QUANTILES of selected t-distributions with df degrees of freedom.  The body of the tables contain quantiles corresponding to various areas under t(df) curves.  For example,  the 0.950 quantile (aka 95th percentile) of the t(3) distribution is 2.353.  In other words, the area under the t(3) curve to the left of 2.353 is 0.950  (see below). 

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                                                      Areas

df |  0.75  0.8   0.85  0.9  0.95  0.975  0.99 0.995 0.997 0.998
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1  | 1     1.376 1.963 3.078 6.31  12.71 31.82 63.66 106.1 159.2
2  | 0.816 1.061 1.386 1.886 2.92  4.303 6.965 9.925 12.85 15.76
3  | 0.765 0.978 1.25  1.638 2.353 3.182 4.541 5.841 6.994 8.053
4  | 0.741 0.941 1.19  1.533 2.132 2.776 3.747 4.604 5.321 5.951
5  | 0.727 0.92  1.156 1.476 2.015 2.571 3.365 4.032 4.57  5.03
6  | 0.718 0.906 1.134 1.44  1.943 2.447 3.143 3.707 4.152 4.524
7  | 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 3.887 4.207
8  | 0.706 0.889 1.108 1.397 1.86  2.306 2.896 3.355 3.705 3.991
9  | 0.703 0.883 1.1   1.383 1.833 2.262 2.821 3.25  3.573 3.835
10 | 0.7   0.879 1.093 1.372 1.812 2.228 2.764 3.169 3.472 3.716

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                                                      Areas

df |  0.75  0.8   0.85  0.9  0.95  0.975  0.99 0.995 0.997 0.998
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11 | 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 3.393 3.624
12 | 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 3.33  3.55
13 | 0.694 0.87  1.079 1.35  1.771 2.16  2.65  3.012 3.278 3.489
14 | 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 3.234 3.438
15 | 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 3.197 3.395
16 | 0.69  0.865 1.071 1.337 1.746 2.12  2.583 2.921 3.165 3.358
17 | 0.689 0.863 1.069 1.333 1.74  2.11  2.567 2.898 3.138 3.326
18 | 0.688 0.862 1.067 1.33  1.734 2.101 2.552 2.878 3.113 3.298
19 | 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.092 3.273
20 | 0.687 0.86  1.064 1.325 1.725 2.086 2.528 2.845 3.073 3.251

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                                                       Areas

df |  0.75  0.8   0.85  0.9  0.95  0.975  0.99 0.995 0.997 0.998
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21 | 0.686 0.859 1.063 1.323 1.721 2.08  2.518 2.831 3.056 3.231
22 | 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.041 3.214
23 | 0.685 0.858 1.06  1.319 1.714 2.069 2.5   2.807 3.027 3.198
24 | 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.014 3.183
25 | 0.684 0.856 1.058 1.316 1.708 2.06  2.485 2.787 3.003 3.17
26 | 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 2.992 3.158
27 | 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 2.982 3.147
28 | 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 2.973 3.136
29 | 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 2.965 3.127
30 | 0.683 0.854 1.055 1.31  1.697 2.042 2.457 2.75  2.957 3.118

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                                                       Areas

df |  0.75  0.8   0.85  0.9  0.95  0.975  0.99 0.995 0.997 0.998
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31 | 0.682 0.853 1.054 1.309 1.696 2.04  2.453 2.744 2.95  3.109
32 | 0.682 0.853 1.054 1.309 1.694 2.037 2.449 2.738 2.943 3.102
33 | 0.682 0.853 1.053 1.308 1.692 2.035 2.445 2.733 2.937 3.094
34 | 0.682 0.852 1.052 1.307 1.691 2.032 2.441 2.728 2.931 3.088
35 | 0.682 0.852 1.052 1.306 1.69  2.03  2.438 2.724 2.926 3.081


40 | 0.681 0.851 1.05  1.303 1.684 2.021 2.423 2.704 2.902 3.055
50 | 0.679 0.849 1.047 1.299 1.676 2.009 2.403 2.678 2.87  3.018
60 | 0.679 0.848 1.045 1.296 1.671 2     2.39  2.66  2.849 2.994
120| 0.677 0.845 1.041 1.289 1.658 1.98  2.358 2.617 2.798 2.935
Inf| 0.674 0.842 1.036 1.282 1.645 1.96  2.326 2.576 2.748 2.878

       

Example: Find the 95th percentile of the t(df=3) distribution.  Go to the row labeled 3 [this is the row that contains quantiles of the t(df=3) distribution] and then over   to the column labeled 0.95.  The table entry is 2.353.  Thus,  the 95th percentile (aka 0.95 quantile) of the t(df=3) distribution is 2.353. (See the picture below.)    Note, that by symmetry of the t-density curves, it follows that the 5th percentile is -2.353.  

 

Page Last Updated:  01/23/2003 03:30 PM -0600 (J.B. Lang)