The following table provides a look-up table for the $T(n)$ distribution with $n$ degrees of freedom at various confidence levels. Specifically for each $n$ and $\alpha$ it provides the values for the inverse CDF of $T(n)$
$$
t_{\frac{\alpha}{2},n} = F_{T(n)}^{-1}\left(1-\frac{\alpha}{2}\right).
$$
The same numbers can be produced via MATLAB using the function tinv(1-alpha/2,n)
.
Note that the bottom of the table has the z-score for the Normal distribution, consistent with the central limit theorem
$(1-\alpha)100\%$ | 50% | 80% | 90% | 95% | 98% | 99% |
---|---|---|---|---|---|---|
$\alpha/2$ | 0.250 | 0.100 | 0.050 | 0.025 | 0.010 | 0.005 |
n = 1 | 1.000 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 |
2 | 0.816 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 |
3 | 0.765 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 |
4 | 0.741 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 |
5 | 0.727 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 |
6 | 0.718 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 |
7 | 0.711 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 |
8 | 0.706 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 |
9 | 0.703 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 |
10 | 0.700 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 |
11 | 0.697 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 |
12 | 0.695 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 |
13 | 0.694 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
14 | 0.692 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 |
15 | 0.691 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
16 | 0.690 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
17 | 0.689 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 |
18 | 0.688 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 |
19 | 0.688 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 |
20 | 0.687 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 |
21 | 0.686 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 |
22 | 0.686 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 |
23 | 0.685 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 |
24 | 0.685 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 |
25 | 0.684 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 |
26 | 0.684 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 |
27 | 0.684 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 |
28 | 0.683 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 |
29 | 0.683 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 |
30 | 0.683 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 |
40 | 0.681 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 |
50 | 0.679 | 1.299 | 1.676 | 2.009 | 2.403 | 2.678 |
60 | 0.679 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 |
70 | 0.678 | 1.294 | 1.667 | 1.994 | 2.381 | 2.648 |
80 | 0.678 | 1.292 | 1.664 | 1.990 | 2.374 | 2.639 |
90 | 0.677 | 1.291 | 1.662 | 1.987 | 2.368 | 2.632 |
100 | 0.677 | 1.290 | 1.660 | 1.984 | 2.364 | 2.626 |
z | 0.674 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |