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Table 1: Standard Normal (z) Distribution Table

Area between 0 and z:

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 0.0190 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 0.2969 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 0.3513 0.3554 0.3577 0.3529 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

3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993

3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995

3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997

3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998

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Table 1: Standard Normal (z) Distribution Table

Table 2: Values of t for Selected Probabilities

One Tail

Table 4a: F-distribution Table: Upper 10% Probability under F-distribution curve

Table 4b: F-distribution Table: Upper 5% Probability under F-distribution curve

Table 4d: F-distribution Table: Upper 1% Probability under F-distribution curve

Table 5: Critical values of Hartley’s Fmax Test: (^) 2 min 2 max max s s F  Upper 5% points (α=0.05)α=0.05) c (numerator degrees of freedom) v 2 3 4 5 6 7 8 9 10 11 12 2 39.00 87.50 142.00 202.00 266.00 333.00 403.00 475.00 550.00 626.00 704. 3 15.40 27.80 39.20 50.70 62.00 72.90 83.50 93.90 104.00 114.00 124. 4 9.60 15.50 20.60 25.20 29.50 33.60 37.50 41.10 44.60 48.00 51. 5 7.15 10.80 13.70 16.30 18.70 20.80 22.90 24.70 26.50 28.20 29. 6 5.82 8.38 10.40 12.10 13.70 15.00 16.30 17.50 18.60 19.70 20. 7 4.99 6.94 8.44 9.70 10.80 11.80 12.70 13.50 14.30 15.10 15. 8 4.43 6.00 7.18 8.12 9.03 9.78 10.50 11.10 11.70 12.20 12. 9 4.03 5.34 6.31 7.11 7.80 8.41 8.95 9.45 9.91 10.30 10. 10 3.72 4.85 5.67 6.34 6.92 7.42 7.87 8.28 8.66 9.01 9. 12 3.28 4.16 4.79 5.30 5.72 6.09 6.42 6.72 7.00 7.25 7. 15 2.86 3.54 4.01 4.37 4.68 4.95 5.19 5.40 5.59 5.77 5. 20 2.46 2.95 3.29 3.54 3.76 3.94 4.10 4.24 4.37 4.49 4. 30 2.07 2.40 2.61 2.78 2.91 3.02 3.12 3.21 3.29 3.36 3. 60 1.67 1.85 1.96 2.04 2.11 2.17 2.22 2.26 2.30 2.33 2. ∞ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1. Upper 1% points (α=0.01)α=0.01) c (numerator degrees of freedom) v 2 3 4 5 6 7 8 9 10 11 12 2 199.00 448.00 729.00 1036.00 1362.00 1705.00 2063.00 2432.00 2813.00 3204.00 3605. 3 47.50 85.00 120.00 151.00 184.00 216.00 249.00 281.00 310.00 337.00 361. 4 23.20 37.00 49.00 59.00 69.00 79.00 89.00 97.00 106.00 113.00 120. 5 14.90 22.00 28.00 33.00 38.00 42.00 46.00 50.00 54.00 57.00 60. 6 11.10 15.50 19.10 22.00 25.00 27.00 30.00 32.00 34.00 36.00 37. 7 8.89 12.10 14.50 16.50 18.40 20.00 22.00 23.00 24.00 26.00 27. 8 7.50 9.90 11.70 13.20 14.50 15.80 16.90 17.90 18.90 19.80 21. 9 6.54 8.50 9.90 11.10 12.10 13.10 13.90 14.70 15.30 16.00 16. 10 5.85 7.40 8.60 9.60 10.40 11.10 11.80 12.40 12.90 13.40 13. 12 4.91 6.10 6.90 7.60 8.20 8.70 9.10 9.50 9.90 10.20 10. 15 4.07 4.90 5.05 6.00 6.40 6.70 7.10 7.30 7.50 7.80 8. 20 3.32 3.80 4.30 4.60 4.90 5.10 5.30 5.50 5.60 5.80 5. 30 2.63 3.00 3.30 3.40 3.60 3.70 3.80 3.90 4.00 4.10 4. 60 1.96 2.20 2.30 2.40 2.40 2.50 2.50 2.60 2.60 2.70 2. ∞ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0. Area between 0 and z:
0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0190 0.0239 0.0279 0.0319 0.
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.
0.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.
0.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.
0.8 0.2881 0.2910 0.2939 0.2969 0.2995 0.3023 0.3051 0.3078 0.3106 0.
0.9 0.3159 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.
1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3513 0.3554 0.3577 0.3529 0.
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.
1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.
2.4 0.4918 0.4920 0.4922 0.4925 0.4927 0.4929 0.4931 0.4932 0.4934 0.
2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.
2.9 0.4981 0.4982 0.4982 0.4983 0.4984 0.4984 0.4985 0.4985 0.4986 0.
3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.
3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.
3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.
3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.
3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.
