t distribution
critical values
How to Use the Table:
- Find your degrees of freedom in the df column and
use that row
to find the next smaller number.
- Read the probability in the top row. Since
your t will probably be
a little bit bigger than the value in the table, your P will be
smaller, eg., P < 0.01
- If your t is to the right of all numbers,
then P < 0.0005 (good!)
- Remember that P < 0.05 is the arbitrary value that
is generally accepted to be significant
(There must be less than a 5% possibility that the difference between
means is due to chance.)
| df |
.25 |
.20 |
.15 |
.10 |
.05 |
.025 |
.02 |
.01 |
.005 |
.0025 |
.001 |
.0005 |
| 1 |
1.000 |
1.376 |
1.963 |
3.078 |
6.314 |
12.71 |
15.89 |
31.82 |
63.66 |
127.3 |
318.3 |
636.6 |
| 2 |
.816 |
1.061 |
1.386 |
1.886 |
2.920 |
4.303 |
4.849 |
6.965 |
9.925 |
14.09 |
22.33 |
31.60 |
| 3 |
.765 |
.978 |
1.250 |
1.638 |
2.353 |
3.182 |
3.482 |
4.541 |
5.841 |
7.453 |
10.21 |
12.92 |
| 4 |
.741 |
.941 |
1.190 |
1.533 |
2.132 |
2.776 |
2.999 |
3.747 |
4.604 |
5.598 |
7.173 |
8.610 |
| 5 |
.727 |
.920 |
1.156 |
1.476 |
2.015 |
2.571 |
2.757 |
3.365 |
4.032 |
4.773 |
5.893 |
6.869 |
| 6 |
.718 |
.906 |
1.134 |
1.440 |
1.943 |
2.447 |
2.612 |
3.143 |
3.707 |
4.317 |
5.208 |
5.959 |
| 7 |
.711 |
.896 |
1.119 |
1.415 |
1.895 |
2.365 |
2.517 |
2.998 |
3.499 |
4.029 |
4.785 |
5.408 |
| 8 |
.706 |
.889 |
1.108 |
1.397 |
1.860 |
2.306 |
2.449 |
2.896 |
3.355 |
3.833 |
4.501 |
5.041 |
| 9 |
.703 |
.883 |
1.100 |
1.383 |
1.833 |
2.262 |
2.398 |
2.821 |
3.250 |
3.690 |
4.297 |
4.781 |
| 10 |
.700 |
.879 |
1.093 |
1.372 |
1.812 |
2.228 |
2.359 |
2.764 |
3.169 |
3.581 |
4.144 |
4.587 |
| 11 |
.697 |
.876 |
1.088 |
1.363 |
1.796 |
2.201 |
2.328 |
2.718 |
3.106 |
3.497 |
4.025 |
4.437 |
| 12 |
.695 |
.873 |
1.083 |
1.356 |
1.782 |
2.179 |
2.303 |
2.681 |
3.055 |
3.428 |
3.930 |
4.318 |
| 13 |
.694 |
.870 |
1.079 |
1.350 |
1.771 |
2.160 |
2.282 |
2.650 |
3.012 |
3.372 |
3.852 |
4.221 |
| 14 |
.692 |
.868 |
1.076 |
1.345 |
1.761 |
2.145 |
2.264 |
2.624 |
2.977 |
3.326 |
3.787 |
4.140 |
| 15 |
.691 |
.866 |
1.074 |
1.341 |
1.753 |
2.131 |
2.249 |
2.602 |
2.947 |
3.286 |
3.733 |
4.073 |
| 16 |
.690 |
.865 |
1.071 |
1.337 |
