15.4: Appendix D- The t-Tables
- Page ID
- 50194
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The critical values shown are for use with non-directional (two-tailed) and directional (one-tailed) t-tests.
|
two-tailed test |
one-tailed test |
||||
|---|---|---|---|---|---|
|
Degrees of Freedom |
alpha level: |
\(\alpha\) = 0.05 |
\(\alpha\) = 0.01 |
\(\alpha\) = 0.05 |
\(\alpha\) = 0.01 |
|
1 |
12.706 |
63.657 |
6.314 |
31.821 |
|
|
2 |
4.303 |
9.925 |
2.920 |
6.965 |
|
|
3 |
3.182 |
5.841 |
2.353 |
4.541 |
|
|
4 |
2.776 |
4.604 |
2.132 |
3.747 |
|
|
5 |
2.571 |
4.032 |
2.015 |
3.365 |
|
|
6 |
2.447 |
3.707 |
1.943 |
3.143 |
|
|
7 |
2.365 |
3.499 |
1.895 |
2.998 |
|
|
8 |
2.306 |
3.355 |
1.860 |
2.896 |
|
|
9 |
2.262 |
3.250 |
1.833 |
2.821 |
|
|
10 |
2.228 |
3.169 |
1.812 |
2.764 |
|
|
11 |
2.201 |
3.106 |
1.796 |
2.718 |
|
|
12 |
2.179 |
3.055 |
1.782 |
2.681 |
|
|
13 |
2.160 |
3.012 |
1.771 |
2.650 |
|
|
14 |
2.145 |
2.977 |
1.761 |
2.624 |
|
|
15 |
2.131 |
2.947 |
1.753 |
2.602 |
|
|
16 |
2.120 |
2.921 |
1.746 |
2.583 |
|
|
17 |
2.110 |
2.898 |
1.740 |
2.567 |
|
|
18 |
2.101 |
2.878 |
1.734 |
2.552 |
|
|
19 |
2.093 |
2.861 |
1.729 |
2.539 |
|
|
20 |
2.086 |
2.845 |
1.725 |
2.528 |
|
|
21 |
2.080 |
2.831 |
1.721 |
2.518 |
|
|
22 |
2.074 |
2.819 |
1.717 |
2.508 |
|
|
23 |
2.069 |
2.807 |
1.714 |
2.500 |
|
|
24 |
2.064 |
2.797 |
1.711 |
2.492 |
|
|
25 |
2.060 |
2.787 |
1.708 |
2.485 |
|
|
26 |
2.056 |
2.779 |
1.706 |
2.479 |
|
|
27 |
2.052 |
2.771 |
1.703 |
2.473 |
|
|
28 |
2.048 |
2.763 |
1.701 |
2.467 |
|
|
29 |
2.045 |
2.756 |
1.699 |
2.462 |
|
|
30 |
2.042 |
2.750 |
1.697 |
2.457 |
|
|
31 |
2.040 |
2.744 |
1.696 |
2.453 |
|
|
32 |
2.037 |
2.738 |
1.694 |
2.449 |
|
|
33 |
2.035 |
2.733 |
1.692 |
2.445 |
|
|
34 |
2.032 |
2.728 |
1.691 |
2.441 |
|
|
35 |
2.030 |
2.724 |
1.690 |
2.438 |
|
|
36 |
2.028 |
2.719 |
1.688 |
2.434 |
|
|
37 |
2.026 |
2.715 |
1.687 |
2.431 |
|
|
38 |
2.024 |
2.712 |
1.686 |
2.429 |
|
|
39 |
2.023 |
2.708 |
1.685 |
2.426 |
|
|
40 |
2.021 |
2.704 |
1.684 |
2.423 |
|