Level 0.5 0.7 0.8 0.9 0.95 0.98 0. Conf. - 0. Two Tails - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 1 1.0000 1.9629 3.0777 6.3138 12.7062 31.8205 63. - 2 0.8165 1.3862 1.8856 2.9200 4.3027 6.9646 9. - 3 0.7649 1.2498 1.6377 2.3534 3.1825 4.5407 5. - 4 0.7407 1.1896 1.5332 2.1318 2.7765 3.7470 4. - 5 0.7267 1.1558 1.4759 2.0150 2.5706 3.3649 4. - 6 0.7176 1.1342 1.4398 1.9432 2.4469 3.1427 3. - 7 0.7111 1.1192 1.4149 1.8946 2.3646 2.9980 3. - 8 0.7064 1.1081 1.3968 1.8595 2.3060 2.8965 3. - 9 0.7027 1.0997 1.3830 1.8331 2.2622 2.8214 3.
- 10 0.6998 1.0931 1.3722 1.8125 2.2281 2.7638 3.
- 11 0.6974 1.0877 1.3634 1.7959 2.2010 2.7181 3.
- 12 0.6955 1.0832 1.3562 1.7823 2.1788 2.6810 3.
- 13 0.6938 1.0795 1.3502 1.7709 2.1604 2.6503 3.
- 14 0.6924 1.0763 1.3450 1.7613 2.1448 2.6245 2.
- 15 0.6912 10.735 1.3406 1.7531 2.1315 2.6025 2.
- 16 0.6901 1.0711 1.3368 1.7459 2.1199 2.5835 2.
- 17 0.6892 1.0690 1.3334 1.7396 2.1098 2.5669 2.
- 18 0.6884 1.0672 1.3304 1.7341 2.1009 2.5524 2.
- 19 0.6876 1.0655 1.3277 1.7291 2.0930 2.5395 2.
- 20 0.6870 1.0640 1.3253 1.7247 2.0860 2.5280 2.
- 21 0.6864 1.0627 1.3232 1.7207 2.0796 2.5177 2.
- 22 0.6858 1.0614 1.3212 1.7171 2.0739 2.5083 2.
- 23 0.6853 1.0603 1.3195 1.7139 2.0687 2.4999 2.
- 24 0.6849 1.0593 1.3178 1.7109 2.0639 2.4922 2.
- 25 0.6844 1.0584 1.3163 1.7081 2.0595 2.4851 2.
- 26 0.6840 1.0575 1.3150 1.7056 2.0555 2.4786 2.
- 27 0.6837 1.0567 1.3137 1.7033 2.0518 2.4727 2.
- 28 0.6834 1.0560 1.3125 1.7011 2.0484 2.4671 2.
- 29 0.6830 1.0533 1.3114 1.6991 2.0452 2.4620 2.
- 30 0.6828 1.0547 1.3104 1.6973 2.0423 2.4573 2.
- 40 0.6807 1.0500 1.3031 1.6839 2.0211 2.4233 2.
- 50 0.6794 1.0473 1.2987 1.6759 2.0086 2.4033 2.
  - ∞ 0.6745 1.0364 1.2816 1.6449 1.9600 2.3264 2. … … -  Table 3: Values of
    -  2   Ex 1: If df = 5, then 10% (0.10) of the distribution is to the right of the critical value of
  - 0.995 0.99 0.975 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.025 0.01 0. between 0.025 and 0.05 (2.5% and 5%)
- 1 0.0000 0.0002 0.0010 0.0039 0.0158 0.1015 0.4549 1.3233 2.7055 3.8415 5.0239 6.6349 7. df (Critical) Values of Chi-Squared
- 2 0.0100 0.0201 0.0506 0.1026 0.2107 0.5754 1.3863 2.7726 4.6052 5.9915 7.3778 9.2103 10.
- 3 0.0717 0.1148 0.2158 0.3519 0.5844 1.2125 2.3660 4.1083 6.2514 7.8147 9.3484 11.3449 12.
- 4 0.2070 0.2971 0.4844 0.7107 1.0636 1.9226 3.3567 5.3853 7.7794 9.4877 11.1433 13.2767 14.
- 5 0.4117 0.5543 0.8312 1.1455 1.6103 2.6746 4.3515 6.6257 9.2364 11.0705 12.8325 15.0863 16.
- 6 0.6757 0.8721 1.2373 1.6354 2.2041 3.4546 5.3481 7.8408 10.6446 12.5916 14.4494 16.8119 18.
- 7 0.9893 1.2390 1.6899 2.1674 2.8331 4.2549 6.3458 9.0372 12.0170 14.0671 16.0128 18.4753 20.
- 8 1.3444 1.6465 2.1797 2.7326 3.4895 5.0706 7.3441 10.2189 13.3616 15.5073 17.5346 20.0902 21.
- 9 1.7349 2.0879 2.7004 3.3251 4.1682 5.8988 8.3428 11.3888 14.6837 16.9190 19.0228 21.6660 23.
10 2.1559 2.5582 3.2470 3.9403 4.8652 6.7372 9.3418 12.5489 15.9872 18.3070 20.4832 23.2093 25.
11 2.6032 3.0535 3.8158 4.5748 5.5778 7.5841 10.3410 13.7007 17.2750 19.6751 21.9201 24.7250 26.
12 3.0738 3.5706 4.4038 5.2260 6.3038 8.4384 11.3403 14.8454 18.5494 21.0261 23.3367 26.2170 28.
13 3.5650 4.1069 5.0088 5.8919 7.0415 9.2991 12.3398 15.9839 19.8119 22.3620 24.7356 27.6883 29.
14 4.0747 4.6604 5.6287 6.5706 7.7895 10.1653 13.3393 17.1169 21.0641 23.6848 26.1190 29.1412 31.
15 4.6009 5.2294 6.2621 7.2609 8.5468 11.0365 14.3389 18.2451 22.3071 24.9958 27.4884 30.5779 32.
16 5.1422 5.8122 6.9077 7.9617 9.3122 11.9122 15.3385 19.3689 23.5418 26.2962 28.8454 31.9999 34.
17 5.6972 6.4078 7.5642 8.6718 10.0852 12.7919 16.3382 20.4887 24.7690 27.5871 30.1910 33.4087 35.
18 6.2648 7.0149 8.2308 9.3905 10.8649 13.6753 17.3379 21.6049 25.9894 28.8693 31.5264 34.8053 37.
19 6.8440 7.6327 8.9065 10.1170 11.6509 14.5620 18.3377 22.7178 27.2036 30.1435 32.8523 36.1909 38.
20 7.4338 8.2604 9.5908 10.8508 12.4426 15.4518 19.3374 23.8277 28.4120 31.4104 34.1696 37.5662 39.
21 8.0337 8.8972 10.2829 11.5913 13.2396 16.3444 20.3372 24.9348 29.6151 32.6706 35.4789 38.9322 41.
22 8.6427 9.5425 10.9823 12.3380 14.0415 17.2396 21.3370 26.0393 30.8133 33.9244 36.7807 40.2894 42.
