13.10: The F-Distribution for Alpha = 0.005
- Page ID
- 54847
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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 for Alpha = 0.005
- 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 | 16211 | 20000 | 21615 | 22500 | 23056 | 23437 | 23715 | 23925 | 24091 | 24224 | 24334 | 24426 | 24505 | 24572 | 24630 | 24836 | 24940 | 25044 | 25148 | 25211 | 25253 |
| 2 | 198.50 | 199.00 | 199.17 | 199.25 | 199.30 | 199.33 | 199.36 | 199.37 | 199.39 | 199.40 | 199.41 | 199.42 | 199.42 | 199.43 | 199.43 | 199.45 | 199.46 | 199.47 | 199.47 | 199.48 | 199.48 |
| 3 | 55.55 | 49.80 | 47.47 | 46.19 | 45.39 | 44.84 | 44.43 | 44.13 | 43.88 | 43.69 | 43.52 | 43.39 | 43.27 | 43.17 | 43.08 | 42.78 | 42.62 | 42.47 | 42.31 | 42.21 | 42.15 |
| 4 | 31.33 | 26.28 | 24.26 | 23.15 | 22.46 | 21.97 | 21.62 | 21.35 | 21.14 | 20.97 | 20.82 | 20.70 | 20.60 | 20.51 | 20.44 | 20.17 | 20.03 | 19.89 | 19.75 | 19.67 | 19.61 |
| 5 | 22.78 | 18.31 | 16.53 | 15.56 | 14.94 | 14.51 | 14.20 | 13.96 | 13.77 | 13.62 | 13.49 | 13.38 | 13.29 | 13.21 | 13.15 | 12.90 | 12.78 | 12.66 | 12.53 | 12.45 | 12.40 |
| 6 | 18.63 | 14.54 | 12.92 | 12.03 | 11.46 | 11.07 | 10.79 | 10.57 | 10.39 | 10.25 | 10.13 | 10.03 | 9.95 | 9.88 | 9.81 | 9.59 | 9.47 | 9.36 | 9.24 | 9.17 | 9.12 |
| 7 | 16.24 | 12.40 | 10.88 | 10.05 | 9.52 | 9.16 | 8.89 | 8.68 | 8.51 | 8.38 | 8.27 | 8.18 | 8.10 | 8.03 | 7.97 | 7.75 | 7.64 | 7.53 | 7.42 | 7.35 | 7.31 |
| 8 | 14.69 | 11.04 | 9.60 | 8.81 | 8.30 | 7.95 | 7.69 | 7.50 | 7.34 | 7.21 | 7.10 | 7.01 | 6.94 | 6.87 | 6.81 | 6.61 | 6.50 | 6.40 | 6.29 | 6.22 | 6.18 |
| 9 | 13.61 | 10.11 | 8.72 | 7.96 | 7.47 | 7.13 | 6.88 | 6.69 | 6.54 | 6.42 | 6.31 | 6.23 | 6.15 | 6.09 | 6.03 | 5.83 | 5.73 | 5.62 | 5.52 | 5.45 | 5.41 |
| 10 | 12.83 | 9.43 | 8.08 | 7.34 | 6.87 | 6.54 | 6.30 | 6.12 | 5.97 | 5.85 | 5.75 | 5.66 | 5.59 | 5.53 | 5.47 | 5.27 | 5.17 | 5.07 | 4.97 | 4.90 | 4.86 |
| 11 | 12.23 | 8.91 | 7.60 | 6.88 | 6.42 | 6.10 | 5.86 | 5.68 | 5.54 | 5.42 | 5.32 | 5.24 | 5.16 | 5.10 | 5.05 | 4.86 | 4.76 | 4.65 | 4.55 | 4.49 | 4.45 |
| 12 | 11.75 | 8.51 | 7.23 | 6.52 | 6.07 | 5.76 | 5.52 | 5.35 | 5.20 | 5.09 | 4.99 | 4.91 | 4.84 | 4.77 | 4.72 | 4.53 | 4.43 | 4.33 | 4.23 | 4.17 | 4.12 |
| 13 | 11.37 | 8.19 | 6.93 | 6.23 | 5.79 | 5.48 | 5.25 | 5.08 | 4.94 | 4.82 | 4.72 | 4.64 | 4.57 | 4.51 | 4.46 | 4.27 | 4.17 | 4.07 | 3.97 | 3.91 | 3.87 |
| 14 | 11.06 | 7.92 | 6.68 | 6.00 | 5.56 | 5.26 | 5.03 | 4.86 | 4.72 | 4.60 | 4.51 | 4.43 | 4.36 | 4.30 | 4.25 | 4.06 | 3.96 | 3.86 | 3.76 | 3.70 | 3.66 |
| 15 | 10.80 | 7.70 | 6.48 | 5.80 | 5.37 | 5.07 | 4.85 | 4.67 | 4.54 | 4.42 | 4.33 | 4.25 | 4.18 | 4.12 | 4.07 | 3.88 | 3.79 | 3.69 | 3.58 | 3.52 | 3.48 |
| 16 | 10.58 | 7.51 | 6.30 | 5.64 | 5.21 | 4.91 | 4.69 | 4.52 | 4.38 | 4.27 | 4.18 | 4.10 | 4.03 | 3.97 | 3.92 | 3.73 | 3.64 | 3.54 | 3.44 | 3.37 | 3.33 |
