Distribution Tables

As compared to probability calculators (e.g., like the one included in STATISTICA), the traditional format of distribution tables like those presented below, has the advantage of showing simultaneously many values and thus allowing the user to examine and quickly explore ranges of probabilities.

Z Table t Table Chi-Square Table F Tables for:	alpha=.10 alpha=.05	alpha=.025 alpha=.01

Note that all table values were calculated using the distribution facilities in STATISTICA BASIC, and they were verified against other published tables.

Standard Normal (Z) Table

The Standard Normal distribution is used in various hypothesis tests including tests on single means, the difference between two means, and tests on proportions. The Standard Normal distribution has a mean of 0 and a standard deviation of 1. The animation above shows various (left) tail areas for this distribution. For more information on the Normal Distribution as it is used in statistical testing, see the chapter on Elementary Concepts. See also, the Normal Distribution.

As shown in the illustration below, the values inside the given table represent the areas under the standard normal curve for values between 0 and the relative z-score. For example, to determine the area under the curve between 0 and 2.36, look in the intersecting cell for the row labeled 2.30 and the column labeld 0.06. The area under the curve is .4909. To determine the area between 0 and a negative value, look in the intersecting cell of the row and column which sums to the absolute value of the number in question. For example, the area under the curve between -1.3 and 0 is equal to the area under the curve between 1.3 and 0, so look at the cell on the 1.3 row and the 0.00 column (the area is 0.4032).

Area between 0 and z

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359

0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753

0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141

0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517

0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879

0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.2224

0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549

0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852

0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133

0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389

1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621

1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830

1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015

1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319

1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545

1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633

1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706

1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767

2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817

2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857

2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890

2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916

2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.4936

2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952

2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964

2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974

2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981

2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.4986

3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990

To index

**Area between 0 and z**
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.0000	0.0040	0.0080	0.0120	0.0160	0.0199	0.0239	0.0279	0.0319	0.0359
0.1	0.0398	0.0438	0.0478	0.0517	0.0557	0.0596	0.0636	0.0675	0.0714	0.0753
0.2	0.0793	0.0832	0.0871	0.0910	0.0948	0.0987	0.1026	0.1064	0.1103	0.1141
0.3	0.1179	0.1217	0.1255	0.1293	0.1331	0.1368	0.1406	0.1443	0.1480	0.1517
0.4	0.1554	0.1591	0.1628	0.1664	0.1700	0.1736	0.1772	0.1808	0.1844	0.1879
0.5	0.1915	0.1950	0.1985	0.2019	0.2054	0.2088	0.2123	0.2157	0.2190	0.2224
0.6	0.2257	0.2291	0.2324	0.2357	0.2389	0.2422	0.2454	0.2486	0.2517	0.2549
0.7	0.2580	0.2611	0.2642	0.2673	0.2704	0.2734	0.2764	0.2794	0.2823	0.2852
0.8	0.2881	0.2910	0.2939	0.2967	0.2995	0.3023	0.3051	0.3078	0.3106	0.3133
0.9	0.3159	0.3186	0.3212	0.3238	0.3264	0.3289	0.3315	0.3340	0.3365	0.3389
1.0	0.3413	0.3438	0.3461	0.3485	0.3508	0.3531	0.3554	0.3577	0.3599	0.3621
1.1	0.3643	0.3665	0.3686	0.3708	0.3729	0.3749	0.3770	0.3790	0.3810	0.3830
1.2	0.3849	0.3869	0.3888	0.3907	0.3925	0.3944	0.3962	0.3980	0.3997	0.4015
1.3	0.4032	0.4049	0.4066	0.4082	0.4099	0.4115	0.4131	0.4147	0.4162	0.4177
1.4	0.4192	0.4207	0.4222	0.4236	0.4251	0.4265	0.4279	0.4292	0.4306	0.4319
1.5	0.4332	0.4345	0.4357	0.4370	0.4382	0.4394	0.4406	0.4418	0.4429	0.4441
1.6	0.4452	0.4463	0.4474	0.4484	0.4495	0.4505	0.4515	0.4525	0.4535	0.4545
1.7	0.4554	0.4564	0.4573	0.4582	0.4591	0.4599	0.4608	0.4616	0.4625	0.4633
1.8	0.4641	0.4649	0.4656	0.4664	0.4671	0.4678	0.4686	0.4693	0.4699	0.4706
1.9	0.4713	0.4719	0.4726	0.4732	0.4738	0.4744	0.4750	0.4756	0.4761	0.4767
2.0	0.4772	0.4778	0.4783	0.4788	0.4793	0.4798	0.4803	0.4808	0.4812	0.4817
2.1	0.4821	0.4826	0.4830	0.4834	0.4838	0.4842	0.4846	0.4850	0.4854	0.4857
2.2	0.4861	0.4864	0.4868	0.4871	0.4875	0.4878	0.4881	0.4884	0.4887	0.4890
2.3	0.4893	0.4896	0.4898	0.4901	0.4904	0.4906	0.4909	0.4911	0.4913	0.4916
2.4	0.4918	0.4920	0.4922	0.4925	0.4927	0.4929	0.4931	0.4932	0.4934	0.4936
2.5	0.4938	0.4940	0.4941	0.4943	0.4945	0.4946	0.4948	0.4949	0.4951	0.4952
2.6	0.4953	0.4955	0.4956	0.4957	0.4959	0.4960	0.4961	0.4962	0.4963	0.4964
2.7	0.4965	0.4966	0.4967	0.4968	0.4969	0.4970	0.4971	0.4972	0.4973	0.4974
2.8	0.4974	0.4975	0.4976	0.4977	0.4977	0.4978	0.4979	0.4979	0.4980	0.4981
2.9	0.4981	0.4982	0.4982	0.4983	0.4984	0.4984	0.4985	0.4985	0.4986	0.4986
3.0	0.4987	0.4987	0.4987	0.4988	0.4988	0.4989	0.4989	0.4989	0.4990	0.4990

Student's t Table

The Shape of the Student's t distribution is determined by the degrees of freedom. As shown in the animation above, its shape changes as the degrees of freedom increases. For more information on how this distribution is used in hypothesis testing, see t-test for independent samples and t-test for dependent samples in the chapter on Basic Statistics and Tables. See also, Student's t Distribution. As indicated by the chart below, the areas given at the top of this table are the right tail areas for the t-value inside the table. To determine the 0.05 critical value from the t-distribution with 6 degrees of freedom, look in the 0.05 column at the 6 row: t_(.05,6) = 1.943180.

t table with right tail probabilities

df\p 0.40 0.25 0.10 0.05 0.025 0.01 0.005 0.0005

1 0.324920 1.000000 3.077684 6.313752 12.70620 31.82052 63.65674 636.6192

2 0.288675 0.816497 1.885618 2.919986 4.30265 6.96456 9.92484 31.5991

3 0.276671 0.764892 1.637744 2.353363 3.18245 4.54070 5.84091 12.9240

4 0.270722 0.740697 1.533206 2.131847 2.77645 3.74695 4.60409 8.6103

5 0.267181 0.726687 1.475884 2.015048 2.57058 3.36493 4.03214 6.8688

6 0.264835 0.717558 1.439756 1.943180 2.44691 3.14267 3.70743 5.9588

7 0.263167 0.711142 1.414924 1.894579 2.36462 2.99795 3.49948 5.4079

8 0.261921 0.706387 1.396815 1.859548 2.30600 2.89646 3.35539 5.0413

9 0.260955 0.702722 1.383029 1.833113 2.26216 2.82144 3.24984 4.7809

10 0.260185 0.699812 1.372184 1.812461 2.22814 2.76377 3.16927 4.5869

11 0.259556 0.697445 1.363430 1.795885 2.20099 2.71808 3.10581 4.4370

12 0.259033 0.695483 1.356217 1.782288 2.17881 2.68100 3.05454 4.3178

13 0.258591 0.693829 1.350171 1.770933 2.16037 2.65031 3.01228 4.2208

14 0.258213 0.692417 1.345030 1.761310 2.14479 2.62449 2.97684 4.1405

15 0.257885 0.691197 1.340606 1.753050 2.13145 2.60248 2.94671 4.0728

16 0.257599 0.690132 1.336757 1.745884 2.11991 2.58349 2.92078 4.0150

17 0.257347 0.689195 1.333379 1.739607 2.10982 2.56693 2.89823 3.9651

18 0.257123 0.688364 1.330391 1.734064 2.10092 2.55238 2.87844 3.9216

19 0.256923 0.687621 1.327728 1.729133 2.09302 2.53948 2.86093 3.8834

20 0.256743 0.686954 1.325341 1.724718 2.08596 2.52798 2.84534 3.8495

21 0.256580 0.686352 1.323188 1.720743 2.07961 2.51765 2.83136 3.8193

22 0.256432 0.685805 1.321237 1.717144 2.07387 2.50832 2.81876 3.7921

23 0.256297 0.685306 1.319460 1.713872 2.06866 2.49987 2.80734 3.7676

24 0.256173 0.684850 1.317836 1.710882 2.06390 2.49216 2.79694 3.7454

25 0.256060 0.684430 1.316345 1.708141 2.05954 2.48511 2.78744 3.7251

26 0.255955 0.684043 1.314972 1.705618 2.05553 2.47863 2.77871 3.7066

27 0.255858 0.683685 1.313703 1.703288 2.05183 2.47266 2.77068 3.6896

28 0.255768 0.683353 1.312527 1.701131 2.04841 2.46714 2.76326 3.6739

29 0.255684 0.683044 1.311434 1.699127 2.04523 2.46202 2.75639 3.6594

30 0.255605 0.682756 1.310415 1.697261 2.04227 2.45726 2.75000 3.6460

inf 0.253347 0.674490 1.281552 1.644854 1.95996 2.32635 2.57583 3.2905

To index

**t table with right tail probabilities**
df\p	0.40	0.25	0.10	0.05	0.025	0.01	0.005	0.0005
1	0.324920	1.000000	3.077684	6.313752	12.70620	31.82052	63.65674	636.6192
2	0.288675	0.816497	1.885618	2.919986	4.30265	6.96456	9.92484	31.5991
3	0.276671	0.764892	1.637744	2.353363	3.18245	4.54070	5.84091	12.9240
4	0.270722	0.740697	1.533206	2.131847	2.77645	3.74695	4.60409	8.6103
5	0.267181	0.726687	1.475884	2.015048	2.57058	3.36493	4.03214	6.8688

6	0.264835	0.717558	1.439756	1.943180	2.44691	3.14267	3.70743	5.9588
7	0.263167	0.711142	1.414924	1.894579	2.36462	2.99795	3.49948	5.4079
8	0.261921	0.706387	1.396815	1.859548	2.30600	2.89646	3.35539	5.0413
9	0.260955	0.702722	1.383029	1.833113	2.26216	2.82144	3.24984	4.7809
10	0.260185	0.699812	1.372184	1.812461	2.22814	2.76377	3.16927	4.5869

11	0.259556	0.697445	1.363430	1.795885	2.20099	2.71808	3.10581	4.4370
12	0.259033	0.695483	1.356217	1.782288	2.17881	2.68100	3.05454	4.3178
13	0.258591	0.693829	1.350171	1.770933	2.16037	2.65031	3.01228	4.2208
14	0.258213	0.692417	1.345030	1.761310	2.14479	2.62449	2.97684	4.1405
15	0.257885	0.691197	1.340606	1.753050	2.13145	2.60248	2.94671	4.0728

16	0.257599	0.690132	1.336757	1.745884	2.11991	2.58349	2.92078	4.0150
17	0.257347	0.689195	1.333379	1.739607	2.10982	2.56693	2.89823	3.9651
18	0.257123	0.688364	1.330391	1.734064	2.10092	2.55238	2.87844	3.9216
19	0.256923	0.687621	1.327728	1.729133	2.09302	2.53948	2.86093	3.8834
20	0.256743	0.686954	1.325341	1.724718	2.08596	2.52798	2.84534	3.8495

21	0.256580	0.686352	1.323188	1.720743	2.07961	2.51765	2.83136	3.8193
22	0.256432	0.685805	1.321237	1.717144	2.07387	2.50832	2.81876	3.7921
23	0.256297	0.685306	1.319460	1.713872	2.06866	2.49987	2.80734	3.7676
24	0.256173	0.684850	1.317836	1.710882	2.06390	2.49216	2.79694	3.7454
25	0.256060	0.684430	1.316345	1.708141	2.05954	2.48511	2.78744	3.7251

26	0.255955	0.684043	1.314972	1.705618	2.05553	2.47863	2.77871	3.7066
27	0.255858	0.683685	1.313703	1.703288	2.05183	2.47266	2.77068	3.6896
28	0.255768	0.683353	1.312527	1.701131	2.04841	2.46714	2.76326	3.6739
29	0.255684	0.683044	1.311434	1.699127	2.04523	2.46202	2.75639	3.6594
30	0.255605	0.682756	1.310415	1.697261	2.04227	2.45726	2.75000	3.6460

inf	0.253347	0.674490	1.281552	1.644854	1.95996	2.32635	2.57583	3.2905

Chi-Square Table

Like the Student's t-Distribution, the Chi-square distribtuion's shape is determined by its degrees of freedom. The animation above shows the shape of the Chi-square distribution as the degrees of freedom increase (1, 2, 5, 10, 25 and 50). For examples of tests of hypothesis which use the Chi-square distribution, see Statistics in crosstabulation tables in the Basic Statistics and Tables chapter as well as the Nonlinear Estimation chapter. See also, Chi-square Distribution. As shown in the illustration below, the values inside this table are critical values of the Chi-square distribution with the corresponding degrees of freedom. To determine the value from a Chi-square distribution (with a specific degree of freedom) which has a given area above it, go to the given area column and the desired degree of freedom row. For example, the .25 critical value for a Chi-square with 4 degrees of freedom is 5.38527. This means that the area to the right of 5.38527 in a Chi-square distribution with 4 degrees of freedom is .25.

Right tail areas for the Chi-square Distribution

df\area .995 .990 .975 .950 .900 .750 .500 .250 .100 .050 .025 .010 .005

1 0.00004 0.00016 0.00098 0.00393 0.01579 0.10153 0.45494 1.32330 2.70554 3.84146 5.02389 6.63490 7.87944

2 0.01003 0.02010 0.05064 0.10259 0.21072 0.57536 1.38629 2.77259 4.60517 5.99146 7.37776 9.21034 10.59663

3 0.07172 0.11483 0.21580 0.35185 0.58437 1.21253 2.36597 4.10834 6.25139 7.81473 9.34840 11.34487 12.83816

4 0.20699 0.29711 0.48442 0.71072 1.06362 1.92256 3.35669 5.38527 7.77944 9.48773 11.14329 13.27670 14.86026

5 0.41174 0.55430 0.83121 1.14548 1.61031 2.67460 4.35146 6.62568 9.23636 11.07050 12.83250 15.08627 16.74960

6 0.67573 0.87209 1.23734 1.63538 2.20413 3.45460 5.34812 7.84080 10.64464 12.59159 14.44938 16.81189 18.54758

7 0.98926 1.23904 1.68987 2.16735 2.83311 4.25485 6.34581 9.03715 12.01704 14.06714 16.01276 18.47531 20.27774

8 1.34441 1.64650 2.17973 2.73264 3.48954 5.07064 7.34412 10.21885 13.36157 15.50731 17.53455 20.09024 21.95495

9 1.73493 2.08790 2.70039 3.32511 4.16816 5.89883 8.34283 11.38875 14.68366 16.91898 19.02277 21.66599 23.58935

10 2.15586 2.55821 3.24697 3.94030 4.86518 6.73720 9.34182 12.54886 15.98718 18.30704 20.48318 23.20925 25.18818

11 2.60322 3.05348 3.81575 4.57481 5.57778 7.58414 10.34100 13.70069 17.27501 19.67514 21.92005 24.72497 26.75685

12 3.07382 3.57057 4.40379 5.22603 6.30380 8.43842 11.34032 14.84540 18.54935 21.02607 23.33666 26.21697 28.29952

13 3.56503 4.10692 5.00875 5.89186 7.04150 9.29907 12.33976 15.98391 19.81193 22.36203 24.73560 27.68825 29.81947

14 4.07467 4.66043 5.62873 6.57063 7.78953 10.16531 13.33927 17.11693 21.06414 23.68479 26.11895 29.14124 31.31935

15 4.60092 5.22935 6.26214 7.26094 8.54676 11.03654 14.33886 18.24509 22.30713 24.99579 27.48839 30.57791 32.80132

16 5.14221 5.81221 6.90766 7.96165 9.31224 11.91222 15.33850 19.36886 23.54183 26.29623 28.84535 31.99993 34.26719

17 5.69722 6.40776 7.56419 8.67176 10.08519 12.79193 16.33818 20.48868 24.76904 27.58711 30.19101 33.40866 35.71847

18 6.26480 7.01491 8.23075 9.39046 10.86494 13.67529 17.33790 21.60489 25.98942 28.86930 31.52638 34.80531 37.15645

19 6.84397 7.63273 8.90652 10.11701 11.65091 14.56200 18.33765 22.71781 27.20357 30.14353 32.85233 36.19087 38.58226

20 7.43384 8.26040 9.59078 10.85081 12.44261 15.45177 19.33743 23.82769 28.41198 31.41043 34.16961 37.56623 39.99685

21 8.03365 8.89720 10.28290 11.59131 13.23960 16.34438 20.33723 24.93478 29.61509 32.67057 35.47888 38.93217 41.40106

22 8.64272 9.54249 10.98232 12.33801 14.04149 17.23962 21.33704 26.03927 30.81328 33.92444 36.78071 40.28936 42.79565

23 9.26042 10.19572 11.68855 13.09051 14.84796 18.13730 22.33688 27.14134 32.00690 35.17246 38.07563 41.63840 44.18128

24 9.88623 10.85636 12.40115 13.84843 15.65868 19.03725 23.33673 28.24115 33.19624 36.41503 39.36408 42.97982 45.55851

25 10.51965 11.52398 13.11972 14.61141 16.47341 19.93934 24.33659 29.33885 34.38159 37.65248 40.64647 44.31410 46.92789

26 11.16024 12.19815 13.84390 15.37916 17.29188 20.84343 25.33646 30.43457 35.56317 38.88514 41.92317 45.64168 48.28988

27 11.80759 12.87850 14.57338 16.15140 18.11390 21.74940 26.33634 31.52841 36.74122 40.11327 43.19451 46.96294 49.64492

28 12.46134 13.56471 15.30786 16.92788 18.93924 22.65716 27.33623 32.62049 37.91592 41.33714 44.46079 48.27824 50.99338

29 13.12115 14.25645 16.04707 17.70837 19.76774 23.56659 28.33613 33.71091 39.08747 42.55697 45.72229 49.58788 52.33562

30 13.78672 14.95346 16.79077 18.49266 20.59923 24.47761 29.33603 34.79974 40.25602 43.77297 46.97924 50.89218 53.67196

To index

**Right tail areas for the *Chi-square* Distribution**
df\area	.995	.990	.975	.950	.900	.750	.500	.250	.100	.050	.025	.010	.005
1	0.00004	0.00016	0.00098	0.00393	0.01579	0.10153	0.45494	1.32330	2.70554	3.84146	5.02389	6.63490	7.87944
2	0.01003	0.02010	0.05064	0.10259	0.21072	0.57536	1.38629	2.77259	4.60517	5.99146	7.37776	9.21034	10.59663
3	0.07172	0.11483	0.21580	0.35185	0.58437	1.21253	2.36597	4.10834	6.25139	7.81473	9.34840	11.34487	12.83816
4	0.20699	0.29711	0.48442	0.71072	1.06362	1.92256	3.35669	5.38527	7.77944	9.48773	11.14329	13.27670	14.86026
5	0.41174	0.55430	0.83121	1.14548	1.61031	2.67460	4.35146	6.62568	9.23636	11.07050	12.83250	15.08627	16.74960

6	0.67573	0.87209	1.23734	1.63538	2.20413	3.45460	5.34812	7.84080	10.64464	12.59159	14.44938	16.81189	18.54758
7	0.98926	1.23904	1.68987	2.16735	2.83311	4.25485	6.34581	9.03715	12.01704	14.06714	16.01276	18.47531	20.27774
8	1.34441	1.64650	2.17973	2.73264	3.48954	5.07064	7.34412	10.21885	13.36157	15.50731	17.53455	20.09024	21.95495
9	1.73493	2.08790	2.70039	3.32511	4.16816	5.89883	8.34283	11.38875	14.68366	16.91898	19.02277	21.66599	23.58935
10	2.15586	2.55821	3.24697	3.94030	4.86518	6.73720	9.34182	12.54886	15.98718	18.30704	20.48318	23.20925	25.18818