23 9.2604 10.1957 11.6886 13.0905 14.8480 18.1373 22.3369 27.1413 32.0069 35.1725 38.0756 41.6384 44.
24 9.8862 10.8564 12.4012 13.8484 15.6587 19.0373 23.3367 28.2412 33.1962 36.4150 39.3641 42.9798 45.
25 10.5197 11.5240 13.1197 14.6114 16.4734 19.9393 24.3366 29.3389 34.3816 37.6525 40.6465 44.3141 46.
26 11.1602 12.1982 13.8439 15.3792 17.2919 20.8434 25.3365 30.4346 35.5632 38.8851 41.9232 45.6417 48.
27 11.8076 12.8785 14.5734 16.1514 18.1139 21.7494 26.3363 31.5284 36.7412 40.1133 43.1945 46.9629 49.
28 12.4613 13.5647 15.3079 16.9279 18.9392 22.6572 27.3362 32.6205 37.9159 41.3371 44.4608 48.2782 50.
29 13.1212 14.2565 16.0471 17.7084 19.7677 23.5666 28.3361 33.7109 39.0875 42.5570 45.7223 49.5879 52.
30 13.7867 14.9535 16.7908 18.4927 20.5992 24.4776 29.3360 34.7997 40.2560 43.7730 46.9792 50.8922 53. - 1 39.863 49.500 53.593 55.833 57.240 58.204 58.906 59.439 59.858 60.195 60.705 61.220 61.740 62.002 62.265 62.529 62.794 63.061 63. df2 df1=1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 8.526 9.000 9.162 9.243 9.293 9.326 9.349 9.367 9.381 9.392 9.408 9.425 9.441 9.450 9.458 9.466 9.475 9.483 9. - 3 5.538 5.462 5.391 5.343 5.309 5.285 5.266 5.252 5.240 5.230 5.216 5.200 5.184 5.176 5.168 5.160 5.151 5.143 5. - 4 4.545 4.325 4.191 4.107 4.051 4.010 3.979 3.955 3.936 3.920 3.896 3.870 3.844 3.831 3.817 3.804 3.790 3.775 3. - 5 4.060 3.780 3.619 3.520 3.453 3.405 3.368 3.339 3.316 3.297 3.268 3.238 3.207 3.191 3.174 3.157 3.140 3.123 3. - 6 3.776 3.463 3.289 3.181 3.108 3.055 3.014 2.983 2.958 2.937 2.905 2.871 2.836 2.818 2.800 2.781 2.762 2.742 2. - 7 3.589 3.257 3.074 2.961 2.883 2.827 2.785 2.752 2.725 2.703 2.668 2.632 2.595 2.575 2.555 2.535 2.514 2.493 2. - 8 3.458 3.113 2.924 2.806 2.726 2.668 2.624 2.589 2.561 2.538 2.502 2.464 2.425 2.404 2.383 2.361 2.339 2.316 2. - 9 3.360 3.006 2.813 2.693 2.611 2.551 2.505 2.469 2.440 2.416 2.379 2.340 2.298 2.277 2.255 2.232 2.208 2.184 2.
- 10 3.285 2.924 2.728 2.605 2.522 2.461 2.414 2.377 2.347 2.323 2.284 2.244 2.201 2.178 2.155 2.132 2.107 2.082 2.
- 11 3.225 2.860 2.660 2.536 2.451 2.389 2.342 2.304 2.274 2.248 2.209 2.167 2.123 2.100 2.076 2.052 2.026 2.000 1.
- 12 3.177 2.807 2.606 2.480 2.394 2.331 2.283 2.245 2.214 2.188 2.147 2.105 2.060 2.036 2.011 1.986 1.960 1.932 1.
- 13 3.136 2.763 2.560 2.434 2.347 2.283 2.234 2.195 2.164 2.138 2.097 2.053 2.007 1.983 1.958 1.931 1.904 1.876 1.
- 14 3.102 2.726 2.522 2.395 2.307 2.243 2.193 2.154 2.122 2.095 2.054 2.010 1.962 1.938 1.912 1.885 1.857 1.828 1.
- 15 3.073 2.695 2.490 2.361 2.273 2.208 2.158 2.119 2.086 2.059 2.017 1.972 1.924 1.899 1.873 1.845 1.817 1.787 1.
- 16 3.048 2.668 2.462 2.333 2.244 2.178 2.128 2.088 2.055 2.028 1.985 1.940 1.891 1.866 1.839 1.811 1.782 1.751 1.
- 17 3.026 2.645 2.437 2.308 2.218 2.152 2.102 2.061 2.028 2.001 1.958 1.912 1.862 1.836 1.809 1.781 1.751 1.719 1.
- 18 3.007 2.624 2.416 2.286 2.196 2.130 2.079 2.038 2.005 1.977 1.933 1.887 1.837 1.810 1.783 1.754 1.723 1.691 1.
- 19 2.990 2.606 2.397 2.266 2.176 2.109 2.058 2.017 1.984 1.956 1.912 1.865 1.814 1.787 1.759 1.730 1.699 1.666 1.
- 20 2.975 2.589 2.380 2.249 2.158 2.091 2.040 1.999 1.965 1.937 1.892 1.845 1.794 1.767 1.738 1.708 1.677 1.643 1.
- 21 2.961 2.575 2.365 2.233 2.142 2.075 2.023 1.982 1.948 1.920 1.875 1.827 1.776 1.748 1.719 1.689 1.657 1.623 1.
- 22 2.949 2.561 2.351 2.219 2.128 2.061 2.008 1.967 1.933 1.904 1.859 1.811 1.759 1.731 1.702 1.671 1.639 1.604 1.
- 23 2.937 2.549 2.339 2.207 2.115 2.047 1.995 1.953 1.919 1.890 1.845 1.796 1.744 1.716 1.686 1.655 1.622 1.587 1.
- 24 2.927 2.538 2.327 2.195 2.103 2.035 1.983 1.941 1.906 1.877 1.832 1.783 1.730 1.702 1.672 1.641 1.607 1.571 1.
- 25 2.918 2.528 2.317 2.184 2.092 2.024 1.971 1.929 1.895 1.866 1.820 1.771 1.718 1.689 1.659 1.627 1.593 1.557 1.
- 26 2.909 2.519 2.307 2.174 2.082 2.014 1.961 1.919 1.884 1.855 1.809 1.760 1.706 1.677 1.647 1.615 1.581 1.544 1.
- 27 2.901 2.511 2.299 2.165 2.073 2.005 1.952 1.909 1.874 1.845 1.799 1.749 1.695 1.666 1.636 1.603 1.569 1.531 1.
- 28 2.894 2.503 2.291 2.157 2.064 1.996 1.943 1.900 1.865 1.836 1.790 1.740 1.685 1.656 1.625 1.593 1.558 1.520 1.
- 29 2.887 2.495 2.283 2.149 2.057 1.988 1.935 1.892 1.857 1.827 1.781 1.731 1.676 1.647 1.616 1.583 1.547 1.509 1.
