F-распределение

Значения F_a(a = 0,1; 0,05; 0,025; 0,01 и 0,005) для различных комбинаций степеней свободы в числи­теле (vj) и знаменателе (v2>.

Пример:

При vj=10 и V2=2 площадь а справа от ^F0,05⁼¹⁹'⁴⁰ Р^авна °i°5. Чтобы найти F^, определяю­щее площадь а в оставшейся части кривой, воспользу­емся соотношением Fi_4X(vi,v2)=l/F_a(v|,v2).

Пример:

F₀₉₅(2,10)=l/19,40=0,05155.

•X	f	X	J					<					to	XJ			loo	a>
I OI00	1*46	49JO	33J9	53JJ	37.24	56.20	56.91	59.44	S9J6		60.71	6IJ2			62 J6		61.01	61J1
	161.4	199.3	213.7		210.2	214.0	216.1	218.9	240J	241.9	243.9	243.9	144 0	24*J				2S4J
0.023	647*	799J	664.2	699.0		937 1		936.7			976.7	9*4.9	993.1	994.1		100*		101»
0.010			J 403													6J0J
					2J056	2141*						246JO					25J37
2 awo	• 526	9JOQO	9.162	9.243	9.293	9J62	9.149	9J67	9.161	9J92	9 406	9.42S	9.441	9.451	9.45Й	4 471	9 441	9.491
0.050	UJI	19.00	19.16	19.25	19J0	19.13	19.13	19J7	19.1*	19 40		I9.4J	19.43		19 46		19.49
	MJ1	1*40	19.17	19.23	19.10	J*J1	**J6	19J7	39 J»	3*40		J* 43	19.43	19.46	19 46	J9.4»	1*4*	19.30
ОЛЮ	9*-»	99.00	99.17	99.25	99 JO	99J1	99 J*	99J7	99 J*	99.40	99.42	99.41	99.45	99.46	99.47	99.46	99.49	99 50
О005	i*»j		199.1	199-2	199 J	199 J	199.4	199.4	199.4	199.4	199.4	1*9.4	1*9.4	19»J	199.3	199.5	199.5	199.5
1 O10D	3JJ*	3 461	IJ*l	3J4J	5J09	3.263	3.2*6	5.252	3.240	5JJ0	3.216	5.100	5.1*4	3.173	3 164		3.144	3.134
	10.1 J	»J32		9.117		6.941	•467	•443	•412	6.7*6	•.743	• 701		*4J4	•417	»J»1	4.554
	17.44	16.04	15 44	15.10	14.66	14.71		14.34	14.47	14.42	14J4	14.23	14.17	14.12	144*		11.96
0.010	34.12	ЗОЛ	29.46			27.91		27.49	27 J3	27.21				16.5*	26JO	26J5	26.24	26.11
OMi	35-53	49.60	47.47	46.19			44.41	44.11	О 46	О 49	OJ9	О 46	417*	42J*	42.47			41 tl
4 0.100	4ЛЗ	4J25		4.107		4.010	1.979	1.933	1.916	1.920			1*44		3.117	1.799	1.77*	1.761
ao»	7.70*	6.944	6.391	4J46	6.256	6.161	6.094	6.041	5.999	9.964	3.912	545*		9.769	3.746	54*9		342*
0.013		ЮДЗ	9.979		9.J64	9.197		• 9*0		•444	• 731	•437	•460	•301		IJ41	•J 19	• 257
aoio	21 JO	ISA)	16.69	13.96	11J2	15.11				I4JS	I4J7	I4J0		U.*l			UJ*	11.46
aoos	JIJ3	26.2»	24.26	21.13		21.97	21.62	11J5	21 14	20.97	20.70		20.17				I9J0	19J2
5 aioo		1.7Ю	3.619	1J20	1.491	1.405	1J66	1JJ9	1J16	1.2*7	JJ64	JJJ*	1J07	1.1*7	1.174		1.126	1.105
		5.766	9.409		1.030	4.950		441*	4.772	4.715	447»		4J56	4J2I	4.4*6	4.444		4J65
0.015	IOjOI	6.434	7.764	7JU	7.146	6.976		6.757	6.661		6.323	6.426	6J29	626*	6.217		64*0
	16.26	11.27			10.97		10.46	10.29	10.16		9.6H	9.712	9J31	9.44*	»J7»	9.21*	9.110