11	2.60322	3.05348	3.81575	4.57481	5.57778	7.58414	10.34100	13.70069	17.27501	19.67514	21.92005	24.72497	26.75685
12	3.07382	3.57057	4.40379	5.22603	6.30380	8.43842	11.34032	14.84540	18.54935	21.02607	23.33666	26.21697	28.29952
13	3.56503	4.10692	5.00875	5.89186	7.04150	9.29907	12.33976	15.98391	19.81193	22.36203	24.73560	27.68825	29.81947
14	4.07467	4.66043	5.62873	6.57063	7.78953	10.16531	13.33927	17.11693	21.06414	23.68479	26.11895	29.14124	31.31935
15	4.60092	5.22935	6.26214	7.26094	8.54676	11.03654	14.33886	18.24509	22.30713	24.99579	27.48839	30.57791	32.80132

16	5.14221	5.81221	6.90766	7.96165	9.31224	11.91222	15.33850	19.36886	23.54183	26.29623	28.84535	31.99993	34.26719
17	5.69722	6.40776	7.56419	8.67176	10.08519	12.79193	16.33818	20.48868	24.76904	27.58711	30.19101	33.40866	35.71847
18	6.26480	7.01491	8.23075	9.39046	10.86494	13.67529	17.33790	21.60489	25.98942	28.86930	31.52638	34.80531	37.15645
19	6.84397	7.63273	8.90652	10.11701	11.65091	14.56200	18.33765	22.71781	27.20357	30.14353	32.85233	36.19087	38.58226
20	7.43384	8.26040	9.59078	10.85081	12.44261	15.45177	19.33743	23.82769	28.41198	31.41043	34.16961	37.56623	39.99685

21	8.03365	8.89720	10.28290	11.59131	13.23960	16.34438	20.33723	24.93478	29.61509	32.67057	35.47888	38.93217	41.40106
22	8.64272	9.54249	10.98232	12.33801	14.04149	17.23962	21.33704	26.03927	30.81328	33.92444	36.78071	40.28936	42.79565
23	9.26042	10.19572	11.68855	13.09051	14.84796	18.13730	22.33688	27.14134	32.00690	35.17246	38.07563	41.63840	44.18128
24	9.88623	10.85636	12.40115	13.84843	15.65868	19.03725	23.33673	28.24115	33.19624	36.41503	39.36408	42.97982	45.55851
25	10.51965	11.52398	13.11972	14.61141	16.47341	19.93934	24.33659	29.33885	34.38159	37.65248	40.64647	44.31410	46.92789

26	11.16024	12.19815	13.84390	15.37916	17.29188	20.84343	25.33646	30.43457	35.56317	38.88514	41.92317	45.64168	48.28988
27	11.80759	12.87850	14.57338	16.15140	18.11390	21.74940	26.33634	31.52841	36.74122	40.11327	43.19451	46.96294	49.64492
28	12.46134	13.56471	15.30786	16.92788	18.93924	22.65716	27.33623	32.62049	37.91592	41.33714	44.46079	48.27824	50.99338
29	13.12115	14.25645	16.04707	17.70837	19.76774	23.56659	28.33613	33.71091	39.08747	42.55697	45.72229	49.58788	52.33562
30	13.78672	14.95346	16.79077	18.49266	20.59923	24.47761	29.33603	34.79974	40.25602	43.77297	46.97924	50.89218	53.67196

F Distribution Tables

The F distribution is a right-skewed distribution used most commonly in Analysis of Variance (see ANOVA/MANOVA). The F distribution is a ratio of two Chi-square distributions, and a specific F distribution is denoted by the degrees of freedom for the numerator Chi-square and the degrees of freedom for the denominator Chi-square. An example of the F_(10,10) distribution is shown in the animation above. When referencing the F distribution, the numerator degrees of freedom are always given first, as switching the order of degrees of freedom changes the distribution (e.g., F_(10,12) does not equal F_(12,10)). For the four F tables below, the rows represent denominator degrees of freedom and the columns represent numerator degrees of freedom. The right tail area is given in the name of the table. For example, to determine the .05 critical value for an F distribution with 10 and 12 degrees of freedom, look in the 10 column (numerator) and 12 row (denominator) of the F Table for alpha=.05. F_{(.05, 10, 12)} = 2.7534.

F Table for alpha=.10 .

df2/df1 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 INF

1 39.86346 49.50000 53.59324 55.83296 57.24008 58.20442 58.90595 59.43898 59.85759 60.19498 60.70521 61.22034 61.74029 62.00205 62.26497 62.52905 62.79428 63.06064 63.32812

2 8.52632 9.00000 9.16179 9.24342 9.29263 9.32553 9.34908 9.36677 9.38054 9.39157 9.40813 9.42471 9.44131 9.44962 9.45793 9.46624 9.47456 9.48289 9.49122

3 5.53832 5.46238 5.39077 5.34264 5.30916 5.28473 5.26619 5.25167 5.24000 5.23041 5.21562 5.20031 5.18448 5.17636 5.16811 5.15972 5.15119 5.14251 5.13370

4 4.54477 4.32456 4.19086 4.10725 4.05058 4.00975 3.97897 3.95494 3.93567 3.91988 3.89553 3.87036 3.84434 3.83099 3.81742 3.80361 3.78957 3.77527 3.76073

5 4.06042 3.77972 3.61948 3.52020 3.45298 3.40451 3.36790 3.33928 3.31628 3.29740 3.26824 3.23801 3.20665 3.19052 3.17408 3.15732 3.14023 3.12279 3.10500

6 3.77595 3.46330 3.28876 3.18076 3.10751 3.05455 3.01446 2.98304 2.95774 2.93693 2.90472 2.87122 2.83634 2.81834 2.79996 2.78117 2.76195 2.74229 2.72216

7 3.58943 3.25744 3.07407 2.96053 2.88334 2.82739 2.78493 2.75158 2.72468 2.70251 2.66811 2.63223 2.59473 2.57533 2.55546 2.53510 2.51422 2.49279 2.47079

8 3.45792 3.11312 2.92380 2.80643 2.72645 2.66833 2.62413 2.58935 2.56124 2.53804 2.50196 2.46422 2.42464 2.40410 2.38302 2.36136 2.33910 2.31618 2.29257

9 3.36030 3.00645 2.81286 2.69268 2.61061 2.55086 2.50531 2.46941 2.44034 2.41632 2.37888 2.33962 2.29832 2.27683 2.25472 2.23196 2.20849 2.18427 2.15923

10 3.28502 2.92447 2.72767 2.60534 2.52164 2.46058 2.41397 2.37715 2.34731 2.32260 2.28405 2.24351 2.20074 2.17843 2.15543 2.13169 2.10716 2.08176 2.05542

11 3.22520 2.85951 2.66023 2.53619 2.45118 2.38907 2.34157 2.30400 2.27350 2.24823 2.20873 2.16709 2.12305 2.10001 2.07621 2.05161 2.02612 1.99965 1.97211

12 3.17655 2.80680 2.60552 2.48010 2.39402 2.33102 2.28278 2.24457 2.21352 2.18776 2.14744 2.10485 2.05968 2.03599 2.01149 1.98610 1.95973 1.93228 1.90361

13 3.13621 2.76317 2.56027 2.43371 2.34672 2.28298 2.23410 2.19535 2.16382 2.13763 2.09659 2.05316 2.00698 1.98272 1.95757 1.93147 1.90429 1.87591 1.84620

14 3.10221 2.72647 2.52222 2.39469 2.30694 2.24256 2.19313 2.15390 2.12195 2.09540 2.05371 2.00953 1.96245 1.93766 1.91193 1.88516 1.85723 1.82800 1.79728

15 3.07319 2.69517 2.48979 2.36143 2.27302 2.20808 2.15818 2.11853 2.08621 2.05932 2.01707 1.97222 1.92431 1.89904 1.87277 1.84539 1.81676 1.78672 1.75505

16 3.04811 2.66817 2.46181 2.33274 2.24376 2.17833 2.12800 2.08798 2.05533 2.02815 1.98539 1.93992 1.89127 1.86556 1.83879 1.81084 1.78156 1.75075 1.71817

17 3.02623 2.64464 2.43743 2.30775 2.21825 2.15239 2.10169 2.06134 2.02839 2.00094 1.95772 1.91169 1.86236 1.83624 1.80901 1.78053 1.75063 1.71909 1.68564

18 3.00698 2.62395 2.41601 2.28577 2.19583 2.12958 2.07854 2.03789 2.00467 1.97698 1.93334 1.88681 1.83685 1.81035 1.78269 1.75371 1.72322 1.69099 1.65671

19 2.98990 2.60561 2.39702 2.26630 2.17596 2.10936 2.05802 2.01710 1.98364 1.95573 1.91170 1.86471 1.81416 1.78731 1.75924 1.72979 1.69876 1.66587 1.63077

20 2.97465 2.58925 2.38009 2.24893 2.15823 2.09132 2.03970 1.99853 1.96485 1.93674 1.89236 1.84494 1.79384 1.76667 1.73822 1.70833 1.67678 1.64326 1.60738

21 2.96096 2.57457 2.36489 2.23334 2.14231 2.07512 2.02325 1.98186 1.94797 1.91967 1.87497 1.82715 1.77555 1.74807 1.71927 1.68896 1.65691 1.62278 1.58615

22 2.94858 2.56131 2.35117 2.21927 2.12794 2.06050 2.00840 1.96680 1.93273 1.90425 1.85925 1.81106 1.75899 1.73122 1.70208 1.67138 1.63885 1.60415 1.56678

23 2.93736 2.54929 2.33873 2.20651 2.11491 2.04723 1.99492 1.95312 1.91888 1.89025 1.84497 1.79643 1.74392 1.71588 1.68643 1.65535 1.62237 1.58711 1.54903

24 2.92712 2.53833 2.32739 2.19488 2.10303 2.03513 1.98263 1.94066 1.90625 1.87748 1.83194 1.78308 1.73015 1.70185 1.67210 1.64067 1.60726 1.57146 1.53270

25 2.91774 2.52831 2.31702 2.18424 2.09216 2.02406 1.97138 1.92925 1.89469 1.86578 1.82000 1.77083 1.71752 1.68898 1.65895 1.62718 1.59335 1.55703 1.51760

26 2.90913 2.51910 2.30749 2.17447 2.08218 2.01389 1.96104 1.91876 1.88407 1.85503 1.80902 1.75957 1.70589 1.67712 1.64682 1.61472 1.58050 1.54368 1.50360

27 2.90119 2.51061 2.29871 2.16546 2.07298 2.00452 1.95151 1.90909 1.87427 1.84511 1.79889 1.74917 1.69514 1.66616 1.63560 1.60320 1.56859 1.53129 1.49057

28 2.89385 2.50276 2.29060 2.15714 2.06447 1.99585 1.94270 1.90014 1.86520 1.83593 1.78951 1.73954 1.68519 1.65600 1.62519 1.59250 1.55753 1.51976 1.47841