- 30 2.881 2.489 2.276 2.142 2.049 1.980 1.927 1.884 1.849 1.819 1.773 1.722 1.667 1.638 1.606 1.573 1.538 1.499 1.
- 40 2.835 2.440 2.226 2.091 1.997 1.927 1.873 1.829 1.793 1.763 1.715 1.662 1.605 1.574 1.541 1.506 1.467 1.425 1.
- 60 2.791 2.393 2.177 2.041 1.946 1.875 1.819 1.775 1.738 1.707 1.657 1.603 1.543 1.511 1.476 1.437 1.395 1.348 1.
120 2.748 2.347 2.130 1.992 1.896 1.824 1.767 1.722 1.684 1.652 1.601 1.545 1.482 1.447 1.409 1.368 1.320 1.265 1. - ∞ 2.706 2.303 2.084 1.945 1.847 1.774 1.717 1.670 1.632 1.599 1.546 1.487 1.421 1.383 1.342 1.295 1.240 1.169 1. - 1 161.448 199.500 215.707 224.583 230.162 233.986 236.768 238.883 240.543 241.882 243.906 245.950 248.013 249.052 250.095 251.143 252.196 253.253 254. df2 df1=1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 18.513 19.000 19.164 19.247 19.296 19.330 19.353 19.371 19.385 19.396 19.413 19.429 19.446 19.454 19.462 19.471 19.479 19.487 19. - 3 10.128 9.552 9.277 9.117 9.014 8.941 8.887 8.845 8.812 8.786 8.745 8.703 8.660 8.639 8.617 8.594 8.572 8.549 8. - 4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.912 5.858 5.803 5.774 5.746 5.717 5.688 5.658 5. - 5 6.608 5.786 5.410 5.192 5.050 4.950 4.876 4.818 4.773 4.735 4.678 4.619 4.558 4.527 4.496 4.464 4.431 4.399 4. - 6 5.987 5.143 4.757 4.534 4.387 4.284 4.207 4.147 4.099 4.060 4.000 3.938 3.874 3.842 3.808 3.774 3.740 3.705 3. - 7 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 3.575 3.511 3.445 3.411 3.376 3.340 3.304 3.267 3. - 8 5.318 4.459 4.066 3.838 3.688 3.581 3.501 3.438 3.388 3.347 3.284 3.218 3.150 3.115 3.079 3.043 3.005 2.967 2. - 9 5.117 4.257 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.073 3.006 2.937 2.901 2.864 2.826 2.787 2.748 2.
- 10 4.965 4.103 3.708 3.478 3.326 3.217 3.136 3.072 3.020 2.978 2.913 2.845 2.774 2.737 2.700 2.661 2.621 2.580 2.
- 11 4.844 3.982 3.587 3.357 3.204 3.095 3.012 2.948 2.896 2.854 2.788 2.719 2.646 2.609 2.571 2.531 2.490 2.448 2.
- 12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.687 2.617 2.544 2.506 2.466 2.426 2.384 2.341 2.
- 13 4.667 3.806 3.411 3.179 3.025 2.915 2.832 2.767 2.714 2.671 2.604 2.533 2.459 2.420 2.380 2.339 2.297 2.252 2.
- 14 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 2.534 2.463 2.388 2.349 2.308 2.266 2.223 2.178 2.
- 15 4.543 3.682 3.287 3.056 2.901 2.791 2.707 2.641 2.588 2.544 2.475 2.403 2.328 2.288 2.247 2.204 2.160 2.114 2.
- 16 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 2.425 2.352 2.276 2.235 2.194 2.151 2.106 2.059 2.
- 17 4.451 3.592 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 2.381 2.308 2.230 2.190 2.148 2.104 2.058 2.011 1.
- 18 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 2.342 2.269 2.191 2.150 2.107 2.063 2.017 1.968 1.
- 19 4.381 3.522 3.127 2.895 2.740 2.628 2.544 2.477 2.423 2.378 2.308 2.234 2.156 2.114 2.071 2.026 1.980 1.930 1.
- 20 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.278 2.203 2.124 2.083 2.039 1.994 1.946 1.896 1.
- 21 4.325 3.467 3.073 2.840 2.685 2.573 2.488 2.421 2.366 2.321 2.250 2.176 2.096 2.054 2.010 1.965 1.917 1.866 1.
- 22 4.301 3.443 3.049 2.817 2.661 2.549 2.464 2.397 2.342 2.297 2.226 2.151 2.071 2.028 1.984 1.938 1.889 1.838 1.
- 23 4.279 3.422 3.028 2.796 2.640 2.528 2.442 2.375 2.320 2.275 2.204 2.128 2.048 2.005 1.961 1.914 1.865 1.813 1.
- 24 4.260 3.403 3.009 2.776 2.621 2.508 2.423 2.355 2.300 2.255 2.183 2.108 2.027 1.984 1.939 1.892 1.842 1.790 1.
- 25 4.242 3.385 2.991 2.759 2.603 2.490 2.405 2.337 2.282 2.237 2.165 2.089 2.008 1.964 1.919 1.872 1.822 1.768 1.
- 26 4.225 3.369 2.975 2.743 2.587 2.474 2.388 2.321 2.266 2.220 2.148 2.072 1.990 1.946 1.901 1.853 1.803 1.749 1.
- 27 4.210 3.354 2.960 2.728 2.572 2.459 2.373 2.305 2.250 2.204 2.132 2.056 1.974 1.930 1.884 1.836 1.785 1.731 1.
- 28 4.196 3.340 2.947 2.714 2.558 2.445 2.359 2.291 2.236 2.190 2.118 2.041 1.959 1.915 1.869 1.820 1.769 1.714 1.
- 29 4.183 3.328 2.934 2.701 2.545 2.432 2.346 2.278 2.223 2.177 2.105 2.028 1.945 1.901 1.854 1.806 1.754 1.698 1.
- 30 4.171 3.316 2.922 2.690 2.534 2.421 2.334 2.266 2.211 2.165 2.092 2.015 1.932 1.887 1.841 1.792 1.740 1.684 1.