0.003	22.7*	16JI	16J1	13J6	14.94	14 31	14.20	11.96	11.77		til*	11.11		11.76			I2J0	12.14
6 aioo	J.776	1.46J	2.2*9	11»l	J.HM			19*1	195»	19J7			2JJ6			2.77»
	3.9*7	3.145	4.737	4J34	4J67	4.2*4	4.20?	4.147	4.099	4.060		1.91*			1.Ю*	1.754	1.712	146*
	MIJ	7-1*0	64*9	6.227	5.9M	3.620			9J21	3.461	SJ66	9J6*	5.16*	3.107	5.069	4.9*0	4.*1S	4*4»
	13.75	10.91	9.7*0	9.146		6.466	«.260		7.976		7.711	7,33*	7J*6	7.296	7.12*	74*1	6.9*7	64*0
O.OOS	MAI	MJ4	U*2	iiai	J 1.46		10.79	10.57	I0J9	KL23	iaoj	941*	95**	9.431	»J3»	9J70		*.*T9
? aioo	3.5*9	3.157			1*B1		17*9						15*5			U13
	3.591	4.737	4J47	4.120	1.972	1.666	1.7*7	1.726	1.677		1.573	Ull	1.445	1.404	1J76	1.119	1.273	ЗЛО
O025	•471	6J41	3.990	1JU	5.2S3	5.119	4.993		4.621	4.761	4.666	4.366	4.467		4J62	4.276	4.210	4.142
ОЛЮ	12.25	»J47		7.647	7.460	7.191	6.991	6.*40			6.469	6J14	6.155	643*	9.992	545*	3.733
0.003	16.24	12.40	104»			9.133	6.665	•47*	6J14	•J*0	• 176	7.9M			7.314	7JS4	7 217	7,076
i aioo	3.451	1.113	2.924	U06								14*4			U*l	U4*
0.050	9J1I	4.439	4.066	341»		J.361	1JO0	1.431	J.J»»	U47	1.2*4	1-216	1.130	1.10*	107*			192»
	7J71	6.039	5.416				4J29	4.411	4J37	4.295		4.101	1.99*	1.917	l.»*4	J.*07	1.71*
0.0I0		•449	7J*1	7.006		6J71	6.17»		5.911			SJ13	3.159	3.261	6.196	5.063		445*
0.003	144*	11.04	9.594	IJ05	•J02	7.932		7.496	7.119	7 211	7.015			6.462	6J96	6.122	6.0**	3*31
9 0.100	JJ60	iJ»o	2JU			2J51					2J7»		12*6			121«	116*
	5.117	4.2»	1J63	1.611	1.462	1J74	1J91		1.179	J.1J7	107.*	J406	1*36	24*1	1*64		173*
	7.10*	3.71 J		4.716	4.464	4J20	4.197	4.102	4.026	3.964	146*	1.769			3J60	1.471	1.401	$333
0.010			6.992	64U				5.467	5JS1		Sill		449*	4.71J		4.517	4.413	4J11
0.005		10.11		7.956	7.471	7.114			6J41	6.417	6.227	6.012		3.706		3.454	3J22	5.1»*
10 O.10O	1.2*5	2.924	2.721			14*1			U47	uu	12*4						10*7
0.030	4.965	4.101	3.706	1.471	111*		1.113			1*7*	191J						2JM	151»
	6.937	5.456	4J16	4.466	4.U6		1.990		1.779	1.717		5JU	1.41*	1J35	Jill	1.221	1.132	1.0*0
0.010	10.04	TJJt		5.9*4	1.616	34*6	9.200		4.941	4.649	4.706	4J5*	4.409	4JI1		4.111		3.909
	12.63	9.427	•4*1			6.943	6J02	6.116	5.966		3.661	5.471	3.274		S.07I	4*02	4.772
ii aioo	JJ2S	2J60		2JJ*		U*9	U42			124*								1.971
04*0	44M	19U	1.567	JJ37	1.104		14t 2	194*	1*96	1U4		171*				1SOT
0.023	6 714		4AM	4.275			3.739	J464	JIM	J.526	J.4J0	JJJ0	1-116	J. 162	J 116			24»!
		7.206	6.217	9.666	9 J16		44*6	4.744		4.319	4.197	4.251	449*		3 941		1.706	3.602
	12.23	69)2			6.422	6.102			3.537		1.116	5.049		4.736	4.634	4.466	4J59	4 226

