From Wikibooks, open books for an open world
| Table of Critical Values, tα,ν, in a Student T-Distribution with ν degrees of freedom and a confidence limit p where α=1–p.
|
|
|
| ν |
Confidence Limits (top) and α (bottom) for a One-Tailed Test.
|
| 60% |
75% |
80% |
85% |
90% |
95% |
97.5% |
98% |
99% |
99.5% |
99.75% |
99.9% |
99.95%
|
| 0.4 |
0.25 |
0.2 |
0.15 |
0.1 |
0.05 |
0.025 |
0.02 |
0.01 |
0.005 |
0.0025 |
0.001 |
0.0005
|
| 1
|
0.32492 |
1.00000 |
1.37638 |
1.96261 |
3.07768 |
6.31375 |
12.70620 |
15.89454 |
31.82052 |
63.65674 |
127.32134 |
318.30884 |
636.61925
|
| 2
|
0.28868 |
0.81650 |
1.06066 |
1.38621 |
1.88562 |
2.91999 |
4.30265 |
4.84873 |
6.96456 |
9.92484 |
14.08905 |
22.32712 |
31.59905
|
| 3
|
0.27667 |
0.76489 |
0.97847 |
1.24978 |
1.63774 |
2.35336 |
3.18245 |
3.48191 |
4.54070 |
5.84091 |
7.45332 |
10.21453 |
12.92398
|
| 4
|
0.27072 |
0.74070 |
0.94096 |
1.18957 |
1.53321 |
2.13185 |
2.77645 |
2.99853 |
3.74695 |
4.60409 |
5.59757 |
7.17318 |
8.61030
|
| 5
|
0.26718 |
0.72669 |
0.91954 |
1.15577 |
1.47588 |
2.01505 |
2.57058 |
2.75651 |
3.36493 |
4.03214 |
4.77334 |
5.89343 |
6.86883
|
| 6
|
0.26483 |
0.71756 |
0.90570 |
1.13416 |
1.43976 |
1.94318 |
2.44691 |
2.61224 |
3.14267 |
3.70743 |
4.31683 |
5.20763 |
5.95882
|
| 7
|
0.26317 |
0.71114 |
0.89603 |
1.11916 |
1.41492 |
1.89458 |
2.36462 |
2.51675 |
2.99795 |
3.49948 |
4.02934 |
4.78529 |
5.40788
|
| 8
|
0.26192 |
0.70639 |
0.88889 |
1.10815 |
1.39682 |
1.85955 |
2.30600 |
2.44898 |
2.89646 |
3.35539 |
3.83252 |
4.50079 |
5.04131
|
| 9
|
0.26096 |
0.70272 |
0.88340 |
1.09972 |
1.38303 |
1.83311 |
2.26216 |
2.39844 |
2.82144 |
3.24984 |
3.68966 |
4.29681 |
4.78091
|
| 10
|
0.26018 |
0.69981 |
0.87906 |
1.09306 |
1.37218 |
1.81246 |
2.22814 |
2.35931 |
2.76377 |
3.16927 |
3.58141 |
4.14370 |
4.58689
|
| 11
|
0.25956 |
0.69745 |
0.87553 |
1.08767 |
1.36343 |
1.79588 |
2.20099 |
2.32814 |
2.71808 |
3.10581 |
3.49661 |
4.02470 |
4.43698
|
| 12
|
0.25903 |
0.69548 |
0.87261 |
1.08321 |
1.35622 |
1.78229 |
2.17881 |
2.30272 |
2.68100 |
3.05454 |
3.42844 |
3.92963 |
4.31779
|
| 13
|
0.25859 |
0.69383 |
0.87015 |
1.07947 |
1.35017 |
1.77093 |
2.16037 |
2.28160 |
2.65031 |
3.01228 |
3.37247 |
3.85198 |
4.22083
|
| 14
|
0.25821 |
0.69242 |
0.86805 |
1.07628 |
1.34503 |
1.76131 |
2.14479 |
2.26378 |
2.62449 |
2.97684 |
3.32570 |
3.78739 |
4.14045
|
| 15
|
0.25789 |
0.69120 |
0.86624 |
1.07353 |
1.34061 |
1.75305 |
2.13145 |
2.24854 |
2.60248 |
2.94671 |
3.28604 |
3.73283 |
4.07277
|
| 16
|
0.25760 |
0.69013 |
0.86467 |
1.07114 |
1.33676 |
1.74588 |
2.11991 |
2.23536 |
2.58349 |
2.92078 |
3.25199 |
3.68615 |
4.01500
|
| 17
|
0.25735 |
0.68920 |
0.86328 |
1.06903 |
1.33338 |
1.73961 |
2.10982 |
2.22385 |
2.56693 |
2.89823 |
3.22245 |
3.64577 |
3.96513
|
| 18
|
0.25712 |
0.68836 |
0.86205 |
1.06717 |
1.33039 |
1.73406 |
2.10092 |
2.21370 |
2.55238 |
2.87844 |
3.19657 |
3.61048 |
3.92165
|
| 19
|
0.25692 |
0.68762 |
0.86095 |
1.06551 |
1.32773 |
1.72913 |
2.09302 |
2.20470 |
2.53948 |
2.86093 |
3.17372 |
3.57940 |
3.88341
|
| 20
|
0.25674 |
0.68695 |
0.85996 |
1.06402 |
1.32534 |
1.72472 |