- 40 4.085 3.232 2.839 2.606 2.450 2.336 2.249 2.180 2.124 2.077 2.004 1.925 1.839 1.793 1.744 1.693 1.637 1.577 1.
- 60 4.001 3.150 2.758 2.525 2.368 2.254 2.167 2.097 2.040 1.993 1.917 1.836 1.748 1.700 1.649 1.594 1.534 1.467 1.
120 3.920 3.072 2.680 2.447 2.290 2.175 2.087 2.016 1.959 1.911 1.834 1.751 1.659 1.608 1.554 1.495 1.429 1.352 1.
- ∞ 3.842 2.996 2.605 2.372 2.214 2.099 2.010 1.938 1.880 1.831 1.752 1.666 1.571 1.517 1.459 1.394 1.318 1.221 1.
  - 1 647.789 799.500 864.163 899.583 921.848 937.111 948.217 956.656 963.285 968.627 976.708 984.867 993.103 997.249 1001.414 1005.598 1009.800 1014.020 1018. df2 df1=1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞
  - 2 38.506 39.000 39.166 39.248 39.298 39.332 39.355 39.373 39.387 39.398 39.415 39.431 39.448 39.456 39.465 39.473 39.481 39.490 39.
  - 3 17.443 16.044 15.439 15.101 14.885 14.735 14.624 14.540 14.473 14.419 14.337 14.253 14.167 14.124 14.081 14.037 13.992 13.947 13.
  - 4 12.218 10.649 9.979 9.605 9.365 9.197 9.074 8.980 8.905 8.844 8.751 8.657 8.560 8.511 8.461 8.411 8.360 8.309 8.
  - 5 10.007 8.434 7.764 7.388 7.146 6.978 6.853 6.757 6.681 6.619 6.525 6.428 6.329 6.278 6.227 6.175 6.123 6.069 6.
  - 6 8.813 7.260 6.599 6.227 5.988 5.820 5.696 5.600 5.523 5.461 5.366 5.269 5.168 5.117 5.065 5.012 4.959 4.904 4.
  - 7 8.073 6.542 5.890 5.523 5.285 5.119 4.995 4.899 4.823 4.761 4.666 4.568 4.467 4.415 4.362 4.309 4.254 4.199 4.
  - 8 7.571 6.060 5.416 5.053 4.817 4.652 4.529 4.433 4.357 4.295 4.200 4.101 4.000 3.947 3.894 3.840 3.784 3.728 3.
  - 9 7.209 5.715 5.078 4.718 4.484 4.320 4.197 4.102 4.026 3.964 3.868 3.769 3.667 3.614 3.560 3.505 3.449 3.392 3.
- 10 6.937 5.456 4.826 4.468 4.236 4.072 3.950 3.855 3.779 3.717 3.621 3.522 3.419 3.365 3.311 3.255 3.198 3.140 3.
- 11 6.724 5.256 4.630 4.275 4.044 3.881 3.759 3.664 3.588 3.526 3.430 3.330 3.226 3.173 3.118 3.061 3.004 2.944 2.
- 12 6.554 5.096 4.474 4.121 3.891 3.728 3.607 3.512 3.436 3.374 3.277 3.177 3.073 3.019 2.963 2.906 2.848 2.787 2.
- 13 6.414 4.965 4.347 3.996 3.767 3.604 3.483 3.388 3.312 3.250 3.153 3.053 2.948 2.893 2.837 2.780 2.720 2.659 2.
- 14 6.298 4.857 4.242 3.892 3.663 3.501 3.380 3.285 3.209 3.147 3.050 2.949 2.844 2.789 2.732 2.674 2.614 2.552 2.
- 15 6.200 4.765 4.153 3.804 3.576 3.415 3.293 3.199 3.123 3.060 2.963 2.862 2.756 2.701 2.644 2.585 2.524 2.461 2.
- 16 6.115 4.687 4.077 3.729 3.502 3.341 3.219 3.125 3.049 2.986 2.889 2.788 2.681 2.625 2.568 2.509 2.447 2.383 2.
- 17 6.042 4.619 4.011 3.665 3.438 3.277 3.156 3.061 2.985 2.922 2.825 2.723 2.616 2.560 2.502 2.442 2.380 2.315 2.
- 18 5.978 4.560 3.954 3.608 3.382 3.221 3.100 3.005 2.929 2.866 2.769 2.667 2.559 2.503 2.445 2.384 2.321 2.256 2.
- 19 5.922 4.508 3.903 3.559 3.333 3.172 3.051 2.956 2.880 2.817 2.720 2.617 2.509 2.452 2.394 2.333 2.270 2.203 2.
- 20 5.872 4.461 3.859 3.515 3.289 3.128 3.007 2.913 2.837 2.774 2.676 2.573 2.465 2.408 2.349 2.287 2.223 2.156 2.
- 21 5.827 4.420 3.819 3.475 3.250 3.090 2.969 2.874 2.798 2.735 2.637 2.534 2.425 2.368 2.308 2.246 2.182 2.114 2.
- 22 5.786 4.383 3.783 3.440 3.215 3.055 2.934 2.839 2.763 2.700 2.602 2.498 2.389 2.332 2.272 2.210 2.145 2.076 2.
- 23 5.750 4.349 3.751 3.408 3.184 3.023 2.902 2.808 2.731 2.668 2.570 2.467 2.357 2.299 2.239 2.176 2.111 2.041 1.
- 24 5.717 4.319 3.721 3.379 3.155 2.995 2.874 2.779 2.703 2.640 2.541 2.437 2.327 2.269 2.209 2.146 2.080 2.010 1.
- 25 5.686 4.291 3.694 3.353 3.129 2.969 2.848 2.753 2.677 2.614 2.515 2.411 2.301 2.242 2.182 2.118 2.052 1.981 1.
- 26 5.659 4.266 3.670 3.329 3.105 2.945 2.824 2.729 2.653 2.590 2.491 2.387 2.276 2.217 2.157 2.093 2.026 1.954 1.
- 27 5.633 4.242 3.647 3.307 3.083 2.923 2.802 2.707 2.631 2.568 2.469 2.364 2.253 2.195 2.133 2.069 2.002 1.930 1.
- 28 5.610 4.221 3.626 3.286 3.063 2.903 2.782 2.687 2.611 2.547 2.448 2.344 2.232 2.174 2.112 2.048 1.980 1.907 1.
- 29 5.588 4.201 3.607 3.267 3.044 2.884 2.763 2.669 2.592 2.529 2.430 2.325 2.213 2.154 2.092 2.028 1.959 1.886 1.
- 30 5.568 4.182 3.589 3.250 3.027 2.867 2.746 2.651 2.575 2.511 2.412 2.307 2.195 2.136 2.074 2.009 1.940 1.866 1.
- 40 5.424 4.051 3.463 3.126 2.904 2.744 2.624 2.529 2.452 2.388 2.288 2.182 2.068 2.007 1.943 1.875 1.803 1.724 1.