статистические таблицы

5»и

13 0.100 0050 0025 0010 0005 14 0.100 О ОМ 0.023 0010 0.003 15 0100 0050 0023 0010 0005 16 0 100 0 050 0.025 0.010 0005 17 0100 0.030 0025 0010 0003 16 0.100 0.050 0025 0.010 0.003 19 0.100 0.050 0.0U 0.010 0.005. 20 0.100 0050 0025 0010 0005 21 0 100 0050 0.025 0010 0.005 22 0.100 0.050 0.025 0010 0.003 23 0.100 0.050 0.023 0.О10 0.003 24 0100 0.050 0.025 0.010 0005

F-распреде ление (продолжение) 'I 'Л т II 0100 ОО50 0025 0010 0005

2.243 2 214 2 166 2 649 2 796 2 75.1 3.512 3430 3.174 4 499 4 366 4 296 5.343 3 202 5.063 2 195 2 164 2 131 2.767 2 714 2 671 3366.1312 3250 4.302 4 191 4 100 ч 076 4 935 4.620 2 154 2 122 2 095 2699 2646 2.602 3 265 3.209 3.147 4 140 4030 3939 4.637 4 717 4 603

2 0.1! 2 011 1970 1936 1.904 2 498 2 406 2 401 2.350 2 296.1006 2 963 2 671 2.600 2.725 3 763 3 701 3 569 3.467 3.361 4412 4.331 4 103 4.037 3 904 1.976 1956 1.913 1.662 1640 2 412 2360 2314 2 261 2 206 2662 26.17 2744 2671 2595 3 57) 3 507 3 373 3 272 3 165 4 151 4 073 3 906 3 760 3 647

2 606 2 460 2.394 2.331 2 263 3 490 3 239 3 106 2 996 2 913 4 474 4 121 J 691.1726 3 007 3 953 5 412 S064 4 621 4 640 7226 6.521 6.071 5757 3525 2.560 2434 1347 2 263 2 234 3411 3 179 3025 2915 2632 4 327 3 996 3.707 3604 3 463 5.739 3 205 4 662 4.620 4.441 6926 6233 5.791 5 462 5 253 3 102 2 726 2522 2.395 2 307 2 243 2.193 4600 3739 -3.344 3.(12 2956 2646 1.764 6 296 4 657 4 222 3.692 3.663 3.301 3 360 8.662 6.513 5.564 5.035 4.095 4.456 4.276 11.06 7.922 6.660 5.996 5.562 5 257 5 031

3177 2607 4747 3665 6 354 5 096 9J30 6927 1173 6510 3 136 2 763 4667 3.606 6414 4965 9074 6701 11.37 6 166

2 147 2 105 2 000
2047 2.617 2.544
.1277 3 177 3.07.1
4 155 4.010 3.656
4 90О 4 721 4 530

2097 2.033 2.007

2.604 2.533 2 439

3 153 3053 2946

3 900 3.613 3.663

4 043 4 460 4.270

2.054 2.010 1962 1933 1.912.1.609 1634 1797

2.554 2463 2-366 2.341 2.306 2.241 2.167 2.131

В 2 732 2 636 2 565 2 467

3.600 3.656 3505 3412 3.346 3213 3.112 5004

J 430

3-073 2.695 2.490 2.301 2.273 2.206 2.156 2.119 2066 2.059 2.017 1.972 1.924 1694 1673 1.626 1.793 1755

