13.12: The F-Distribution Table for Alpha = 0.025
- Page ID
- 54856
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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 F-Distribution Table for Alpha = 0.025
- The first row is the degrees of freedom of the numerator = n1 – 1
- The first column is the degrees of freedom of the numerator = n2 – 1.
| Degrees of Freedom of the Denominator | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 20 | 24 | 30 | 40 | 50 | 60 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 648 | 800 | 864 | 900 | 922 | 937 | 948 | 957 | 963 | 969 | 973 | 977 | 980 | 983 | 985 | 993 | 997 | 1001 | 1006 | 1008 | 1010 |
| 2 | 38.51 | 39.00 | 39.17 | 39.25 | 39.30 | 39.33 | 39.36 | 39.37 | 39.39 | 39.40 | 39.41 | 39.41 | 39.42 | 39.43 | 39.43 | 39.45 | 39.46 | 39.46 | 39.47 | 39.48 | 39.48 |
| 3 | 17.44 | 16.04 | 15.44 | 15.10 | 14.88 | 14.73 | 14.62 | 14.54 | 14.47 | 14.42 | 14.37 | 14.34 | 14.30 | 14.28 | 14.25 | 14.17 | 14.12 | 14.08 | 14.04 | 14.01 | 13.99 |
| 4 | 12.22 | 10.65 | 9.98 | 9.60 | 9.36 | 9.20 | 9.07 | 8.98 | 8.90 | 8.84 | 8.79 | 8.75 | 8.71 | 8.68 | 8.66 | 8.56 | 8.51 | 8.46 | 8.41 | 8.38 | 8.36 |
| 5 | 10.01 | 8.43 | 7.76 | 7.39 | 7.15 | 6.98 | 6.85 | 6.76 | 6.68 | 6.62 | 6.57 | 6.52 | 6.49 | 6.46 | 6.43 | 6.33 | 6.28 | 6.23 | 6.18 | 6.14 | 6.12 |
| 6 | 8.81 | 7.26 | 6.60 | 6.23 | 5.99 | 5.82 | 5.70 | 5.60 | 5.52 | 5.46 | 5.41 | 5.37 | 5.33 | 5.30 | 5.27 | 5.17 | 5.12 | 5.07 | 5.01 | 4.98 | 4.96 |
| 7 | 8.07 | 6.54 | 5.89 | 5.52 | 5.29 | 5.12 | 4.99 | 4.90 | 4.82 | 4.76 | 4.71 | 4.67 | 4.63 | 4.60 | 4.57 | 4.47 | 4.41 | 4.36 | 4.31 | 4.28 | 4.25 |
| 8 | 7.57 | 6.06 | 5.42 | 5.05 | 4.82 | 4.65 | 4.53 | 4.43 | 4.36 | 4.30 | 4.24 | 4.20 | 4.16 | 4.13 | 4.10 | 4.00 | 3.95 | 3.89 | 3.84 | 3.81 | 3.78 |
| 9 | 7.21 | 5.71 | 5.08 | 4.72 | 4.48 | 4.32 | 4.20 | 4.10 | 4.03 | 3.96 | 3.91 | 3.87 | 3.83 | 3.80 | 3.77 | 3.67 | 3.61 | 3.56 | 3.51 | 3.47 | 3.45 |
| 10 | 6.94 | 5.46 | 4.83 | 4.47 | 4.24 | 4.07 | 3.95 | 3.85 | 3.78 | 3.72 | 3.66 | 3.62 | 3.58 | 3.55 | 3.52 | 3.42 | 3.37 | 3.31 | 3.26 | 3.22 | 3.20 |
| 11 | 6.72 | 5.26 | 4.63 | 4.28 | 4.04 | 3.88 | 3.76 | 3.66 | 3.59 | 3.53 | 3.47 | 3.43 | 3.39 | 3.36 | 3.33 | 3.23 | 3.17 | 3.12 | 3.06 | 3.03 | 3.00 |
| 12 | 6.55 | 5.10 | 4.47 | 4.12 | 3.89 | 3.73 | 3.61 | 3.51 | 3.44 | 3.37 | 3.32 | 3.28 | 3.24 | 3.21 | 3.18 | 3.07 | 3.02 | 2.96 | 2.91 | 2.87 | 2.85 |
| 13 | 6.41 | 4.97 | 4.35 | 4.00 | 3.77 | 3.60 | 3.48 | 3.39 | 3.31 | 3.25 | 3.20 | 3.15 | 3.12 | 3.08 | 3.05 | 2.95 | 2.89 | 2.84 | 2.78 | 2.74 | 2.72 |
| 14 | 6.30 | 4.86 | 4.24 | 3.89 | 3.66 | 3.50 | 3.38 | 3.29 | 3.21 | 3.15 | 3.09 | 3.05 | 3.01 | 2.98 | 2.95 | 2.84 | 2.79 | 2.73 | 2.67 | 2.64 | 2.61 |
| 15 | 6.20 | 4.77 | 4.15 | 3.80 | 3.58 | 3.41 | 3.29 | 3.20 | 3.12 | 3.06 | 3.01 | 2.96 | 2.92 | 2.89 | 2.86 | 2.76 | 2.70 | 2.64 | 2.59 | 2.55 | 2.52 |