- 60 5.286 3.925 3.343 3.008 2.786 2.627 2.507 2.412 2.334 2.270 2.169 2.061 1.945 1.882 1.815 1.744 1.667 1.581 1.
120 5.152 3.805 3.227 2.894 2.674 2.515 2.395 2.299 2.222 2.157 2.055 1.945 1.825 1.760 1.690 1.614 1.530 1.433 1.
- ∞ 5.024 3.689 3.116 2.786 2.567 2.408 2.288 2.192 2.114 2.048 1.945 1.833 1.709 1.640 1.566 1.484 1.388 1.268 1.
  - 1 4052.18 4999.50 5403.35 5624.58 5763.65 5858.99 5928.36 5981.07 6022.47 6055.85 6106.32 6157.29 6208.73 6234.63 6260.65 6286.78 6313.03 6339.39 6365. df2 df1=1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞
  - 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.
  - 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.
  - 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.
  - 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.
  - 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.
  - 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.
  - 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.
  - 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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.
- ∞ 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.
df k = - 1 8.929 13.437 16.358 18.488 20.150 21.504 22.642 23.621 24.477 25.237 25.918 26.536 27. - 2 4.129 5.733 6.772 7.538 8.139 8.633 9.049 9.409 9.725 10.006 10.259 10.488 10. - 3 3.328 4.467 5.199 5.738 6.162 6.511 6.806 7.062 7.287 7.487 7.667 7.831 7. - 4 3.015 3.976 4.586 5.035 5.388 5.679 5.926 6.139 6.327 6.494 6.645 6.783 6. - 5 2.850 3.717 4.264 4.664 4.979 5.238 5.458 5.648 5.816 5.965 6.100 6.223 6. - 6 2.748 3.558 4.065 4.435 4.726 4.966 5.168 5.344 5.499 5.637 5.762 5.875 5. - 7 2.679 3.451 3.931 4.280 4.555 4.780 4.971 5.137 5.283 5.413 5.530 5.637 5. - 8 2.630 3.374 3.834 4.169 4.431 4.646 4.829 4.987 5.126 5.250 5.362 5.464 5. - 9 2.592 3.316 3.761 4.084 4.337 4.545 4.721 4.873 5.007 5.126 5.234 5.333 5. - 10 2.563 3.270 3.704 4.018 4.264 4.465 4.636 4.783 4.913 5.029 5.134 5.229 5. - 11 2.540 3.234 3.658 3.965 4.205 4.401 4.567 4.711 4.838 4.951 5.053 5.145 5. - 12 2.521 3.204 3.621 3.921 4.156 4.349 4.511 4.652 4.776 4.886 4.986 5.076 5. - 13 2.504 3.179 3.589 3.885 4.116 4.304 4.464 4.602 4.724 4.832 4.930 5.019 5. - 14 2.491 3.158 3.563 3.854 4.081 4.267 4.424 4.560 4.679 4.786 4.882 4.969 5. - 15 2.479 3.140 3.540 3.828 4.052 4.235 4.390 4.524 4.641 4.746 4.841 4.927 5. - 16 2.469 3.124 3.520 3.804 4.026 4.207 4.360 4.492 4.608 4.712 4.805 4.890 4. - 17 2.460 3.110 3.503 3.784 4.003 4.182 4.334 4.464 4.579 4.681 4.774 4.857 4. - 18 2.452 3.098 3.487 3.766 3.984 4.161 4.310 4.440 4.553 4.654 4.746 4.829 4. - 19 2.445 3.087 3.474 3.751 3.966 4.142 4.290 4.418 4.530 4.630 4.721 4.803 4. - 20 2.439 3.077 3.462 3.736 3.950 4.124 4.271 4.398 4.510 4.609 4.699 4.780 4. - 21 2.433 3.069 3.451 3.724 3.936 4.109 4.255 4.380 4.491 4.590 4.678 4.759 4. - 22 2.428 3.061 3.441 3.712 3.923 4.095 4.239 4.364 4.474 4.572 4.660 4.740 4. - 23 2.424 3.054 3.432 3.701 3.911 4.082 4.226 4.350 4.459 4.556 4.644 4.723 4. - 24 2.420 3.047 3.423 3.692 3.900 4.070 4.213 4.336 4.445 4.541 4.628 4.707 4. - 25 2.416 3.041 3.416 3.683 3.890 4.059 4.201 4.324 4.432 4.528 4.614 4.693 4. - 26 2.412 3.036 3.409 3.675 3.881 4.049 4.191 4.313 4.420 4.515 4.601 4.680 4. - 27 2.409 3.030 3.402 3.667 3.873 4.040 4.181 4.302 4.409 4.504 4.590 4.667 4. - 28 2.406 3.026 3.396 3.660 3.865 4.032 4.172 4.293 4.399 4.493 4.579 4.656 4. - 29 2.403 3.021 3.391 3.654 3.858 4.024 4.163 4.284 4.389 4.484 4.568 4.645 4. - 30 2.400 3.017 3.386 3.648 3.851 4.016 4.155 4.275 4.381 4.474 4.559 4.635 4. - 31 2.398 3.013 3.381 3.642 3.845 4.009 4.148 4.268 4.372 4.466 4.550 4.626 4. - 32 2.396 3.010 3.376 3.637 3.839 4.003 4.141 4.260 4.365 4.458 4.541 4.617 4. - 33 2.393 3.006 3.372 3.632 3.833 3.997 4.135 4.253 4.357 4.450 4.533 4.609 4. - 34 2.391 3.003 3.368 3.627 3.828 3.991 4.129 4.247 4.351 4.443 4.526 4.602 4. - 35 2.389 3.000 3.364 3.623 3.823 3.986 4.123 4.241 4.344 4.436 4.519 4.594 4. - 36 2.388 2.998 3.361 3.619 3.819 3.981 4.117 4.235 4.338 4.430 4.512 4.588 4. - 37 2.386 2.995 3.357 3.615 3.814 3.976 4.112 4.230 4.332 4.424 4.506 4.581 4. - 38 2.384 2.992 3.354 3.611 3.810 3.972 4.107 4.224 4.327 4.418 4.500 4.575 4. - 39 2.383 2.990 3.351 3.608 3.806 3.967 4.103 4.220 4.322 4.413 4.495 4.569 4. - 40 2.381 2.988 3.348 3.605 3.802 3.963 4.099 4.215 4.317 4.408 4.490 4.564 4. - 48 2.372 2.973 3.330 3.583 3.778 3.937 4.070 4.185 4.285 4.375 4.455 4.528 4. - 60 2.363 2.959 3.312 3.562 3.755 3.911 4.042 4.155 4.254 4.342 4.421 4.493 4. - 80 2.353 2.945 3.294 3.541 3.731 3.885 4.014 4.125 4.223 4.309 4.387 4.457 4.