29 2.88703 2.49548 2.28307 2.14941 2.05658 1.98781 1.93452 1.89184 1.85679 1.82741 1.78081 1.73060 1.67593 1.64655 1.61551 1.58253 1.54721 1.50899 1.46704

30 2.88069 2.48872 2.27607 2.14223 2.04925 1.98033 1.92692 1.88412 1.84896 1.81949 1.77270 1.72227 1.66731 1.63774 1.60648 1.57323 1.53757 1.49891 1.45636

40 2.83535 2.44037 2.22609 2.09095 1.99682 1.92688 1.87252 1.82886 1.79290 1.76269 1.71456 1.66241 1.60515 1.57411 1.54108 1.50562 1.46716 1.42476 1.37691

60 2.79107 2.39325 2.17741 2.04099 1.94571 1.87472 1.81939 1.77483 1.73802 1.70701 1.65743 1.60337 1.54349 1.51072 1.47554 1.43734 1.39520 1.34757 1.29146

120 2.74781 2.34734 2.12999 1.99230 1.89587 1.82381 1.76748 1.72196 1.68425 1.65238 1.60120 1.54500 1.48207 1.44723 1.40938 1.36760 1.32034 1.26457 1.19256

inf 2.70554 2.30259 2.08380 1.94486 1.84727 1.77411 1.71672 1.67020 1.63152 1.59872 1.54578 1.48714 1.42060 1.38318 1.34187 1.29513 1.23995 1.16860 1.00000

To index

F Table for alpha=.05 .

df2/df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	INF
1	39.86346	49.50000	53.59324	55.83296	57.24008	58.20442	58.90595	59.43898	59.85759	60.19498	60.70521	61.22034	61.74029	62.00205	62.26497	62.52905	62.79428	63.06064	63.32812
2	8.52632	9.00000	9.16179	9.24342	9.29263	9.32553	9.34908	9.36677	9.38054	9.39157	9.40813	9.42471	9.44131	9.44962	9.45793	9.46624	9.47456	9.48289	9.49122
3	5.53832	5.46238	5.39077	5.34264	5.30916	5.28473	5.26619	5.25167	5.24000	5.23041	5.21562	5.20031	5.18448	5.17636	5.16811	5.15972	5.15119	5.14251	5.13370
4	4.54477	4.32456	4.19086	4.10725	4.05058	4.00975	3.97897	3.95494	3.93567	3.91988	3.89553	3.87036	3.84434	3.83099	3.81742	3.80361	3.78957	3.77527	3.76073
5	4.06042	3.77972	3.61948	3.52020	3.45298	3.40451	3.36790	3.33928	3.31628	3.29740	3.26824	3.23801	3.20665	3.19052	3.17408	3.15732	3.14023	3.12279	3.10500

6	3.77595	3.46330	3.28876	3.18076	3.10751	3.05455	3.01446	2.98304	2.95774	2.93693	2.90472	2.87122	2.83634	2.81834	2.79996	2.78117	2.76195	2.74229	2.72216
7	3.58943	3.25744	3.07407	2.96053	2.88334	2.82739	2.78493	2.75158	2.72468	2.70251	2.66811	2.63223	2.59473	2.57533	2.55546	2.53510	2.51422	2.49279	2.47079
8	3.45792	3.11312	2.92380	2.80643	2.72645	2.66833	2.62413	2.58935	2.56124	2.53804	2.50196	2.46422	2.42464	2.40410	2.38302	2.36136	2.33910	2.31618	2.29257
9	3.36030	3.00645	2.81286	2.69268	2.61061	2.55086	2.50531	2.46941	2.44034	2.41632	2.37888	2.33962	2.29832	2.27683	2.25472	2.23196	2.20849	2.18427	2.15923
10	3.28502	2.92447	2.72767	2.60534	2.52164	2.46058	2.41397	2.37715	2.34731	2.32260	2.28405	2.24351	2.20074	2.17843	2.15543	2.13169	2.10716	2.08176	2.05542

11	3.22520	2.85951	2.66023	2.53619	2.45118	2.38907	2.34157	2.30400	2.27350	2.24823	2.20873	2.16709	2.12305	2.10001	2.07621	2.05161	2.02612	1.99965	1.97211
12	3.17655	2.80680	2.60552	2.48010	2.39402	2.33102	2.28278	2.24457	2.21352	2.18776	2.14744	2.10485	2.05968	2.03599	2.01149	1.98610	1.95973	1.93228	1.90361
13	3.13621	2.76317	2.56027	2.43371	2.34672	2.28298	2.23410	2.19535	2.16382	2.13763	2.09659	2.05316	2.00698	1.98272	1.95757	1.93147	1.90429	1.87591	1.84620
14	3.10221	2.72647	2.52222	2.39469	2.30694	2.24256	2.19313	2.15390	2.12195	2.09540	2.05371	2.00953	1.96245	1.93766	1.91193	1.88516	1.85723	1.82800	1.79728
15	3.07319	2.69517	2.48979	2.36143	2.27302	2.20808	2.15818	2.11853	2.08621	2.05932	2.01707	1.97222	1.92431	1.89904	1.87277	1.84539	1.81676	1.78672	1.75505

16	3.04811	2.66817	2.46181	2.33274	2.24376	2.17833	2.12800	2.08798	2.05533	2.02815	1.98539	1.93992	1.89127	1.86556	1.83879	1.81084	1.78156	1.75075	1.71817
17	3.02623	2.64464	2.43743	2.30775	2.21825	2.15239	2.10169	2.06134	2.02839	2.00094	1.95772	1.91169	1.86236	1.83624	1.80901	1.78053	1.75063	1.71909	1.68564
18	3.00698	2.62395	2.41601	2.28577	2.19583	2.12958	2.07854	2.03789	2.00467	1.97698	1.93334	1.88681	1.83685	1.81035	1.78269	1.75371	1.72322	1.69099	1.65671
19	2.98990	2.60561	2.39702	2.26630	2.17596	2.10936	2.05802	2.01710	1.98364	1.95573	1.91170	1.86471	1.81416	1.78731	1.75924	1.72979	1.69876	1.66587	1.63077
20	2.97465	2.58925	2.38009	2.24893	2.15823	2.09132	2.03970	1.99853	1.96485	1.93674	1.89236	1.84494	1.79384	1.76667	1.73822	1.70833	1.67678	1.64326	1.60738

21	2.96096	2.57457	2.36489	2.23334	2.14231	2.07512	2.02325	1.98186	1.94797	1.91967	1.87497	1.82715	1.77555	1.74807	1.71927	1.68896	1.65691	1.62278	1.58615
22	2.94858	2.56131	2.35117	2.21927	2.12794	2.06050	2.00840	1.96680	1.93273	1.90425	1.85925	1.81106	1.75899	1.73122	1.70208	1.67138	1.63885	1.60415	1.56678
23	2.93736	2.54929	2.33873	2.20651	2.11491	2.04723	1.99492	1.95312	1.91888	1.89025	1.84497	1.79643	1.74392	1.71588	1.68643	1.65535	1.62237	1.58711	1.54903
24	2.92712	2.53833	2.32739	2.19488	2.10303	2.03513	1.98263	1.94066	1.90625	1.87748	1.83194	1.78308	1.73015	1.70185	1.67210	1.64067	1.60726	1.57146	1.53270
25	2.91774	2.52831	2.31702	2.18424	2.09216	2.02406	1.97138	1.92925	1.89469	1.86578	1.82000	1.77083	1.71752	1.68898	1.65895	1.62718	1.59335	1.55703	1.51760

26	2.90913	2.51910	2.30749	2.17447	2.08218	2.01389	1.96104	1.91876	1.88407	1.85503	1.80902	1.75957	1.70589	1.67712	1.64682	1.61472	1.58050	1.54368	1.50360
27	2.90119	2.51061	2.29871	2.16546	2.07298	2.00452	1.95151	1.90909	1.87427	1.84511	1.79889	1.74917	1.69514	1.66616	1.63560	1.60320	1.56859	1.53129	1.49057
28	2.89385	2.50276	2.29060	2.15714	2.06447	1.99585	1.94270	1.90014	1.86520	1.83593	1.78951	1.73954	1.68519	1.65600	1.62519	1.59250	1.55753	1.51976	1.47841
29	2.88703	2.49548	2.28307	2.14941	2.05658	1.98781	1.93452	1.89184	1.85679	1.82741	1.78081	1.73060	1.67593	1.64655	1.61551	1.58253	1.54721	1.50899	1.46704
30	2.88069	2.48872	2.27607	2.14223	2.04925	1.98033	1.92692	1.88412	1.84896	1.81949	1.77270	1.72227	1.66731	1.63774	1.60648	1.57323	1.53757	1.49891	1.45636

40	2.83535	2.44037	2.22609	2.09095	1.99682	1.92688	1.87252	1.82886	1.79290	1.76269	1.71456	1.66241	1.60515	1.57411	1.54108	1.50562	1.46716	1.42476	1.37691
60	2.79107	2.39325	2.17741	2.04099	1.94571	1.87472	1.81939	1.77483	1.73802	1.70701	1.65743	1.60337	1.54349	1.51072	1.47554	1.43734	1.39520	1.34757	1.29146
120	2.74781	2.34734	2.12999	1.99230	1.89587	1.82381	1.76748	1.72196	1.68425	1.65238	1.60120	1.54500	1.48207	1.44723	1.40938	1.36760	1.32034	1.26457	1.19256
inf	2.70554	2.30259	2.08380	1.94486	1.84727	1.77411	1.71672	1.67020	1.63152	1.59872	1.54578	1.48714	1.42060	1.38318	1.34187	1.29513	1.23995	1.16860	1.00000

df2/df1 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 INF

1 161.4476 199.5000 215.7073 224.5832 230.1619 233.9860 236.7684 238.8827 240.5433 241.8817 243.9060 245.9499 248.0131 249.0518 250.0951 251.1432 252.1957 253.2529 254.3144

2 18.5128 19.0000 19.1643 19.2468 19.2964 19.3295 19.3532 19.3710 19.3848 19.3959 19.4125 19.4291 19.4458 19.4541 19.4624 19.4707 19.4791 19.4874 19.4957

3 10.1280 9.5521 9.2766 9.1172 9.0135 8.9406 8.8867 8.8452 8.8123 8.7855 8.7446 8.7029 8.6602 8.6385 8.6166 8.5944 8.5720 8.5494 8.5264

4 7.7086 6.9443 6.5914 6.3882 6.2561 6.1631 6.0942 6.0410 5.9988 5.9644 5.9117 5.8578 5.8025 5.7744 5.7459 5.7170 5.6877 5.6581 5.6281