1.746 |
2.120 |
2.235 |
2.583 |
2.921 |
3.252 |
3.686 |
4.015 |
| 17 |
.689 |
.863 |
1.069 |
1.333 |
1.740 |
2.110 |
2.224 |
2.567 |
2.898 |
3.222 |
3.646 |
3.965 |
| 18 |
.688 |
.862 |
1.067 |
1.330 |
1.734 |
2.101 |
2.214 |
2.552 |
2.878 |
3.197 |
3.611 |
3.922 |
| 19 |
.688 |
.861 |
1.066 |
1.328 |
1.729 |
2.093 |
2.205 |
2.539 |
2.861 |
3.174 |
3.579 |
3.883 |
| 20 |
.687 |
.860 |
1.064 |
1.325 |
1.725 |
2.086 |
2.197 |
2.528 |
2.845 |
3.153 |
3.552 |
3.850 |
| 21 |
.663. |
.859 |
1.063 |
1.323 |
1.721 |
2.080 |
2.189 |
2.518 |
2.831 |
3.135 |
3.527 |
3.819 |
| 22 |
.686 |
.858 |
1.061 |
1.321 |
1.717 |
2.074 |
2.183 |
2.508 |
2.819 |
3.119 |
3.505 |
3.792 |
| 23 |
.685 |
.858 |
1.060 |
1.319 |
1.714 |
2.069 |
2.177 |
2.500 |
2.807 |
3.104 |
3.485 |
3.768 |
| 24 |
.685 |
.857 |
1.059 |
1.318 |
1.711 |
2.064 |
2.172 |
2.492 |
2.797 |
3.091 |
3.467 |
3.745 |
| 25 |
.684 |
.856 |
1.058 |
1.316 |
1.708 |
2.060 |
2.167 |
2.485 |
2.787 |
3.078 |
3.450 |
3.725 |
| 26 |
.684 |
.856 |
1.058 |
1.315 |
1.706 |
2.056 |
2.162 |
2.479 |
2.779 |
3.067 |
3.435 |
3.707 |
| 27 |
.684 |
.855 |
1.057 |
1.314 |
1.703 |
2.052 |
2.15 |
2.473 |
2.771 |
3.057 |
3.421 |
3.690 |
| 28 |
.683 |
.855 |
1.056 |
1.313 |
1.701 |
2.048 |
2.154 |
2.467 |
2.763 |
3.047 |
3.408 |
3.674 |
| 29 |
.683 |
.854 |
1.055 |
1.311 |
1.699 |
2.045 |
2.150 |
2.462 |
2.756 |
3.038 |
3.396 |
3.659 |
| 30 |
.683 |
.854 |
1.055 |
1.310 |
1.697 |
2.042 |
2.147 |
2.457 |
2.750 |
3.030 |
3.385 |
3.646 |
| 40 |
.681 |
.851 |
1.050 |
1.303 |
1.684 |
2.021 |
2.123 |
2.423 |
2.704 |
2.971 |
3.307 |
3.551 |
| 50 |
.679 |
.849 |
1.047 |
1.295 |
1.676 |
2.009 |
2.109 |
2.403 |
2.678 |
2.937 |
3.261 |
3.496 |
| 60 |
.679 |
.848 |
1.045 |
1.296 |
1.671 |
2.000 |
2.099 |
2.390 |
2.660 |
2.915 |
3.232 |
3.460 |
| 80 |
.678 |
.846 |
1.043 |
1.292 |
1.664 |
1.990 |
2.088 |
2.374 |
2.639 |
2.887 |
3.195 |
3.416 |
| 100 |
.677 |
.845 |
1.042 |
1.290 |
1.660 |
1.984 |
2.081 |
2.364 |
2.626 |
2.871 |
3.174 |
3.390 |
| 1000 |
.675 |
.842 |
1.037 |
1.282 |
1.646 |
1.962 |
2.056 |
2.330 |
2.581 |
2.813 |
3.098 |
3.300 |
| inf. |
.674 |
.841 |
1.036 |
1.282 |
1.64 |
1.960 |
2.054 |
2.326 |
2.576 |
2.807 |
3.091 |
3.291 |