- 120 2.344 2.930 3.276 3.520 3.707 3.859 3.986 4.096 4.191 4.276 4.353 4.422 4.
- 240 2.335 2.916 3.258 3.499 3.684 3.834 3.959 4.066 4.160 4.244 4.319 4.386 4. - ∞ 2.326 2.902 3.240 3.478 3.661 3.808 3.931 4.037 4.129 4.211 4.285 4.351 4.
df k = Table 6b: The Studentized range critical value: q(0.05, (k, df)) - 1 17.969 26.976 32.819 37.082 40.408 43.119 45.397 47.357 49.071 50.592 51.957 53.194 54. - 2 6.085 8.331 9.798 10.881 11.734 12.435 13.027 13.539 13.988 14.389 14.749 15.076 15. - 3 4.501 5.910 6.825 7.502 8.037 8.478 8.852 9.177 9.462 9.717 9.946 10.155 10. - 4 3.926 5.040 5.757 6.287 6.706 7.053 7.347 7.602 7.826 8.027 8.208 8.373 8. - 5 3.635 4.602 5.218 5.673 6.033 6.330 6.582 6.801 6.995 7.167 7.323 7.466 7. - 6 3.460 4.339 4.896 5.305 5.628 5.895 6.122 6.319 6.493 6.649 6.789 6.917 7. - 7 3.344 4.165 4.681 5.060 5.359 5.606 5.815 5.997 6.158 6.302 6.431 6.550 6. - 8 3.261 4.041 4.529 4.886 5.167 5.399 5.596 5.767 5.918 6.053 6.175 6.287 6. - 9 3.199 3.948 4.415 4.755 5.024 5.244 5.432 5.595 5.738 5.867 5.983 6.089 6. - 10 3.151 3.877 4.327 4.654 4.912 5.124 5.304 5.460 5.598 5.722 5.833 5.935 6. - 11 3.113 3.820 4.256 4.574 4.823 5.028 5.202 5.353 5.486 5.605 5.713 5.811 5. - 12 3.081 3.773 4.199 4.508 4.750 4.950 5.119 5.265 5.395 5.510 5.615 5.710 5. - 13 3.055 3.734 4.151 4.453 4.690 4.884 5.049 5.192 5.318 5.431 5.533 5.625 5. - 14 3.033 3.701 4.111 4.407 4.639 4.829 4.990 5.130 5.253 5.364 5.463 5.554 5. - 15 3.014 3.673 4.076 4.367 4.595 4.782 4.940 5.077 5.198 5.306 5.403 5.492 5. - 16 2.998 3.649 4.046 4.333 4.557 4.741 4.896 5.031 5.150 5.256 5.352 5.439 5. - 17 2.984 3.628 4.020 4.303 4.524 4.705 4.858 4.991 5.108 5.212 5.306 5.392 5. - 18 2.971 3.609 3.997 4.276 4.494 4.673 4.824 4.955 5.071 5.173 5.266 5.351 5. - 19 2.960 3.593 3.977 4.253 4.468 4.645 4.794 4.924 5.037 5.139 5.231 5.314 5. - 20 2.950 3.578 3.958 4.232 4.445 4.620 4.768 4.895 5.008 5.108 5.199 5.282 5. - 21 2.941 3.565 3.942 4.213 4.424 4.597 4.743 4.870 4.981 5.081 5.170 5.252 5. - 22 2.933 3.553 3.927 4.196 4.405 4.577 4.722 4.847 4.957 5.056 5.144 5.225 5. - 23 2.926 3.542 3.914 4.180 4.388 4.558 4.702 4.826 4.935 5.033 5.121 5.201 5. - 24 2.919 3.532 3.901 4.166 4.373 4.541 4.684 4.807 4.915 5.012 5.099 5.179 5. - 25 2.913 3.523 3.890 4.153 4.358 4.526 4.667 4.789 4.897 4.993 5.079 5.158 5. - 26 2.907 3.514 3.880 4.141 4.345 4.511 4.652 4.773 4.880 4.975 5.061 5.139 5. - 27 2.902 3.506 3.870 4.130 4.333 4.498 4.638 4.758 4.864 4.959 5.044 5.122 5. - 28 2.897 3.499 3.861 4.120 4.322 4.486 4.625 4.745 4.850 4.944 5.029 5.106 5. - 29 2.892 3.493 3.853 4.111 4.311 4.475 4.613 4.732 4.837 4.930 5.014 5.091 5. - 30 2.888 3.486 3.845 4.102 4.301 4.464 4.601 4.720 4.824 4.917 5.001 5.077 5. - 31 2.884 3.481 3.838 4.094 4.292 4.454 4.591 4.709 4.812 4.905 4.988 5.064 5. - 32 2.881 3.475 3.832 4.086 4.284 4.445 4.581 4.698 4.802 4.894 4.976 5.052 5. - 33 2.877 3.470 3.825 4.079 4.276 4.436 4.572 4.689 4.791 4.883 4.965 5.040 5. - 34 2.874 3.465 3.820 4.072 4.268 4.428 4.563 4.680 4.782 4.873 4.955 5.030 5. - 35 2.871 3.461 3.814 4.066 4.261 4.421 4.555 4.671 4.773 4.863 4.945 5.020 5. - 36 2.868 3.457 3.809 4.060 4.255 4.414 4.547 4.663 4.764 4.855 4.936 5.010 5. - 37 2.865 3.453 3.804 4.054 4.249 4.407 4.540 4.655 4.756 4.846 4.927 5.001 5. - 38 2.863 3.449 3.799 4.049 4.243 4.400 4.533 4.648 4.749 4.838 4.919 4.993 5. - 39 2.861 3.445 3.795 4.044 4.237 4.394 4.527 4.641 4.741 4.831 4.911 4.985 5. - 40 2.858 3.442 3.791 4.039 4.232 4.388 4.521 4.634 4.735 4.824 4.904 4.977 5. - 48 2.843 3.420 3.764 4.008 4.197 4.351 4.481 4.592 4.690 4.777 4.856 4.927 4. - 60 2.829 3.399 3.737 3.977 4.163 4.314 4.441 4.550 4.646 4.732 4.808 4.878 4. - 80 2.814 3.377 3.711 3.947 4.129 4.277 4.402 4.509 4.603 4.686 4.761 4.829 4.
- 120 2.800 3.356 3.685 3.917 4.096 4.241 4.363 4.468 4.560 4.641 4.714 4.781 4.