5 6.6079 5.7861 5.4095 5.1922 5.0503 4.9503 4.8759 4.8183 4.7725 4.7351 4.6777 4.6188 4.5581 4.5272 4.4957 4.4638 4.4314 4.3985 4.3650

6 5.9874 5.1433 4.7571 4.5337 4.3874 4.2839 4.2067 4.1468 4.0990 4.0600 3.9999 3.9381 3.8742 3.8415 3.8082 3.7743 3.7398 3.7047 3.6689

7 5.5914 4.7374 4.3468 4.1203 3.9715 3.8660 3.7870 3.7257 3.6767 3.6365 3.5747 3.5107 3.4445 3.4105 3.3758 3.3404 3.3043 3.2674 3.2298

8 5.3177 4.4590 4.0662 3.8379 3.6875 3.5806 3.5005 3.4381 3.3881 3.3472 3.2839 3.2184 3.1503 3.1152 3.0794 3.0428 3.0053 2.9669 2.9276

9 5.1174 4.2565 3.8625 3.6331 3.4817 3.3738 3.2927 3.2296 3.1789 3.1373 3.0729 3.0061 2.9365 2.9005 2.8637 2.8259 2.7872 2.7475 2.7067

10 4.9646 4.1028 3.7083 3.4780 3.3258 3.2172 3.1355 3.0717 3.0204 2.9782 2.9130 2.8450 2.7740 2.7372 2.6996 2.6609 2.6211 2.5801 2.5379

11 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.9480 2.8962 2.8536 2.7876 2.7186 2.6464 2.6090 2.5705 2.5309 2.4901 2.4480 2.4045

12 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 2.7964 2.7534 2.6866 2.6169 2.5436 2.5055 2.4663 2.4259 2.3842 2.3410 2.2962

13 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 2.6710 2.6037 2.5331 2.4589 2.4202 2.3803 2.3392 2.2966 2.2524 2.2064

14 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.6022 2.5342 2.4630 2.3879 2.3487 2.3082 2.2664 2.2229 2.1778 2.1307

15 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.5437 2.4753 2.4034 2.3275 2.2878 2.2468 2.2043 2.1601 2.1141 2.0658

16 4.4940 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 2.4247 2.3522 2.2756 2.2354 2.1938 2.1507 2.1058 2.0589 2.0096

17 4.4513 3.5915 3.1968 2.9647 2.8100 2.6987 2.6143 2.5480 2.4943 2.4499 2.3807 2.3077 2.2304 2.1898 2.1477 2.1040 2.0584 2.0107 1.9604

18 4.4139 3.5546 3.1599 2.9277 2.7729 2.6613 2.5767 2.5102 2.4563 2.4117 2.3421 2.2686 2.1906 2.1497 2.1071 2.0629 2.0166 1.9681 1.9168

19 4.3807 3.5219 3.1274 2.8951 2.7401 2.6283 2.5435 2.4768 2.4227 2.3779 2.3080 2.2341 2.1555 2.1141 2.0712 2.0264 1.9795 1.9302 1.8780

20 4.3512 3.4928 3.0984 2.8661 2.7109 2.5990 2.5140 2.4471 2.3928 2.3479 2.2776 2.2033 2.1242 2.0825 2.0391 1.9938 1.9464 1.8963 1.8432

21 4.3248 3.4668 3.0725 2.8401 2.6848 2.5727 2.4876 2.4205 2.3660 2.3210 2.2504 2.1757 2.0960 2.0540 2.0102 1.9645 1.9165 1.8657 1.8117

22 4.3009 3.4434 3.0491 2.8167 2.6613 2.5491 2.4638 2.3965 2.3419 2.2967 2.2258 2.1508 2.0707 2.0283 1.9842 1.9380 1.8894 1.8380 1.7831

23 4.2793 3.4221 3.0280 2.7955 2.6400 2.5277 2.4422 2.3748 2.3201 2.2747 2.2036 2.1282 2.0476 2.0050 1.9605 1.9139 1.8648 1.8128 1.7570

24 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 2.3002 2.2547 2.1834 2.1077 2.0267 1.9838 1.9390 1.8920 1.8424 1.7896 1.7330

25 4.2417 3.3852 2.9912 2.7587 2.6030 2.4904 2.4047 2.3371 2.2821 2.2365 2.1649 2.0889 2.0075 1.9643 1.9192 1.8718 1.8217 1.7684 1.7110

26 4.2252 3.3690 2.9752 2.7426 2.5868 2.4741 2.3883 2.3205 2.2655 2.2197 2.1479 2.0716 1.9898 1.9464 1.9010 1.8533 1.8027 1.7488 1.6906

27 4.2100 3.3541 2.9604 2.7278 2.5719 2.4591 2.3732 2.3053 2.2501 2.2043 2.1323 2.0558 1.9736 1.9299 1.8842 1.8361 1.7851 1.7306 1.6717

28 4.1960 3.3404 2.9467 2.7141 2.5581 2.4453 2.3593 2.2913 2.2360 2.1900 2.1179 2.0411 1.9586 1.9147 1.8687 1.8203 1.7689 1.7138 1.6541

29 4.1830 3.3277 2.9340 2.7014 2.5454 2.4324 2.3463 2.2783 2.2229 2.1768 2.1045 2.0275 1.9446 1.9005 1.8543 1.8055 1.7537 1.6981 1.6376

30 4.1709 3.3158 2.9223 2.6896 2.5336 2.4205 2.3343 2.2662 2.2107 2.1646 2.0921 2.0148 1.9317 1.8874 1.8409 1.7918 1.7396 1.6835 1.6223

40 4.0847 3.2317 2.8387 2.6060 2.4495 2.3359 2.2490 2.1802 2.1240 2.0772 2.0035 1.9245 1.8389 1.7929 1.7444 1.6928 1.6373 1.5766 1.5089

60 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.0970 2.0401 1.9926 1.9174 1.8364 1.7480 1.7001 1.6491 1.5943 1.5343 1.4673 1.3893

120 3.9201 3.0718 2.6802 2.4472 2.2899 2.1750 2.0868 2.0164 1.9588 1.9105 1.8337 1.7505 1.6587 1.6084 1.5543 1.4952 1.4290 1.3519 1.2539

inf 3.8415 2.9957 2.6049 2.3719 2.2141 2.0986 2.0096 1.9384 1.8799 1.8307 1.7522 1.6664 1.5705 1.5173 1.4591 1.3940 1.3180 1.2214 1.0000

To index

F Table for alpha=.025 .

df2/df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	INF
1	161.4476	199.5000	215.7073	224.5832	230.1619	233.9860	236.7684	238.8827	240.5433	241.8817	243.9060	245.9499	248.0131	249.0518	250.0951	251.1432	252.1957	253.2529	254.3144
2	18.5128	19.0000	19.1643	19.2468	19.2964	19.3295	19.3532	19.3710	19.3848	19.3959	19.4125	19.4291	19.4458	19.4541	19.4624	19.4707	19.4791	19.4874	19.4957
3	10.1280	9.5521	9.2766	9.1172	9.0135	8.9406	8.8867	8.8452	8.8123	8.7855	8.7446	8.7029	8.6602	8.6385	8.6166	8.5944	8.5720	8.5494	8.5264
4	7.7086	6.9443	6.5914	6.3882	6.2561	6.1631	6.0942	6.0410	5.9988	5.9644	5.9117	5.8578	5.8025	5.7744	5.7459	5.7170	5.6877	5.6581	5.6281
5	6.6079	5.7861	5.4095	5.1922	5.0503	4.9503	4.8759	4.8183	4.7725	4.7351	4.6777	4.6188	4.5581	4.5272	4.4957	4.4638	4.4314	4.3985	4.3650

6	5.9874	5.1433	4.7571	4.5337	4.3874	4.2839	4.2067	4.1468	4.0990	4.0600	3.9999	3.9381	3.8742	3.8415	3.8082	3.7743	3.7398	3.7047	3.6689
7	5.5914	4.7374	4.3468	4.1203	3.9715	3.8660	3.7870	3.7257	3.6767	3.6365	3.5747	3.5107	3.4445	3.4105	3.3758	3.3404	3.3043	3.2674	3.2298
8	5.3177	4.4590	4.0662	3.8379	3.6875	3.5806	3.5005	3.4381	3.3881	3.3472	3.2839	3.2184	3.1503	3.1152	3.0794	3.0428	3.0053	2.9669	2.9276
9	5.1174	4.2565	3.8625	3.6331	3.4817	3.3738	3.2927	3.2296	3.1789	3.1373	3.0729	3.0061	2.9365	2.9005	2.8637	2.8259	2.7872	2.7475	2.7067
10	4.9646	4.1028	3.7083	3.4780	3.3258	3.2172	3.1355	3.0717	3.0204	2.9782	2.9130	2.8450	2.7740	2.7372	2.6996	2.6609	2.6211	2.5801	2.5379

11	4.8443	3.9823	3.5874	3.3567	3.2039	3.0946	3.0123	2.9480	2.8962	2.8536	2.7876	2.7186	2.6464	2.6090	2.5705	2.5309	2.4901	2.4480	2.4045
12	4.7472	3.8853	3.4903	3.2592	3.1059	2.9961	2.9134	2.8486	2.7964	2.7534	2.6866	2.6169	2.5436	2.5055	2.4663	2.4259	2.3842	2.3410	2.2962
13	4.6672	3.8056	3.4105	3.1791	3.0254	2.9153	2.8321	2.7669	2.7144	2.6710	2.6037	2.5331	2.4589	2.4202	2.3803	2.3392	2.2966	2.2524	2.2064
14	4.6001	3.7389	3.3439	3.1122	2.9582	2.8477	2.7642	2.6987	2.6458	2.6022	2.5342	2.4630	2.3879	2.3487	2.3082	2.2664	2.2229	2.1778	2.1307
15	4.5431	3.6823	3.2874	3.0556	2.9013	2.7905	2.7066	2.6408	2.5876	2.5437	2.4753	2.4034	2.3275	2.2878	2.2468	2.2043	2.1601	2.1141	2.0658

16	4.4940	3.6337	3.2389	3.0069	2.8524	2.7413	2.6572	2.5911	2.5377	2.4935	2.4247	2.3522	2.2756	2.2354	2.1938	2.1507	2.1058	2.0589	2.0096
17	4.4513	3.5915	3.1968	2.9647	2.8100	2.6987	2.6143	2.5480	2.4943	2.4499	2.3807	2.3077	2.2304	2.1898	2.1477	2.1040	2.0584	2.0107	1.9604
18	4.4139	3.5546	3.1599	2.9277	2.7729	2.6613	2.5767	2.5102	2.4563	2.4117	2.3421	2.2686	2.1906	2.1497	2.1071	2.0629	2.0166	1.9681	1.9168
19	4.3807	3.5219	3.1274	2.8951	2.7401	2.6283	2.5435	2.4768	2.4227	2.3779	2.3080	2.2341	2.1555	2.1141	2.0712	2.0264	1.9795	1.9302	1.8780
20	4.3512	3.4928	3.0984	2.8661	2.7109	2.5990	2.5140	2.4471	2.3928	2.3479	2.2776	2.2033	2.1242	2.0825	2.0391	1.9938	1.9464	1.8963	1.8432

