312 10.2834 9.1164 8.2875 11.4637 9.5221 po1e .4712 6.8724 f 6.5847 5.7“7 5.222
43、7 4.8395 4.5550 5.9876 5.2852 .8173 4.4844 4.2361 ,。7nau1 11.2442 10.3549 孔66359.1118 8.6622 9 .5784 8.8921 8.3541 7 .9218 7.5674 7.6712 7.1963 6.8200 6.5148 6.2626 6.4217 6.0711 5.7910 5.5623 5.3721 5.3160 5.0643 4.8616 4.6950 4.555品4.3357 4.1617 4.0205 3.9036 3.8052 4.0440 日;3.6634 3.5764 12345 11
44、111 8.2892 7.9751 7.7072 7.4761 7 .2748 7.2719 7.0219 6.8078 6.6225 6.4606 ?$785 00502 57186 auau弓,ZJ句. 6:55 S.2117 5.0746 4.9560 4.8526 4.7616 4.4374 4.3359 4.2479 4. 1708 4.1027 j-1川.6491 3.5861 3.5307 3.4817 if t 678PO 嘈,11町、,也7 .0980 6.9416 6.8021 6.6771 6.5644 6.3179 6.1914 6.0783 5. 9768 5.885
45、1 5.3579 S.2648 51813 5.1061 5.0380 4.6809 4.6088 4.5441 4.4857 4.4327 4.0421 e880 .9392 .8951 3.8550 3:;在!tm flm 12345 22222 6.4623 6.3694 6.2845 6.2067 晶.13505.8018 5.7259 S.6565 .5927 .5339 4.9761 4.9195 4.8676 4.8199 4.7758 4.3844 4.3402 4.2996 4.2622 4.2276 3.8183 3.7848 3.7539 3.7254 3.6990 :m
46、 47890 吨EJJKJS36.0075 5.8975 5.8017 .7176 .6430 5.4291 S.3386 S.2596 5.1900 5.1283 4.6970 4.6288 4.5690 4.5163 4.4695 4.1657 4.1119 4.0648 4.0231 3.9860 3.6517 3.6106 3.5744 3.5424 3.5138 m 2.9953 2.9680 2. 9440 2.9227 z.037 iio i: 5.4893 5.3698 5.2743 队19625.1312 5.0007 4.9013 ;:那- 4.7021 4.3724 4.
47、2965 4.2355 4.1854 4.1436 3. 9090 3.8486 3.8000 3.7599 3.7265 3.4544 3.4077 3.3700 fl :m i:;那:1 e3n53俑,25)和p=0.90,几叭,内问2.02406.64 GB 4018.4” F分布分c.数褒的内战町2p川,叶Fp (Vi.Vz) I fF v, Vz I (vz问F叫W州dF=pJo B均).( v严句句nF川2-t(Vz叩川唰!1r,12dF=p 1 Jo B 2)。例E对于(v, v,)工俑,55)和p;0.90,几(v1, vz) = I. 78456, 68 GB 4088 .C-”
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