| 17 | 10.38 | 7.35 | 6.16 | 5.50 | 5.07 | 4.78 | 4.56 | 4.39 | 4.25 | 4.14 | 4.05 | 3.97 | 3.90 | 3.84 | 3.79 | 3.61 | 3.51 | 3.41 | 3.31 | 3.25 | 3.21 |
| 18 | 10.22 | 7.21 | 6.03 | 5.37 | 4.96 | 4.66 | 4.44 | 4.28 | 4.14 | 4.03 | 3.94 | 3.86 | 3.79 | 3.73 | 3.68 | 3.50 | 3.40 | 3.30 | 3.20 | 3.14 | 3.10 |
| 19 | 10.07 | 7.09 | 5.92 | 5.27 | 4.85 | 4.56 | 4.34 | 4.18 | 4.04 | 3.93 | 3.84 | 3.76 | 3.70 | 3.64 | 3.59 | 3.40 | 3.31 | 3.21 | 3.11 | 3.04 | 3.00 |
| 20 | 9.94 | 6.99 | 5.82 | 5.17 | 4.76 | 4.47 | 4.26 | 4.09 | 3.96 | 3.85 | 3.76 | 3.68 | 3.61 | 3.55 | 3.50 | 3.32 | 3.22 | 3.12 | 3.02 | 2.96 | 2.92 |
| 21 | 9.83 | 6.89 | 5.73 | 5.09 | 4.68 | 4.39 | 4.18 | 4.01 | 3.88 | 3.77 | 3.68 | 3.60 | 3.54 | 3.48 | 3.43 | 3.24 | 3.15 | 3.05 | 2.95 | 2.88 | 2.84 |
| 22 | 9.73 | 6.81 | 5.65 | 5.02 | 4.61 | 4.32 | 4.11 | 3.94 | 3.81 | 3.70 | 3.61 | 3.54 | 3.47 | 3.41 | 3.36 | 3.18 | 3.08 | 2.98 | 2.88 | 2.82 | 2.77 |
| 23 | 9.63 | 6.73 | 5.58 | 4.95 | 4.54 | 4.26 | 4.05 | 3.88 | 3.75 | 3.64 | 3.55 | 3.47 | 3.41 | 3.35 | 3.30 | 3.12 | 3.02 | 2.92 | 2.82 | 2.76 | 2.71 |
| 24 | 9.55 | 6.66 | 5.52 | 4.89 | 4.49 | 4.20 | 3.99 | 3.83 | 3.69 | 3.59 | 3.50 | 3.42 | 3.35 | 3.30 | 3.25 | 3.06 | 2.97 | 2.87 | 2.77 | 2.70 | 2.66 |
| 25 | 9.48 | 6.60 | 5.46 | 4.84 | 4.43 | 4.15 | 3.94 | 3.78 | 3.64 | 3.54 | 3.45 | 3.37 | 3.30 | 3.25 | 3.20 | 3.01 | 2.92 | 2.82 | 2.72 | 2.65 | 2.61 |
| 26 | 9.41 | 6.54 | 5.41 | 4.79 | 4.38 | 4.10 | 3.89 | 3.73 | 3.60 | 3.49 | 3.40 | 3.33 | 3.26 | 3.20 | 3.15 | 2.97 | 2.87 | 2.77 | 2.67 | 2.61 | 2.56 |
| 27 | 9.34 | 6.49 | 5.36 | 4.74 | 4.34 | 4.06 | 3.85 | 3.69 | 3.56 | 3.45 | 3.36 | 3.28 | 3.22 | 3.16 | 3.11 | 2.93 | 2.83 | 2.73 | 2.63 | 2.57 | 2.52 |
| 28 | 9.28 | 6.44 | 5.32 | 4.70 | 4.30 | 4.02 | 3.81 | 3.65 | 3.52 | 3.41 | 3.32 | 3.25 | 3.18 | 3.12 | 3.07 | 2.89 | 2.79 | 2.69 | 2.59 | 2.53 | 2.48 |
| 29 | 9.23 | 6.40 | 5.28 | 4.66 | 4.26 | 3.98 | 3.77 | 3.61 | 3.48 | 3.38 | 3.29 | 3.21 | 3.15 | 3.09 | 3.04 | 2.86 | 2.76 | 2.66 | 2.56 | 2.49 | 2.45 |
| 30 | 9.18 | 6.35 | 5.24 | 4.62 | 4.23 | 3.95 | 3.74 | 3.58 | 3.45 | 3.34 | 3.25 | 3.18 | 3.11 | 3.06 | 3.01 | 2.82 | 2.73 | 2.63 | 2.52 | 2.46 | 2.42 |
| 40 | 8.83 | 6.07 | 4.98 | 4.37 | 3.99 | 3.71 | 3.51 | 3.35 | 3.22 | 3.12 | 3.03 | 2.95 | 2.89 | 2.83 | 2.78 | 2.60 | 2.50 | 2.40 | 2.30 | 2.23 | 2.18 |
| 50 | 8.63 | 5.90 | 4.83 | 4.23 | 3.85 | 3.58 | 3.38 | 3.22 | 3.09 | 2.99 | 2.90 | 2.82 | 2.76 | 2.70 | 2.65 | 2.47 | 2.37 | 2.27 | 2.16 | 2.10 | 2.05 |
| 60 | 8.49 | 5.79 | 4.73 | 4.14 | 3.76 | 3.49 | 3.29 | 3.13 | 3.01 | 2.90 | 2.82 | 2.74 | 2.68 | 2.62 | 2.57 | 2.39 | 2.29 | 2.19 | 2.08 | 2.01 | 1.96 |
Table \(\PageIndex{1}\): The F-Distribution Table for α = 0.005
Author
"13.10: The F-Distribution for Alpha = 0.005" by Alfie Swan is in the Public Domain, CC0