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16.2: t Distribution Table (t Table)

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    The \(t\) table lists critical values for one- and two-tailed tests at several levels of significance, arranged into columns. Each column contains two levels of significance, separated by a slash (/). These two values refer to the level of significance for a one-tailed test (i.e., the proportion in one tail) / the level of significance for a two-tailed test (i.e., the proportion in two tails combined).

    The rows of the \(t\) table list degrees of freedom up to \(df = 120\) in order to use the appropriate distribution curve. It does not, however, list all possible degrees of freedom in this range, because that would take too many rows. If a problem requires you to find critical values and the exact degrees of freedom is not listed, round down to the next smallest number. For example, if you have 48 people in your sample, the degrees of freedom are N − 1 = 48 − 1 = 47; however, 47 doesn’t appear on our table, so we round down and use the critical values for \(df = 40\), even though 50 is closer.

    Pay close attention to ensure you select the correct column and row for your specific \(t\)-test.

    t Table
    df .25 / .50 .20 / .40 .15 / .30 .10 / .20 .05 / .10 .025 / .05 .01 / .02 .005 / .01 .0005 / .001
    1 1.000 1.376 1.963 3.078 6.314 12.706 31.821 63.657 636.578
    2 0.816 1.061 1.386 1.886 2.920 4.303 6.965 9.925 31.600
    3 0.765 1.978 1.250 1.638 2.353 3.182 4.541 5.841 12.924
    4 0.741 1.941 1.190 1.533 2.132 2.776 3.747 4.604 8.610
    5 0.727 0.920 1.156 1.476 2.015 2.571 3.365 4.032 6.869
    6 0.718 0.906 1.134 1.440 1.943 2.447 3.143 3.707 5.959
    7 0.711 0.896 1.119 1.415 1.895 2.365 2.998 3.499 5.408
    8 0.706 0.889 1.108 1.397 1.860 2.306 2.896 3.355 5.041
    9 0.703 0.883 1.100 1.383 1.833 2.262 2.821 3.250 4.781
    10 0.700 0.879 1.093 1.372 1.812 2.228 2.764 3.169 4.587
    11 0.697 0.876 1.088 1.363 1.796 2.201 2.718 3.106 4.437
    12 0.695 0.873 1.083 1.356 1.782 2.179 2.681 3.055 4.318
    13 0.694 0.870 1.079 1.350 1.771 2.160 2.650 3.012 4.221
    14 0.692 0.868 1.076 1.345 1.761 2.145 2.624 2.977 4.140
    15 0.691 0.866 1.074 1.341 1.753 2.131 2.602 2.947 4.073
    16 0.690 0.865 1.071 1.337 1.746 2.120 2.583 2.921 4.015
    17 0.689 0.863 1.069 1.333 1.740 2.110 2.567 2.898 3.965
    18 0.688 0.862 1.067 1.330 1.734 2.101 2.552 2.878 3.922
    19 0.688 0.861 1.066 1.328 1.729 2.093 2.539 2.861 3.883
    20 0.687 0.860 1.064 1.325 1.725 2.086 2.528 2.845 3.850
    21 0.686 0.859 1.063 1.323 1.721 2.080 2.518 2.831 3.819
    22 0.686 0.858 1.061 1.321 1.717 2.074 2.508 2.819 3.792
    23 0.685 0.858 1.060 1.319 1.714 2.069 2.500 2.807 3.768
    24 0.685 0.857 1.059 1.318 1.711 2.064 2.492 2.797 3.745
    25 0.684 0.856 1.058 1.316 1.708 2.060 2.485 2.787 3.725
    26 0.684 0.856 1.058 1.315 1.706 2.056 2.479 2.779 3.707
    27 0.684 0.855 1.057 1.314 1.703 2.052 2.473 2.771 3.689
    28 0.683 0.855 1.056 1.313 1.701 2.048 2.467 2.763 3.674
    29 0.683 0.854 1.055 1.311 1.699 2.045 2.462 2.756 3.660
    30 0.683 0.854 1.055 1.310 1.697 2.042 2.457 2.750 3.646
    40 0.681 0.851 1.050 1.303 1.684 2.021 2.423 2.704 3.551
    60 0.679 0.848 1.045 1.296 1.671 2.000 2.390 2.660 3.460
    120 0.677 0.845 1.041 1.289 1.658 1.980 2.358 2.617 3.373
    \(\infty\) 0.674 0.842 1.036 1.282 1.645 1.960 2.326 2.576 3.290

    Adapted from “Tabla t” by Jsmura/Wikimedia Commons, CC BY-SA 4.0.

    This table taken from Cote et al, 2021, shared under a CC BY-NC-SA 4.0 license.

    16.2: t Distribution Table (t Table) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.