47 / 68
Table 5 : PERCENTAGE POINTS OF THE
t
DISTRIBUTION
Table 5 gives the value of
t
α,ν
with the respective value of
α
and
ν
(degrees of freedom) where
t
α,ν
0
α
α
=
Γ[(
ν
+1)
/
2]
√
πν
Γ(
ν/
2)
∞
t
α,ν
1 +
x
2
ν
−
(
ν
+1)
/
2
dx
ν
0.0005 0.001 0.0025 0.003 0.005 0.01 0.025 0.03 0.05 0.1
1 636.6192 318.3088 127.3213 106.1002 63.6567 31.8205 12.7062 10.5789 6.3138 3.0777
2 31.5991 22.3271 14.0890 12.8518 9.9248 6.9646 4.3027 3.8964 2.9200 1.8856
3 12.9240 10.2145 7.4533 6.9944 5.8409 4.5407 3.1824 2.9505 2.3534 1.6377
4 8.6103 7.1732 5.5976 5.3214 4.6041 3.7469 2.7764 2.6008 2.1318 1.5332
5 6.8688 5.8934 4.7733 4.5703 4.0321 3.3649 2.5706 2.4216 2.0150 1.4759
6 5.9588 5.2076 4.3168 4.1517 3.7074 3.1427 2.4469 2.3133 1.9432 1.4398
7 5.4079 4.7853 4.0293 3.8868 3.4995 2.9980 2.3646 2.2409 1.8946 1.4149
8 5.0413 4.5008 3.8325 3.7049 3.3554 2.8965 2.3060 2.1892 1.8595 1.3968
9 4.7809 4.2968 3.6897 3.5726 3.2498 2.8214 2.2622 2.1504 1.8331 1.3830
10 4.5869 4.1437 3.5814 3.4721 3.1693 2.7638 2.2281 2.1202 1.8125 1.3722
11 4.4370 4.0247 3.4966 3.3933 3.1058 2.7181 2.2010 2.0961 1.7959 1.3634
12 4.3178 3.9296 3.4284 3.3298 3.0545 2.6810 2.1788 2.0764 1.7823 1.3562
13 4.2208 3.8520 3.3725 3.2777 3.0123 2.6503 2.1604 2.0600 1.7709 1.3502
14 4.1405 3.7874 3.3257 3.2341 2.9768 2.6245 2.1448 2.0462 1.7613 1.3450
15 4.0728 3.7328 3.2860 3.1970 2.9467 2.6025 2.1314 2.0343 1.7531 1.3406
16 4.0150 3.6862 3.2520 3.1653 2.9208 2.5835 2.1199 2.0240 1.7459 1.3368
17 3.9651 3.6458 3.2224 3.1376 2.8982 2.5669 2.1098 2.0150 1.7396 1.3334
18 3.9216 3.6105 3.1966 3.1135 2.8784 2.5524 2.1009 2.0071 1.7341 1.3304
19 3.8834 3.5794 3.1737 3.0921 2.8609 2.5395 2.0930 2.0000 1.7291 1.3277
20 3.8495 3.5518 3.1534 3.0731 2.8453 2.5280 2.0860 1.9937 1.7247 1.3253
21 3.8193 3.5272 3.1352 3.0560 2.8314 2.5176 2.0796 1.9880 1.7207 1.3232
22 3.7921 3.5050 3.1188 3.0407 2.8188 2.5083 2.0739 1.9829 1.7171 1.3212
23 3.7676 3.4850 3.1040 3.0268 2.8073 2.4999 2.0687 1.9782 1.7139 1.3195
24 3.7454 3.4668 3.0905 3.0142 2.7969 2.4922 2.0639 1.9740 1.7109 1.3178
25 3.7251 3.4502 3.0782 3.0026 2.7874 2.4851 2.0595 1.9701 1.7081 1.3163
26 3.7066 3.4350 3.0669 2.9921 2.7787 2.4786 2.0555 1.9665 1.7056 1.3150
27 3.6896 3.4210 3.0565 2.9823 2.7707 2.4727 2.0518 1.9632 1.7033 1.3137
28 3.6739 3.4082 3.0469 2.9733 2.7633 2.4671 2.0484 1.9601 1.7011 1.3125
29 3.6594 3.3962 3.0380 2.9650 2.7564 2.4620 2.0452 1.9573 1.6991 1.3114
30 3.6460 3.3852 3.0298 2.9573 2.7500 2.4573 2.0423 1.9546 1.6973 1.3104
35 3.5911 3.3400 2.9960 2.9256 2.7238 2.4377 2.0301 1.9438 1.6896 1.3062
40 3.5510 3.3069 2.9712 2.9022 2.7045 2.4233 2.0211 1.9357 1.6839 1.3031
45 3.5203 3.2815 2.9521 2.8843 2.6896 2.4121 2.0141 1.9294 1.6794 1.3006
50 3.4960 3.2614 2.9370 2.8701 2.6778 2.4033 2.0086 1.9244 1.6759 1.2987
55 3.4764 3.2451 2.9247 2.8586 2.6682 2.3961 2.0040 1.9204 1.6730 1.2971
60 3.4602 3.2317 2.9146 2.8490 2.6603 2.3901 2.0003 1.9170 1.6706 1.2958
65 3.4466 3.2204 2.9060 2.8410 2.6536 2.3851 1.9971 1.9142 1.6686 1.2947
70 3.4350 3.2108 2.8987 2.8341 2.6479 2.3808 1.9944 1.9118 1.6669 1.2938