21	4.3248	3.4668	3.0725	2.8401	2.6848	2.5727	2.4876	2.4205	2.3660	2.3210	2.2504	2.1757	2.0960	2.0540	2.0102	1.9645	1.9165	1.8657	1.8117
22	4.3009	3.4434	3.0491	2.8167	2.6613	2.5491	2.4638	2.3965	2.3419	2.2967	2.2258	2.1508	2.0707	2.0283	1.9842	1.9380	1.8894	1.8380	1.7831
23	4.2793	3.4221	3.0280	2.7955	2.6400	2.5277	2.4422	2.3748	2.3201	2.2747	2.2036	2.1282	2.0476	2.0050	1.9605	1.9139	1.8648	1.8128	1.7570
24	4.2597	3.4028	3.0088	2.7763	2.6207	2.5082	2.4226	2.3551	2.3002	2.2547	2.1834	2.1077	2.0267	1.9838	1.9390	1.8920	1.8424	1.7896	1.7330
25	4.2417	3.3852	2.9912	2.7587	2.6030	2.4904	2.4047	2.3371	2.2821	2.2365	2.1649	2.0889	2.0075	1.9643	1.9192	1.8718	1.8217	1.7684	1.7110

26	4.2252	3.3690	2.9752	2.7426	2.5868	2.4741	2.3883	2.3205	2.2655	2.2197	2.1479	2.0716	1.9898	1.9464	1.9010	1.8533	1.8027	1.7488	1.6906
27	4.2100	3.3541	2.9604	2.7278	2.5719	2.4591	2.3732	2.3053	2.2501	2.2043	2.1323	2.0558	1.9736	1.9299	1.8842	1.8361	1.7851	1.7306	1.6717
28	4.1960	3.3404	2.9467	2.7141	2.5581	2.4453	2.3593	2.2913	2.2360	2.1900	2.1179	2.0411	1.9586	1.9147	1.8687	1.8203	1.7689	1.7138	1.6541
29	4.1830	3.3277	2.9340	2.7014	2.5454	2.4324	2.3463	2.2783	2.2229	2.1768	2.1045	2.0275	1.9446	1.9005	1.8543	1.8055	1.7537	1.6981	1.6376
30	4.1709	3.3158	2.9223	2.6896	2.5336	2.4205	2.3343	2.2662	2.2107	2.1646	2.0921	2.0148	1.9317	1.8874	1.8409	1.7918	1.7396	1.6835	1.6223

40	4.0847	3.2317	2.8387	2.6060	2.4495	2.3359	2.2490	2.1802	2.1240	2.0772	2.0035	1.9245	1.8389	1.7929	1.7444	1.6928	1.6373	1.5766	1.5089
60	4.0012	3.1504	2.7581	2.5252	2.3683	2.2541	2.1665	2.0970	2.0401	1.9926	1.9174	1.8364	1.7480	1.7001	1.6491	1.5943	1.5343	1.4673	1.3893
120	3.9201	3.0718	2.6802	2.4472	2.2899	2.1750	2.0868	2.0164	1.9588	1.9105	1.8337	1.7505	1.6587	1.6084	1.5543	1.4952	1.4290	1.3519	1.2539
inf	3.8415	2.9957	2.6049	2.3719	2.2141	2.0986	2.0096	1.9384	1.8799	1.8307	1.7522	1.6664	1.5705	1.5173	1.4591	1.3940	1.3180	1.2214	1.0000

df2/df1 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 INF

1 647.7890 799.5000 864.1630 899.5833 921.8479 937.1111 948.2169 956.6562 963.2846 968.6274 976.7079 984.8668 993.1028 997.2492 1001.414 1005.598 1009.800 1014.020 1018.258

2 38.5063 39.0000 39.1655 39.2484 39.2982 39.3315 39.3552 39.3730 39.3869 39.3980 39.4146 39.4313 39.4479 39.4562 39.465 39.473 39.481 39.490 39.498

3 17.4434 16.0441 15.4392 15.1010 14.8848 14.7347 14.6244 14.5399 14.4731 14.4189 14.3366 14.2527 14.1674 14.1241 14.081 14.037 13.992 13.947 13.902

4 12.2179 10.6491 9.9792 9.6045 9.3645 9.1973 9.0741 8.9796 8.9047 8.8439 8.7512 8.6565 8.5599 8.5109 8.461 8.411 8.360 8.309 8.257

5 10.0070 8.4336 7.7636 7.3879 7.1464 6.9777 6.8531 6.7572 6.6811 6.6192 6.5245 6.4277 6.3286 6.2780 6.227 6.175 6.123 6.069 6.015

6 8.8131 7.2599 6.5988 6.2272 5.9876 5.8198 5.6955 5.5996 5.5234 5.4613 5.3662 5.2687 5.1684 5.1172 5.065 5.012 4.959 4.904 4.849

7 8.0727 6.5415 5.8898 5.5226 5.2852 5.1186 4.9949 4.8993 4.8232 4.7611 4.6658 4.5678 4.4667 4.4150 4.362 4.309 4.254 4.199 4.142

8 7.5709 6.0595 5.4160 5.0526 4.8173 4.6517 4.5286 4.4333 4.3572 4.2951 4.1997 4.1012 3.9995 3.9472 3.894 3.840 3.784 3.728 3.670

9 7.2093 5.7147 5.0781 4.7181 4.4844 4.3197 4.1970 4.1020 4.0260 3.9639 3.8682 3.7694 3.6669 3.6142 3.560 3.505 3.449 3.392 3.333

10 6.9367 5.4564 4.8256 4.4683 4.2361 4.0721 3.9498 3.8549 3.7790 3.7168 3.6209 3.5217 3.4185 3.3654 3.311 3.255 3.198 3.140 3.080

11 6.7241 5.2559 4.6300 4.2751 4.0440 3.8807 3.7586 3.6638 3.5879 3.5257 3.4296 3.3299 3.2261 3.1725 3.118 3.061 3.004 2.944 2.883

12 6.5538 5.0959 4.4742 4.1212 3.8911 3.7283 3.6065 3.5118 3.4358 3.3736 3.2773 3.1772 3.0728 3.0187 2.963 2.906 2.848 2.787 2.725

13 6.4143 4.9653 4.3472 3.9959 3.7667 3.6043 3.4827 3.3880 3.3120 3.2497 3.1532 3.0527 2.9477 2.8932 2.837 2.780 2.720 2.659 2.595

14 6.2979 4.8567 4.2417 3.8919 3.6634 3.5014 3.3799 3.2853 3.2093 3.1469 3.0502 2.9493 2.8437 2.7888 2.732 2.674 2.614 2.552 2.487

15 6.1995 4.7650 4.1528 3.8043 3.5764 3.4147 3.2934 3.1987 3.1227 3.0602 2.9633 2.8621 2.7559 2.7006 2.644 2.585 2.524 2.461 2.395

16 6.1151 4.6867 4.0768 3.7294 3.5021 3.3406 3.2194 3.1248 3.0488 2.9862 2.8890 2.7875 2.6808 2.6252 2.568 2.509 2.447 2.383 2.316

17 6.0420 4.6189 4.0112 3.6648 3.4379 3.2767 3.1556 3.0610 2.9849 2.9222 2.8249 2.7230 2.6158 2.5598 2.502 2.442 2.380 2.315 2.247

18 5.9781 4.5597 3.9539 3.6083 3.3820 3.2209 3.0999 3.0053 2.9291 2.8664 2.7689 2.6667 2.5590 2.5027 2.445 2.384 2.321 2.256 2.187

19 5.9216 4.5075 3.9034 3.5587 3.3327 3.1718 3.0509 2.9563 2.8801 2.8172 2.7196 2.6171 2.5089 2.4523 2.394 2.333 2.270 2.203 2.133

20 5.8715 4.4613 3.8587 3.5147 3.2891 3.1283 3.0074 2.9128 2.8365 2.7737 2.6758 2.5731 2.4645 2.4076 2.349 2.287 2.223 2.156 2.085

21 5.8266 4.4199 3.8188 3.4754 3.2501 3.0895 2.9686 2.8740 2.7977 2.7348 2.6368 2.5338 2.4247 2.3675 2.308 2.246 2.182 2.114 2.042

22 5.7863 4.3828 3.7829 3.4401 3.2151 3.0546 2.9338 2.8392 2.7628 2.6998 2.6017 2.4984 2.3890 2.3315 2.272 2.210 2.145 2.076 2.003

23 5.7498 4.3492 3.7505 3.4083 3.1835 3.0232 2.9023 2.8077 2.7313 2.6682 2.5699 2.4665 2.3567 2.2989 2.239 2.176 2.111 2.041 1.968

24 5.7166 4.3187 3.7211 3.3794 3.1548 2.9946 2.8738 2.7791 2.7027 2.6396 2.5411 2.4374 2.3273 2.2693 2.209 2.146 2.080 2.010 1.935

25 5.6864 4.2909 3.6943 3.3530 3.1287 2.9685 2.8478 2.7531 2.6766 2.6135 2.5149 2.4110 2.3005 2.2422 2.182 2.118 2.052 1.981 1.906

26 5.6586 4.2655 3.6697 3.3289 3.1048 2.9447 2.8240 2.7293 2.6528 2.5896 2.4908 2.3867 2.2759 2.2174 2.157 2.093 2.026 1.954 1.878

27 5.6331 4.2421 3.6472 3.3067 3.0828 2.9228 2.8021 2.7074 2.6309 2.5676 2.4688 2.3644 2.2533 2.1946 2.133 2.069 2.002 1.930 1.853

28 5.6096 4.2205 3.6264 3.2863 3.0626 2.9027 2.7820 2.6872 2.6106 2.5473 2.4484 2.3438 2.2324 2.1735 2.112 2.048 1.980 1.907 1.829

29 5.5878 4.2006 3.6072 3.2674 3.0438 2.8840 2.7633 2.6686 2.5919 2.5286 2.4295 2.3248 2.2131 2.1540 2.092 2.028 1.959 1.886 1.807

30 5.5675 4.1821 3.5894 3.2499 3.0265 2.8667 2.7460 2.6513 2.5746 2.5112 2.4120 2.3072 2.1952 2.1359 2.074 2.009 1.940 1.866 1.787