J662 3267 3056 2.901 1790 1707 2641 2 566 2544 2.475 2 403 2.326 2 260 2 247 2 178 2123 2060

6200 4763 4 153 3 604 3.576 3415 3.293 3 199 3 123 3060 2963 1662 1756 2469 26-14 1540 2474 2395

6.683 6.339 3417 4693 4.356 4-318 4.142 4.004 3.695 3.605 3666 3.322 3.372 3 276 3.214 3.081 2977 2.666

1060 7 701 6 476 5603 3.372 3 071 4.647 4 674 4 536 4 424 4150 4.070 3 663 3 766 5 087 3 523 3 394 3 260

1178 2 741 3.341 4202 4.913 2132 2699 3.277 4 102 4.779

3046 4.494 6.1)3 6 531 1056 3016 4.451 6.042 6400 10.36

2.666 2.462 3.634 3139 4.666 4 077 6.226 3.292 7 314 6.303 2645 1437 3 592 3.197 4.619 4.011 6112 3.165 7 334 6 156

2333 3 007 3729 4.773 3.636 2.306 2965 3.665 4.669 5.497

1244 2.652 3501 4 437 5.212 2216 1810 3438 4336 3 075

2.128 2.637 3.219 4.026 4.692 2102 2614 3 136 3927 4559

2066 2055 2026 2.591 1536 2.494 3.125 3 049 1966 3.690 3 760 3 691 4.321 4.364 4 272 2.061 1018 2.001 2346 2494 2430 3061 2.983 2922 3791 3.682 3.593 4369 4 254 4.142

1985 1.940 1.891 1660 1839 1.793 1.757 1716

2.425 1352 2.276 1227 2.194 2.124 1068 2.010

2869 1766 2661 2.614 2 568 2472 1396 2316

3.553 3.409 3.239 3.163 3.101 1967 2.663 1733

4.099 3.920 3.734 3.616 3.539 3.373 3.246 3.112

1.936 1912 1862 1631 1809 1763 1726 1666

Л20 1960

2623 2723 2616 2346 2 302 2403 2.329 2 247

3 435 3 312 3 162 3.068 3.003 2 669 2 764 2 653

3971 3.793 3.607 3.492 3.412 3246 3119 1984

1637 1.917 2.167 2300 1873 1.631 1878 1133 1469 1776 1.607 1.643 1.083 1421 1690 1.586 1612 2042 1360 1614 1.567 1.783 1003 2J05 1343 1.549 1.757 1.966 1256 1464 1.533 1733 1.933 1211 1424

3007 1614 1416 12*6 2196 2 130 1079 1036 1.003 1.997 1.933 1667 16J7 1.605 1763 1736 1698

4.414 3.355 3.160 1.926 2773 1661 1.377 2510 1456 1411 2342 1269 1191 1141 1.107 2.033 1.978

5.976 4.560 3.954 3608 3.362 3.221 3.100 3005 1929 2666 2 769 2.667 1.559 1491 2 445 1347 2169

6.263 6013 3092 4.579 4.246 4.015 3.641 3.703 3.397 3.506 3.371 3.127 3.077 1983 1919 1.764 1676

10.22 7.213 6026 3373 4956 4663 4.443 4 276 4 141 4030 3 660 3663 3 496 3.362 3.303 3 130 3009

1990 1606 2.397 1266 2176 1109 2.036 2 017 1.984 1.956 1.912 1.863 1.614 1.762 1759 1711 1.673

4.361 3522 3 127 2893 1740 1.618 2344 1477 1423 1376 2306 2134 1155 1106 2.071 1999 1.940

I860 2817 1720 1617 1509 1441 1394 2.295 1217