The t-distribution is a probability distribution with a symmetrical, bell-shaped curve (similar to the standard normal curve), the shape of which is affected by a parameter known as the “degrees of freedom.” We used t-distributions in Chapter 8 of this book to compute confidence intervals. In that usage, the degrees of freedom controlled how far out you had to go (in terms of standard deviations) on the t-distribution curve from the mean to encompass a given percentage of values. The higher the degrees of freedom, the larger the interval on the curve.
Table A-1 gives t-distribution values for various probabilities, with each row representing 1 additional degree of freedom. Those values in the column for 0.05 (95%) were used in Chapter 8.
DF |
Probabilities | ||||||
0.2 |
0.1 |
0.05 |
0.02 |
0.01 |
0.002 |
0.001 | |
1 |
3.078 |
6.314 |
12.706 |
31.82 |
63.66 |
318.3 |
637 |
2 |
1.886 |
2.92 |
4.303 |
6.965 |
9.925 |
22.33 |
31.6 |
3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
10.21 |
12.92 |
4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
7.173 |
8.61 |
5 |
1.476 |
2.015 |
2.571 |
3.365 |
4.032 |
5.893 |
6.869 |
6 |
1.44 |
1.943 |
2.447 |
3.143 |
3.707 |
5.208 |
5.959 |
7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
4.785 |
5.408 |
8 |
1.397 |
1.86 |
2.306 |
2.896 |
3.355 |
4.501 |
5.041 |
9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.25 |
4.297 |
4.781 |
10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.144 |
4.587 |
11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.025 |
4.437 |
12 |
1.356 |
1.782 |
2.179 |
2.681 |
3.055 |
3.93 |
4.318 |
13 |
1.35 |
1.771 |
2.16 |
2.65 |
3.012 |
3.852 |
4.221 |
14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
3.787 |
4.14 |
15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
3.733 |
4.073 |
16 |
1.337 |
1.746 |
2.12 |
2.583 |
2.921 |
3.686 |
4.015 |
17 |
1.333 |
1.74 |
2.11 |
2.567 |
2.898 |
3.646 |
3.965 |
18 |
1.33 |
1.734 |
2.101 |
2.552 |
2.878 |
3.61 |
3.922 |
19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.579 |
3.883 |
20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.552 |
3.85 |
21 |
1.323 |
1.721 |
2.08 |
2.518 |
2.831 |
3.527 |
3.819 |
22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.505 |
3.792 |
23 |
1.319 |
1.714 |
2.069 |
2.5 |
2.807 |
3.485 |
3.768 |
24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.467 |
3.745 |
25 |
1.316 |
1.708 |
2.06 |
2.485 |
2.787 |
3.45 |
3.725 |
26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.435 |
3.707 |
27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.421 |
3.69 |
28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.408 |
3.674 |
29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.396 |
3.659 |
30 |
1.31 |
1.697 |
2.042 |
2.457 |
2.75 |
3.385 |
3.646 |
32 |
1.309 |
1.694 |
2.037 |
2.449 |
2.738 |
3.365 |
3.622 |
34 |
1.307 |
1.691 |
2.032 |
2.441 |
2.728 |
3.348 |
3.601 |
36 |
1.306 |
1.688 |
2.028 |
2.434 |
2.719 |
3.333 |
3.582 |
38 |
1.304 |
1.686 |
2.024 |
2.429 |
2.712 |
3.319 |
3.566 |
40 |
1.303 |
1.684 |
2.021 |
2.423 |
2.704 |
3.307 |
3.551 |
42 |
1.302 |
1.682 |
2.018 |
2.418 |
2.698 |
3.296 |
3.538 |
44 |
1.301 |
1.68 |
2.015 |
2.414 |
2.692 |
3.286 |
3.526 |
46 |
1.3 |
1.679 |
2.013 |
2.41 |
2.687 |
3.277 |
3.515 |
48 |
1.299 |
1.677 |
2.011 |
2.407 |
2.682 |
3.269 |
3.505 |
50 |
1.299 |
1.676 |
2.009 |
2.403 |
2.678 |
3.261 |
3.496 |
55 |
1.297 |
1.673 |
2.004 |
2.396 |
2.668 |
3.245 |
3.476 |
60 |
1.296 |
1.671 |
2 |
2.39 |
2.66 |
3.232 |
3.46 |
65 |
1.295 |
1.669 |
1.997 |
2.385 |
2.654 |
3.22 |
3.447 |
70 |
1.294 |
1.667 |
1.994 |
2.381 |
2.648 |
3.211 |
3.435 |
80 |
1.292 |
1.664 |
1.99 |
2.374 |
2.639 |
3.195 |
3.416 |
100 |
1.29 |
1.66 |
1.984 |
2.364 |
2.626 |
3.174 |
3.39 |
150 |
1.287 |
1.655 |
1.976 |
2.351 |
2.609 |
3.145 |
3.357 |
200 |
1.286 |
1.653 |
1.972 |
2.345 |
2.601 |
3.131 |
3.34 |
3.149.28.145