40 5.4239 4.0510 3.4633 3.1261 2.9037 2.7444 2.6238 2.5289 2.4519 2.3882 2.2882 2.1819 2.0677 2.0069 1.943 1.875 1.803 1.724 1.637

60 5.2856 3.9253 3.3425 3.0077 2.7863 2.6274 2.5068 2.4117 2.3344 2.2702 2.1692 2.0613 1.9445 1.8817 1.815 1.744 1.667 1.581 1.482

120 5.1523 3.8046 3.2269 2.8943 2.6740 2.5154 2.3948 2.2994 2.2217 2.1570 2.0548 1.9450 1.8249 1.7597 1.690 1.614 1.530 1.433 1.310

inf 5.0239 3.6889 3.1161 2.7858 2.5665 2.4082 2.2875 2.1918 2.1136 2.0483 1.9447 1.8326 1.7085 1.6402 1.566 1.484 1.388 1.268 1.000

To index

F Table for alpha=.01 .

df2/df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	INF
1	647.7890	799.5000	864.1630	899.5833	921.8479	937.1111	948.2169	956.6562	963.2846	968.6274	976.7079	984.8668	993.1028	997.2492	1001.414	1005.598	1009.800	1014.020	1018.258
2	38.5063	39.0000	39.1655	39.2484	39.2982	39.3315	39.3552	39.3730	39.3869	39.3980	39.4146	39.4313	39.4479	39.4562	39.465	39.473	39.481	39.490	39.498
3	17.4434	16.0441	15.4392	15.1010	14.8848	14.7347	14.6244	14.5399	14.4731	14.4189	14.3366	14.2527	14.1674	14.1241	14.081	14.037	13.992	13.947	13.902
4	12.2179	10.6491	9.9792	9.6045	9.3645	9.1973	9.0741	8.9796	8.9047	8.8439	8.7512	8.6565	8.5599	8.5109	8.461	8.411	8.360	8.309	8.257
5	10.0070	8.4336	7.7636	7.3879	7.1464	6.9777	6.8531	6.7572	6.6811	6.6192	6.5245	6.4277	6.3286	6.2780	6.227	6.175	6.123	6.069	6.015

6	8.8131	7.2599	6.5988	6.2272	5.9876	5.8198	5.6955	5.5996	5.5234	5.4613	5.3662	5.2687	5.1684	5.1172	5.065	5.012	4.959	4.904	4.849
7	8.0727	6.5415	5.8898	5.5226	5.2852	5.1186	4.9949	4.8993	4.8232	4.7611	4.6658	4.5678	4.4667	4.4150	4.362	4.309	4.254	4.199	4.142
8	7.5709	6.0595	5.4160	5.0526	4.8173	4.6517	4.5286	4.4333	4.3572	4.2951	4.1997	4.1012	3.9995	3.9472	3.894	3.840	3.784	3.728	3.670
9	7.2093	5.7147	5.0781	4.7181	4.4844	4.3197	4.1970	4.1020	4.0260	3.9639	3.8682	3.7694	3.6669	3.6142	3.560	3.505	3.449	3.392	3.333
10	6.9367	5.4564	4.8256	4.4683	4.2361	4.0721	3.9498	3.8549	3.7790	3.7168	3.6209	3.5217	3.4185	3.3654	3.311	3.255	3.198	3.140	3.080

11	6.7241	5.2559	4.6300	4.2751	4.0440	3.8807	3.7586	3.6638	3.5879	3.5257	3.4296	3.3299	3.2261	3.1725	3.118	3.061	3.004	2.944	2.883
12	6.5538	5.0959	4.4742	4.1212	3.8911	3.7283	3.6065	3.5118	3.4358	3.3736	3.2773	3.1772	3.0728	3.0187	2.963	2.906	2.848	2.787	2.725
13	6.4143	4.9653	4.3472	3.9959	3.7667	3.6043	3.4827	3.3880	3.3120	3.2497	3.1532	3.0527	2.9477	2.8932	2.837	2.780	2.720	2.659	2.595
14	6.2979	4.8567	4.2417	3.8919	3.6634	3.5014	3.3799	3.2853	3.2093	3.1469	3.0502	2.9493	2.8437	2.7888	2.732	2.674	2.614	2.552	2.487
15	6.1995	4.7650	4.1528	3.8043	3.5764	3.4147	3.2934	3.1987	3.1227	3.0602	2.9633	2.8621	2.7559	2.7006	2.644	2.585	2.524	2.461	2.395

16	6.1151	4.6867	4.0768	3.7294	3.5021	3.3406	3.2194	3.1248	3.0488	2.9862	2.8890	2.7875	2.6808	2.6252	2.568	2.509	2.447	2.383	2.316
17	6.0420	4.6189	4.0112	3.6648	3.4379	3.2767	3.1556	3.0610	2.9849	2.9222	2.8249	2.7230	2.6158	2.5598	2.502	2.442	2.380	2.315	2.247
18	5.9781	4.5597	3.9539	3.6083	3.3820	3.2209	3.0999	3.0053	2.9291	2.8664	2.7689	2.6667	2.5590	2.5027	2.445	2.384	2.321	2.256	2.187
19	5.9216	4.5075	3.9034	3.5587	3.3327	3.1718	3.0509	2.9563	2.8801	2.8172	2.7196	2.6171	2.5089	2.4523	2.394	2.333	2.270	2.203	2.133
20	5.8715	4.4613	3.8587	3.5147	3.2891	3.1283	3.0074	2.9128	2.8365	2.7737	2.6758	2.5731	2.4645	2.4076	2.349	2.287	2.223	2.156	2.085

21	5.8266	4.4199	3.8188	3.4754	3.2501	3.0895	2.9686	2.8740	2.7977	2.7348	2.6368	2.5338	2.4247	2.3675	2.308	2.246	2.182	2.114	2.042
22	5.7863	4.3828	3.7829	3.4401	3.2151	3.0546	2.9338	2.8392	2.7628	2.6998	2.6017	2.4984	2.3890	2.3315	2.272	2.210	2.145	2.076	2.003
23	5.7498	4.3492	3.7505	3.4083	3.1835	3.0232	2.9023	2.8077	2.7313	2.6682	2.5699	2.4665	2.3567	2.2989	2.239	2.176	2.111	2.041	1.968
24	5.7166	4.3187	3.7211	3.3794	3.1548	2.9946	2.8738	2.7791	2.7027	2.6396	2.5411	2.4374	2.3273	2.2693	2.209	2.146	2.080	2.010	1.935
25	5.6864	4.2909	3.6943	3.3530	3.1287	2.9685	2.8478	2.7531	2.6766	2.6135	2.5149	2.4110	2.3005	2.2422	2.182	2.118	2.052	1.981	1.906

26	5.6586	4.2655	3.6697	3.3289	3.1048	2.9447	2.8240	2.7293	2.6528	2.5896	2.4908	2.3867	2.2759	2.2174	2.157	2.093	2.026	1.954	1.878
27	5.6331	4.2421	3.6472	3.3067	3.0828	2.9228	2.8021	2.7074	2.6309	2.5676	2.4688	2.3644	2.2533	2.1946	2.133	2.069	2.002	1.930	1.853
28	5.6096	4.2205	3.6264	3.2863	3.0626	2.9027	2.7820	2.6872	2.6106	2.5473	2.4484	2.3438	2.2324	2.1735	2.112	2.048	1.980	1.907	1.829
29	5.5878	4.2006	3.6072	3.2674	3.0438	2.8840	2.7633	2.6686	2.5919	2.5286	2.4295	2.3248	2.2131	2.1540	2.092	2.028	1.959	1.886	1.807
30	5.5675	4.1821	3.5894	3.2499	3.0265	2.8667	2.7460	2.6513	2.5746	2.5112	2.4120	2.3072	2.1952	2.1359	2.074	2.009	1.940	1.866	1.787

40	5.4239	4.0510	3.4633	3.1261	2.9037	2.7444	2.6238	2.5289	2.4519	2.3882	2.2882	2.1819	2.0677	2.0069	1.943	1.875	1.803	1.724	1.637
60	5.2856	3.9253	3.3425	3.0077	2.7863	2.6274	2.5068	2.4117	2.3344	2.2702	2.1692	2.0613	1.9445	1.8817	1.815	1.744	1.667	1.581	1.482
120	5.1523	3.8046	3.2269	2.8943	2.6740	2.5154	2.3948	2.2994	2.2217	2.1570	2.0548	1.9450	1.8249	1.7597	1.690	1.614	1.530	1.433	1.310
inf	5.0239	3.6889	3.1161	2.7858	2.5665	2.4082	2.2875	2.1918	2.1136	2.0483	1.9447	1.8326	1.7085	1.6402	1.566	1.484	1.388	1.268	1.000

df2/df1 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 INF

1 4052.181 4999.500 5403.352 5624.583 5763.650 5858.986 5928.356 5981.070 6022.473 6055.847 6106.321 6157.285 6208.730 6234.631 6260.649 6286.782 6313.030 6339.391 6365.864

2 98.503 99.000 99.166 99.249 99.299 99.333 99.356 99.374 99.388 99.399 99.416 99.433 99.449 99.458 99.466 99.474 99.482 99.491 99.499

3 34.116 30.817 29.457 28.710 28.237 27.911 27.672 27.489 27.345 27.229 27.052 26.872 26.690 26.598 26.505 26.411 26.316 26.221 26.125

4 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 14.374 14.198 14.020 13.929 13.838 13.745 13.652 13.558 13.463

5 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.158 10.051 9.888 9.722 9.553 9.466 9.379 9.291 9.202 9.112 9.020

6 13.745 10.925 9.780 9.148 8.746 8.466 8.260 8.102 7.976 7.874 7.718 7.559 7.396 7.313 7.229 7.143 7.057 6.969 6.880

7 12.246 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.620 6.469 6.314 6.155 6.074 5.992 5.908 5.824 5.737 5.650

8 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 5.667 5.515 5.359 5.279 5.198 5.116 5.032 4.946 4.859

9 10.561 8.022 6.992 6.422 6.057 5.802 5.613 5.467 5.351 5.257 5.111 4.962 4.808 4.729 4.649 4.567 4.483 4.398 4.311

10 10.044 7.559 6.552 5.994 5.636 5.386 5.200 5.057 4.942 4.849 4.706 4.558 4.405 4.327 4.247 4.165 4.082 3.996 3.909

11 9.646 7.206 6.217 5.668 5.316 5.069 4.886 4.744 4.632 4.539 4.397 4.251 4.099 4.021 3.941 3.860 3.776 3.690 3.602

12 9.330 6.927 5.953 5.412 5.064 4.821 4.640 4.499 4.388 4.296 4.155 4.010 3.858 3.780 3.701 3.619 3.535 3.449 3.361

13 9.074 6.701 5.739 5.205 4.862 4.620 4.441 4.302 4.191 4.100 3.960 3.815 3.665 3.587 3.507 3.425 3.341 3.255 3.165

14 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 3.800 3.656 3.505 3.427 3.348 3.266 3.181 3.094 3.004

15 8.683 6.359 5.417 4.893 4.556 4.318 4.142 4.004 3.895 3.805 3.666 3.522 3.372 3.294 3.214 3.132 3.047 2.959 2.868

16 8.531 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 3.553 3.409 3.259 3.181 3.101 3.018 2.933 2.845 2.753

17 8.400 6.112 5.185 4.669 4.336 4.102 3.927 3.791 3.682 3.593 3.455 3.312 3.162 3.084 3.003 2.920 2.835 2.746 2.653

18 8.285 6.013 5.092 4.579 4.248 4.015 3.841 3.705 3.597 3.508 3.371 3.227 3.077 2.999 2.919 2.835 2.749 2.660 2.566

19 8.185 5.926 5.010 4.500 4.171 3.939 3.765 3.631 3.523 3.434 3.297 3.153 3.003 2.925 2.844 2.761 2.674 2.584 2.489

20 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 3.231 3.088 2.938 2.859 2.778 2.695 2.608 2.517 2.421

21 8.017 5.780 4.874 4.369 4.042 3.812 3.640 3.506 3.398 3.310 3.173 3.030 2.880 2.801 2.720 2.636 2.548 2.457 2.360

22 7.945 5.719 4.817 4.313 3.988 3.758 3.587 3.453 3.346 3.258 3.121 2.978 2.827 2.749 2.667 2.583 2.495 2.403 2.305

23 7.881 5.664 4.765 4.264 3.939 3.710 3.539 3.406 3.299 3.211 3.074 2.931 2.781 2.702 2.620 2.535 2.447 2.354 2.256

24 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3.256 3.168 3.032 2.889 2.738 2.659 2.577 2.492 2.403 2.310 2.211

25 7.770 5.568 4.675 4.177 3.855 3.627 3.457 3.324 3.217 3.129 2.993 2.850 2.699 2.620 2.538 2.453 2.364 2.270 2.169

26 7.721 5.526 4.637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 2.958 2.815 2.664 2.585 2.503 2.417 2.327 2.233 2.131

27 7.677 5.488 4.601 4.106 3.785 3.558 3.388 3.256 3.149 3.062 2.926 2.783 2.632 2.552 2.470 2.384 2.294 2.198 2.097

28 7.636 5.453 4.568 4.074 3.754 3.528 3.358 3.226 3.120 3.032 2.896 2.753 2.602 2.522 2.440 2.354 2.263 2.167 2.064

29 7.598 5.420 4.538 4.045 3.725 3.499 3.330 3.198 3.092 3.005 2.868 2.726 2.574 2.495 2.412 2.325 2.234 2.138 2.034

30 7.562 5.390 4.510 4.018 3.699 3.473 3.304 3.173 3.067 2.979 2.843 2.700 2.549 2.469 2.386 2.299 2.208 2.111 2.006

40 7.314 5.179 4.313 3.828 3.514 3.291 3.124 2.993 2.888 2.801 2.665 2.522 2.369 2.288 2.203 2.114 2.019 1.917 1.805

60 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.718 2.632 2.496 2.352 2.198 2.115 2.028 1.936 1.836 1.726 1.601

120 6.851 4.787 3.949 3.480 3.174 2.956 2.792 2.663 2.559 2.472 2.336 2.192 2.035 1.950 1.860 1.763 1.656 1.533 1.381

inf 6.635 4.605 3.782 3.319 3.017 2.802 2.639 2.511 2.407 2.321 2.185 2.039 1.878 1.791 1.696 1.592 1.473 1.325 1.000

To index

df2/df1	1	2	3	4	5	6	7	8	9	10	12	15	20	24	30	40	60	120	INF
1	4052.181	4999.500	5403.352	5624.583	5763.650	5858.986	5928.356	5981.070	6022.473	6055.847	6106.321	6157.285	6208.730	6234.631	6260.649	6286.782	6313.030	6339.391	6365.864
2	98.503	99.000	99.166	99.249	99.299	99.333	99.356	99.374	99.388	99.399	99.416	99.433	99.449	99.458	99.466	99.474	99.482	99.491	99.499
3	34.116	30.817	29.457	28.710	28.237	27.911	27.672	27.489	27.345	27.229	27.052	26.872	26.690	26.598	26.505	26.411	26.316	26.221	26.125
4	21.198	18.000	16.694	15.977	15.522	15.207	14.976	14.799	14.659	14.546	14.374	14.198	14.020	13.929	13.838	13.745	13.652	13.558	13.463
5	16.258	13.274	12.060	11.392	10.967	10.672	10.456	10.289	10.158	10.051	9.888	9.722	9.553	9.466	9.379	9.291	9.202	9.112	9.020

6	13.745	10.925	9.780	9.148	8.746	8.466	8.260	8.102	7.976	7.874	7.718	7.559	7.396	7.313	7.229	7.143	7.057	6.969	6.880
7	12.246	9.547	8.451	7.847	7.460	7.191	6.993	6.840	6.719	6.620	6.469	6.314	6.155	6.074	5.992	5.908	5.824	5.737	5.650
8	11.259	8.649	7.591	7.006	6.632	6.371	6.178	6.029	5.911	5.814	5.667	5.515	5.359	5.279	5.198	5.116	5.032	4.946	4.859
9	10.561	8.022	6.992	6.422	6.057	5.802	5.613	5.467	5.351	5.257	5.111	4.962	4.808	4.729	4.649	4.567	4.483	4.398	4.311
10	10.044	7.559	6.552	5.994	5.636	5.386	5.200	5.057	4.942	4.849	4.706	4.558	4.405	4.327	4.247	4.165	4.082	3.996	3.909

11	9.646	7.206	6.217	5.668	5.316	5.069	4.886	4.744	4.632	4.539	4.397	4.251	4.099	4.021	3.941	3.860	3.776	3.690	3.602
12	9.330	6.927	5.953	5.412	5.064	4.821	4.640	4.499	4.388	4.296	4.155	4.010	3.858	3.780	3.701	3.619	3.535	3.449	3.361
13	9.074	6.701	5.739	5.205	4.862	4.620	4.441	4.302	4.191	4.100	3.960	3.815	3.665	3.587	3.507	3.425	3.341	3.255	3.165
14	8.862	6.515	5.564	5.035	4.695	4.456	4.278	4.140	4.030	3.939	3.800	3.656	3.505	3.427	3.348	3.266	3.181	3.094	3.004
15	8.683	6.359	5.417	4.893	4.556	4.318	4.142	4.004	3.895	3.805	3.666	3.522	3.372	3.294	3.214	3.132	3.047	2.959	2.868

16	8.531	6.226	5.292	4.773	4.437	4.202	4.026	3.890	3.780	3.691	3.553	3.409	3.259	3.181	3.101	3.018	2.933	2.845	2.753
17	8.400	6.112	5.185	4.669	4.336	4.102	3.927	3.791	3.682	3.593	3.455	3.312	3.162	3.084	3.003	2.920	2.835	2.746	2.653
18	8.285	6.013	5.092	4.579	4.248	4.015	3.841	3.705	3.597	3.508	3.371	3.227	3.077	2.999	2.919	2.835	2.749	2.660	2.566
19	8.185	5.926	5.010	4.500	4.171	3.939	3.765	3.631	3.523	3.434	3.297	3.153	3.003	2.925	2.844	2.761	2.674	2.584	2.489
20	8.096	5.849	4.938	4.431	4.103	3.871	3.699	3.564	3.457	3.368	3.231	3.088	2.938	2.859	2.778	2.695	2.608	2.517	2.421

21	8.017	5.780	4.874	4.369	4.042	3.812	3.640	3.506	3.398	3.310	3.173	3.030	2.880	2.801	2.720	2.636	2.548	2.457	2.360
22	7.945	5.719	4.817	4.313	3.988	3.758	3.587	3.453	3.346	3.258	3.121	2.978	2.827	2.749	2.667	2.583	2.495	2.403	2.305
23	7.881	5.664	4.765	4.264	3.939	3.710	3.539	3.406	3.299	3.211	3.074	2.931	2.781	2.702	2.620	2.535	2.447	2.354	2.256
24	7.823	5.614	4.718	4.218	3.895	3.667	3.496	3.363	3.256	3.168	3.032	2.889	2.738	2.659	2.577	2.492	2.403	2.310	2.211
25	7.770	5.568	4.675	4.177	3.855	3.627	3.457	3.324	3.217	3.129	2.993	2.850	2.699	2.620	2.538	2.453	2.364	2.270	2.169

26	7.721	5.526	4.637	4.140	3.818	3.591	3.421	3.288	3.182	3.094	2.958	2.815	2.664	2.585	2.503	2.417	2.327	2.233	2.131
27	7.677	5.488	4.601	4.106	3.785	3.558	3.388	3.256	3.149	3.062	2.926	2.783	2.632	2.552	2.470	2.384	2.294	2.198	2.097
28	7.636	5.453	4.568	4.074	3.754	3.528	3.358	3.226	3.120	3.032	2.896	2.753	2.602	2.522	2.440	2.354	2.263	2.167	2.064
29	7.598	5.420	4.538	4.045	3.725	3.499	3.330	3.198	3.092	3.005	2.868	2.726	2.574	2.495	2.412	2.325	2.234	2.138	2.034
30	7.562	5.390	4.510	4.018	3.699	3.473	3.304	3.173	3.067	2.979	2.843	2.700	2.549	2.469	2.386	2.299	2.208	2.111	2.006

40	7.314	5.179	4.313	3.828	3.514	3.291	3.124	2.993	2.888	2.801	2.665	2.522	2.369	2.288	2.203	2.114	2.019	1.917	1.805
60	7.077	4.977	4.126	3.649	3.339	3.119	2.953	2.823	2.718	2.632	2.496	2.352	2.198	2.115	2.028	1.936	1.836	1.726	1.601
120	6.851	4.787	3.949	3.480	3.174	2.956	2.792	2.663	2.559	2.472	2.336	2.192	2.035	1.950	1.860	1.763	1.656	1.533	1.381
inf	6.635	4.605	3.782	3.319	3.017	2.802	2.639	2.511	2.407	2.321	2.185	2.039	1.878	1.791	1.696	1.592	1.473	1.325	1.000