16.3: t Distribution Table
- Page ID
- 49386
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)t Distribution Table (t Table)
|
df |
Proportion (a) in One tail |
||||||||
|
.25 |
.20 |
.15 |
.10 |
.05 |
.025 |
.01 |
.005 |
.0005 |
|
|
Proportion (a) in Two tails combined |
|||||||||
|
.50 |
.40 |
.30 |
.20 |
.10 |
.05 |
.02 |
.01 |
.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 |
|
∞ |
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.