| 16 | 6.12 | 4.69 | 4.08 | 3.73 | 3.50 | 3.34 | 3.22 | 3.12 | 3.05 | 2.99 | 2.93 | 2.89 | 2.85 | 2.82 | 2.79 | 2.68 | 2.63 | 2.57 | 2.51 | 2.47 | 2.45 |
| 17 | 6.04 | 4.62 | 4.01 | 3.66 | 3.44 | 3.28 | 3.16 | 3.06 | 2.98 | 2.92 | 2.87 | 2.82 | 2.79 | 2.75 | 2.72 | 2.62 | 2.56 | 2.50 | 2.44 | 2.41 | 2.38 |
| 18 | 5.98 | 4.56 | 3.95 | 3.61 | 3.38 | 3.22 | 3.10 | 3.01 | 2.93 | 2.87 | 2.81 | 2.77 | 2.73 | 2.70 | 2.67 | 2.56 | 2.50 | 2.44 | 2.38 | 2.35 | 2.32 |
| 19 | 5.92 | 4.51 | 3.90 | 3.56 | 3.33 | 3.17 | 3.05 | 2.96 | 2.88 | 2.82 | 2.76 | 2.72 | 2.68 | 2.65 | 2.62 | 2.51 | 2.45 | 2.39 | 2.33 | 2.30 | 2.27 |
| 20 | 5.87 | 4.46 | 3.86 | 3.51 | 3.29 | 3.13 | 3.01 | 2.91 | 2.84 | 2.77 | 2.72 | 2.68 | 2.64 | 2.60 | 2.57 | 2.46 | 2.41 | 2.35 | 2.29 | 2.25 | 2.22 |
| 21 | 5.83 | 4.42 | 3.82 | 3.48 | 3.25 | 3.09 | 2.97 | 2.87 | 2.80 | 2.73 | 2.68 | 2.64 | 2.60 | 2.56 | 2.53 | 2.42 | 2.37 | 2.31 | 2.25 | 2.21 | 2.18 |
| 22 | 5.79 | 4.38 | 3.78 | 3.44 | 3.22 | 3.05 | 2.93 | 2.84 | 2.76 | 2.70 | 2.65 | 2.60 | 2.56 | 2.53 | 2.50 | 2.39 | 2.33 | 2.27 | 2.21 | 2.17 | 2.14 |
| 23 | 5.75 | 4.35 | 3.75 | 3.41 | 3.18 | 3.02 | 2.90 | 2.81 | 2.73 | 2.67 | 2.62 | 2.57 | 2.53 | 2.50 | 2.47 | 2.36 | 2.30 | 2.24 | 2.18 | 2.14 | 2.11 |
| 24 | 5.72 | 4.32 | 3.72 | 3.38 | 3.15 | 2.99 | 2.87 | 2.78 | 2.70 | 2.64 | 2.59 | 2.54 | 2.50 | 2.47 | 2.44 | 2.33 | 2.27 | 2.21 | 2.15 | 2.11 | 2.08 |
| 25 | 5.69 | 4.29 | 3.69 | 3.35 | 3.13 | 2.97 | 2.85 | 2.75 | 2.68 | 2.61 | 2.56 | 2.51 | 2.48 | 2.44 | 2.41 | 2.30 | 2.24 | 2.18 | 2.12 | 2.08 | 2.05 |
| 26 | 5.66 | 4.27 | 3.67 | 3.33 | 3.10 | 2.94 | 2.82 | 2.73 | 2.65 | 2.59 | 2.54 | 2.49 | 2.45 | 2.42 | 2.39 | 2.28 | 2.22 | 2.16 | 2.09 | 2.05 | 2.03 |
| 27 | 5.63 | 4.24 | 3.65 | 3.31 | 3.08 | 2.92 | 2.80 | 2.71 | 2.63 | 2.57 | 2.51 | 2.47 | 2.43 | 2.39 | 2.36 | 2.25 | 2.19 | 2.13 | 2.07 | 2.03 | 2.00 |
| 28 | 5.61 | 4.22 | 3.63 | 3.29 | 3.06 | 2.90 | 2.78 | 2.69 | 2.61 | 2.55 | 2.49 | 2.45 | 2.41 | 2.37 | 2.34 | 2.23 | 2.17 | 2.11 | 2.05 | 2.01 | 1.98 |
| 29 | 5.59 | 4.20 | 3.61 | 3.27 | 3.04 | 2.88 | 2.76 | 2.67 | 2.59 | 2.53 | 2.48 | 2.43 | 2.39 | 2.36 | 2.32 | 2.21 | 2.15 | 2.09 | 2.03 | 1.99 | 1.96 |
| 30 | 5.57 | 4.18 | 3.59 | 3.25 | 3.03 | 2.87 | 2.75 | 2.65 | 2.57 | 2.51 | 2.46 | 2.41 | 2.37 | 2.34 | 2.31 | 2.20 | 2.14 | 2.07 | 2.01 | 1.97 | 1.94 |
| 40 | 5.42 | 4.05 | 3.46 | 3.13 | 2.90 | 2.74 | 2.62 | 2.53 | 2.45 | 2.39 | 2.33 | 2.29 | 2.25 | 2.21 | 2.18 | 2.07 | 2.01 | 1.94 | 1.88 | 1.83 | 1.80 |
| 50 | 5.34 | 3.97 | 3.39 | 3.05 | 2.83 | 2.67 | 2.55 | 2.46 | 2.38 | 2.32 | 2.26 | 2.22 | 2.18 | 2.14 | 2.11 | 1.99 | 1.93 | 1.87 | 1.80 | 1.75 | 1.72 |
| 60 | 5.29 | 3.93 | 3.34 | 3.01 | 2.79 | 2.63 | 2.51 | 2.41 | 2.33 | 2.27 | 2.22 | 2.17 | 2.13 | 2.09 | 2.06 | 1.94 | 1.88 | 1.82 | 1.74 | 1.70 | 1.67 |
Table \(\PageIndex{1}\): The F-Distribution Table for α = 0.025
Author
"13.12: The F-Distribution Table for Alpha = 0.025" by Alfie Swan is in the Public Domain, CC0