75 3.4250 3.2025 2.8924 2.8282 2.6430 2.3771 1.9921 1.9097 1.6654 1.2929
80 3.4163 3.1953 2.8870 2.8231 2.6387 2.3739 1.9901 1.9078 1.6641 1.2922
85 3.4087 3.1889 2.8822 2.8185 2.6349 2.3710 1.9883 1.9062 1.6630 1.2916
90 3.4019 3.1833 2.8779 2.8145 2.6316 2.3685 1.9867 1.9048 1.6620 1.2910
100 3.3905 3.1737 2.8707 2.8077 2.6259 2.3642 1.9840 1.9024 1.6602 1.2901
150 3.3566 3.1455 2.8492 2.7875 2.6090 2.3515 1.9759 1.8951 1.6551 1.2872
300 3.3233 3.1176 2.8279 2.7675 2.5923 2.3388 1.9679 1.8879 1.6499 1.2844
37
Table 5 : PERCENTAGE POINTS OF THE
t
DISTRIBUTION
Table 5 gives the value of
t
α,ν
with the respective value of
α
and
ν
(degrees of freedom) where
t
α,ν
0
α
α
=
Γ[(
ν
+1)
/
2]
√
πν
Γ(
ν/
2)
∞
t
α,ν
1 +
x
2
ν
−
(
ν
+1)
/
2
dx
ν
0.0005 0 001 0.0 25 0 003 0.005 0.01 0.0 5 0.03 0.05 0.1
1 636.6192 318.3088 127.3213 106.1002 63.6567 31.8205 12.7062 10.5789 6 1 8 3 07
2 31.5991 22.3271 14.0890 12.8518 9 92 8 6 9646 4 3027 3 8964 9200 8856
3 12.9240 10.2145 7 45
6 9944 5 8409 4 5407 3 1824 9505 3534 6377
4 8 6103 7 1732 5 5976 5 32 4 4 6 41 7 69 77 4 6008 2 1318 5 32
5 6 8688 5 8934
773
4 5703 4 0321 3 3649 570
4216 2 0150 75
6
9588 5 2 76 4 3168 4 1517
707 3 1427 44 9 3133 9432 439
7 5 407
7853 4 02 3
8868
49 5 9980 3 46 24 9
946 4149
8 5 0413
5008
8325
7049
3554 8965 3060
89
59
968
9
7809
2968
6897
5726
249
8214
622 1504 8331 8 0
0
5869 4 1437
581
4721
1693 7638 22 1 1202 81 5 72
1
4370 4 0247
4966
3933
1058 7181 2010
961
95
634
2
3178
9296
4 84
3298 3 0545
810
78
7 4
82
562
3
220
85 0
3725
27 7 3 0123
503
60
600
709 5 2
4
1405
7 74
3257
2341
76
624
448
462
613 450
5 4 0728
732
860
9 0
9467 6025
314
343
531 406
6 4 0150
862
2520
653
9208
835
19
240
459
68
7
9651
6458
2224
1376
982
669 1098
15
3 6 334
18
9216
6105
966
11 5
784
524 1009 2 0071
3 1 304
19
834
794
737
921
609
395
930 2 000
91
77
0
8495
518
534
731
453
2 0
860
937
247
53
1
8193
5272
352
5 0
314 5176
796
8 0
207 232
2
921
5050
1188
407
8188 5083
7
829
71 212
3
676
850
1040
268
80 3
999
687
82
139
95
4
454
668
905 3 0142
969
922
639
740
109
78
5
7251
502
782 3 00 6
874
851
95
701
81
63
6
7066
350
6
921
787
786
555
65
56
50
7
8 6
4210
565
823
707
7 7
518
632 7033
37
28
739
408
469
73
633
6 1
84
601 7011
25
29
6594
962 3 038
6 0
564
620
452
573
9 1 114
3
646
852 3 0298
9573 2 500
57
423
546
973 104
3
911
3400
960
9256
7238
377
30
438
8 6
62
4
551
3069
712
9022
7045
2
211
357
83 3031
4
5203
815
521
843
896 412
1 1
9
94 3006
5
960
6 4
370
701
778 4033
86
244
59
87
5
7 4
451
247
586
682
96 2 0040
204
730
71
6
602 3.2317 2.9146 2.8490 2.6603 2.3901 2.0003 1.9170 1.6706 1.2958
6
466
204
9060
410
5 6
85
7
142
86
47
7
350
2108
987
34
479
808
44
11
69
38
7
250
2025
9 4
2 2
430
71
921
97
54
29
8
163
95
8 0
231
87
739
901
7
41
22
85
4087
889
822
185
34
710
83
62
30
16
90
4019
833
779
814
316
68
867 9048
620 910
1
905
737
707
80 7
6259
642
840 9024
602 901
150 3.3566 3.1455 2.8492 2.7875 2.6090 2.3515 1.9759 1.8951 1.6551 1.2872
300 3.3233 3.1176 2.8279 2.7675 2.5923 2.3388 1.9679 1.8879 1.6499 1.2844
37