- 240 2.786 3.335 3.659 3.887 4.063 4.205 4.324 4.427 4.517 4.596 4.668 4.733 4.
  - ∞ 2.772 3.314 3.633 3.858 4.030 4.170 4.286 4.387 4.474 4.552 4.622 4.685 4.
df k = Table 6c: The Studentized range critical value: q(0.01, (k, df)) - 1 90.024 35.041 164.258 185.575 202.210 215.769 227.166 236.966 245.542 253.151 259.979 266.165 271. - 2 14.036 19.019 22.294 24.717 26.629 28.201 29.530 30.679 31.689 32.589 33.398 34.134 34. - 3 8.260 10.619 12.170 13.324 14.241 14.998 15.641 16.199 16.691 17.130 17.526 17.887 18. - 4 6.511 8.120 9.173 9.958 10.583 11.101 11.542 11.925 12.264 12.567 12.840 13.090 13. - 5 5.702 6.976 7.804 8.421 8.913 9.321 9.669 9.971 10.239 10.479 10.696 10.894 11. - 6 5.243 6.331 7.033 7.556 7.972 8.318 8.612 8.869 9.097 9.300 9.485 9.653 9. - 7 4.949 5.919 6.542 7.005 7.373 7.678 7.939 8.166 8.367 8.548 8.711 8.860 8. - 8 4.745 5.635 6.204 6.625 6.959 7.237 7.474 7.680 7.863 8.027 8.176 8.311 8. - 9 4.596 5.428 5.957 6.347 6.657 6.915 7.134 7.325 7.494 7.646 7.784 7.910 8.
- 10 4.482 5.270 5.769 6.136 6.428 6.669 6.875 7.054 7.213 7.356 7.485 7.603 7.
- 11 4.392 5.146 5.621 5.970 6.247 6.476 6.671 6.841 6.992 7.127 7.250 7.362 7.
- 12 4.320 5.046 5.502 5.836 6.101 6.320 6.507 6.670 6.814 6.943 7.060 7.166 7.
- 13 4.260 4.964 5.404 5.726 5.981 6.192 6.372 6.528 6.666 6.791 6.903 7.006 7.
- 14 4.210 4.895 5.322 5.634 5.881 6.085 6.258 6.409 6.543 6.663 6.772 6.871 6.
- 15 4.167 4.836 5.252 5.556 5.796 5.994 6.162 6.309 6.438 6.555 6.660 6.756 6.
- 16 4.131 4.786 5.192 5.489 5.722 5.915 6.079 6.222 6.348 6.461 6.564 6.658 6.
- 17 4.099 4.742 5.140 5.430 5.659 5.847 6.007 6.147 6.270 6.380 6.480 6.572 6.
- 18 4.071 4.703 5.094 5.379 5.603 5.787 5.944 6.081 6.201 6.309 6.407 6.496 6.
- 19 4.046 4.669 5.054 5.334 5.553 5.735 5.889 6.022 6.141 6.246 6.342 6.430 6.
- 20 4.024 4.639 5.018 5.293 5.510 5.688 5.839 5.970 6.086 6.190 6.285 6.370 6.
- 21 4.004 4.612 4.986 5.257 5.470 5.646 5.794 5.924 6.038 6.140 6.233 6.317 6.
- 22 3.986 4.588 4.957 5.225 5.435 5.608 5.754 5.882 5.994 6.095 6.186 6.269 6.
- 23 3.970 4.566 4.931 5.195 5.403 5.573 5.718 5.844 5.955 6.054 6.144 6.226 6.
- 24 3.955 4.546 4.907 5.168 5.373 5.542 5.685 5.809 5.919 6.017 6.105 6.186 6.
- 25 3.942 4.527 4.885 5.144 5.347 5.513 5.655 5.778 5.886 5.983 6.070 6.150 6.
- 26 3.930 4.510 4.865 5.121 5.322 5.487 5.627 5.749 5.856 5.951 6.038 6.117 6.
- 27 3.918 4.495 4.847 5.101 5.300 5.463 5.602 5.722 5.828 5.923 6.008 6.087 6.
- 28 3.908 4.481 4.830 5.082 5.279 5.441 5.578 5.697 5.802 5.896 5.981 6.058 6.
- 29 3.898 4.467 4.814 5.064 5.260 5.420 5.556 5.674 5.778 5.871 5.955 6.032 6.
- 30 3.889 4.455 4.799 5.048 5.242 5.401 5.536 5.653 5.756 5.848 5.932 6.008 6.
- 31 3.881 4.443 4.786 5.032 5.225 5.383 5.517 5.633 5.736 5.827 5.910 5.985 6.
- 32 3.873 4.433 4.773 5.018 5.210 5.367 5.500 5.615 5.716 5.807 5.889 5.964 6.
- 33 3.865 4.423 4.761 5.005 5.195 5.351 5.483 5.598 5.698 5.789 5.870 5.944 6.
- 34 3.859 4.413 4.750 4.992 5.181 5.336 5.468 5.581 5.682 5.771 5.852 5.926 5.
- 35 3.852 4.404 4.739 4.980 5.169 5.323 5.453 5.566 5.666 5.755 5.835 5.908 5.
- 36 3.846 4.396 4.729 4.969 5.156 5.310 5.439 5.552 5.651 5.739 5.819 5.892 5.
- 37 3.840 4.388 4.720 4.959 5.145 5.298 5.427 5.538 5.637 5.725 5.804 5.876 5.
- 38 3.835 4.381 4.711 4.949 5.134 5.286 5.414 5.526 5.623 5.711 5.790 5.862 5.
- 39 3.830 4.374 4.703 4.940 5.124 5.275 5.403 5.513 5.611 5.698 5.776 5.848 5.
- 40 3.825 4.367 4.695 4.931 5.114 5.265 5.392 5.502 5.599 5.685 5.764 5.835 5.
- 48 3.793 4.324 4.644 4.874 5.052 5.198 5.322 5.428 5.522 5.606 5.681 5.750 5.
- 60 3.762 4.282 4.594 4.818 4.991 5.133 5.253 5.356 5.447 5.528 5.601 5.667 5.
- 80 3.732 4.241 4.545 4.763 4.931 5.069 5.185 5.284 5.372 5.451 5.521 5.585 5.
120 3.702 4.200 4.497 4.709 4.872 5.005 5.118 5.214 5.299 5.375 5.443 5.505 5.
240 3.672 4.160 4.450 4.655 4.814 4.943 5.052 5.145 5.227 5.300 5.366 5.426 5.
- ∞ 3.643 4.120 4.403 4.603 4.757 4.882 4.987 5.078 5.157 5.227 5.290 5.348 5.

Standard Normal Distribution Table - Statistics II |, Study notes of Statistics

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Table 1: Standard Normal (z) Distribution Table

Table 2: Values of t for Selected Probabilities

One Tail