2.08596 |
2.19666 |
2.52798 |
2.84534 |
3.15340 |
3.55181 |
3.84952
|
| 21
|
0.25658 |
0.68635 |
0.85907 |
1.06267 |
1.32319 |
1.72074 |
2.07961 |
2.18943 |
2.51765 |
2.83136 |
3.13521 |
3.52715 |
3.81928
|
| 22
|
0.25643 |
0.68581 |
0.85827 |
1.06145 |
1.32124 |
1.71714 |
2.07387 |
2.18289 |
2.50832 |
2.81876 |
3.11882 |
3.50499 |
3.79213
|
| 23
|
0.25630 |
0.68531 |
0.85753 |
1.06034 |
1.31946 |
1.71387 |
2.06866 |
2.17696 |
2.49987 |
2.80734 |
3.10400 |
3.48496 |
3.76763
|
| 24
|
0.25617 |
0.68485 |
0.85686 |
1.05932 |
1.31784 |
1.71088 |
2.06390 |
2.17154 |
2.49216 |
2.79694 |
3.09051 |
3.46678 |
3.74540
|
| 25
|
0.25606 |
0.68443 |
0.85624 |
1.05838 |
1.31635 |
1.70814 |
2.05954 |
2.16659 |
2.48511 |
2.78744 |
3.07820 |
3.45019 |
3.72514
|
| 26
|
0.25595 |
0.68404 |
0.85567 |
1.05752 |
1.31497 |
1.70562 |
2.05553 |
2.16203 |
2.47863 |
2.77871 |
3.06691 |
3.43500 |
3.70661
|
| 27
|
0.25586 |
0.68368 |
0.85514 |
1.05673 |
1.31370 |
1.70329 |
2.05183 |
2.15782 |
2.47266 |
2.77068 |
3.05652 |
3.42103 |
3.68959
|
| 28
|
0.25577 |
0.68335 |
0.85465 |
1.05599 |
1.31253 |
1.70113 |
2.04841 |
2.15393 |
2.46714 |
2.76326 |
3.04693 |
3.40816 |
3.67391
|
| 29
|
0.25568 |
0.68304 |
0.85419 |
1.05530 |
1.31143 |
1.69913 |
2.04523 |
2.15033 |
2.46202 |
2.75639 |
3.03805 |
3.39624 |
3.65941
|
| 30
|
0.25561 |
0.68276 |
0.85377 |
1.05466 |
1.31042 |
1.69726 |
2.04227 |
2.14697 |
2.45726 |
2.75000 |
3.02980 |
3.38518 |
3.64596
|
| 40
|
0.25504 |
0.68067 |
0.85070 |
1.05005 |
1.30308 |
1.68385 |
2.02108 |
2.12291 |
2.42326 |
2.70446 |
2.97117 |
3.30688 |
3.55097
|
| 50
|
0.25470 |
0.67943 |
0.84887 |
1.04729 |
1.29871 |
1.67591 |
2.00856 |
2.10872 |
2.40327 |
2.67779 |
2.93696 |
3.26141 |
3.49601
|
| 60
|
0.25447 |
0.67860 |
0.84765 |
1.04547 |
1.29582 |
1.67065 |
2.00030 |
2.09936 |
2.39012 |
2.66028 |
2.91455 |
3.23171 |
3.46020
|
| 70
|
0.25431 |
0.67801 |
0.84679 |
1.04417 |
1.29376 |
1.66691 |
1.99444 |
2.09273 |
2.38081 |
2.64790 |
2.89873 |
3.21079 |
3.43501
|
| 80
|
0.25419 |
0.67757 |
0.84614 |
1.04320 |
1.29222 |
1.66412 |
1.99006 |
2.08778 |
2.37387 |
2.63869 |
2.88697 |
3.19526 |
3.41634
|
| 90
|
0.25410 |
0.67723 |
0.84563 |
1.04244 |
1.29103 |
1.66196 |
1.98667 |
2.08394 |
2.36850 |
2.63157 |
2.87788 |
3.18327 |
3.40194
|
| 100
|
0.25402 |
0.67695 |
0.84523 |
1.04184 |
1.29007 |
1.66023 |
1.98397 |
2.08088 |
2.36422 |
2.62589 |
2.87065 |
3.17374 |
3.39049
|
| 500
|
0.25348 |
0.67498 |
0.84234 |
1.03751 |
1.28325 |
1.64791 |
1.96472 |
2.05912 |
2.33383 |
2.58570 |
2.81955 |
3.10661 |
3.31009
|
| 1000
|
0.25341 |
0.67474 |
0.84198 |
1.03697 |
1.28240 |
1.64638 |
1.96234 |
2.05643 |
2.33008 |
2.58075 |
2.81328 |
3.09840 |
3.30028
|
| ∞
|
0.25335 |
0.67449 |
0.84162 |
1.03643 |
1.28155 |
1.64485 |
1.95996 |
2.05375 |
2.32635 |
2.57583 |
2.80703 |
3.09023 |
3.29053
|
Explanatory Notes
- For a Two-Tailed Test, use the α here that corresponds to half the two-tailed α.
- For example if a two-tailed confidence limit of 90% is desired (α=0.1), use a one-tailed α from this table of 0.05
- In the limit ν=∞, this distribution is equivalent to a normal distribution X~N(0,1)
|
