4.3: Appendix C- Critical Values for F (F Table)
- Page ID
- 48659
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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 in this table are for \(p = .05\).
|
\(df\): Denominator (Within) |
\(df\): Numerator (Between) |
||||||||||||||
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
14 |
16 |
20 |
|
|
1 |
161 |
200 |
216 |
225 |
230 |
234 |
237 |
239 |
241 |
242 |
243 |
244 |
245 |
246 |
248 |
|
2 |
18.51 |
19.00 |
19.16 |
19.25 |
19.30 |
19.33 |
19.36 |
19.37 |
19.38 |
19.39 |
19.40 |
19.41 |
19.42 |
19.43 |
19.44 |
|
3 |
10.13 |
9.55 |
9.28 |
9.12 |
9.01 |
8.94 |
8.88 |
8.84 |
8.81 |
8.78 |
8.76 |
8.74 |
8.71 |
8.69 |
8.66 |
|
4 |
7.71 |
6.94 |
6.59 |
6.39 |
6.26 |
6.16 |
6.09 |
6.04 |
6.00 |
5.96 |
5.93 |
5.91 |
5.87 |
5.84 |
5.80 |
|
5 |
6.61 |
5.79 |
5.41 |
5.19 |
5.05 |
4.95 |
4.88 |
4.82 |
4.78 |
4.74 |
4.70 |
4.68 |
4.64 |
4.60 |
4.56 |
|
6 |
5.99 |
5.14 |
4.76 |
4.53 |
4.39 |
4.28 |
4.21 |
4.15 |
4.10 |
4.06 |
4.03 |
4.00 |
3.96 |
3.92 |
3.87 |
|
7 |
5.59 |
4.74 |
4.35 |
4.12 |
3.97 |
3.87 |
3.79 |
3.73 |
3.68 |
3.63 |
3.60 |
3.57 |
3.52 |
3.49 |
3.44 |
|
8 |
5.32 |
4.46 |
4.07 |
3.84 |
3.69 |
3.58 |
3.50 |
3.44 |
3.39 |
3.34 |
3.31 |
3.28 |
3.23 |
3.20 |
3.15 |
|
9 |
5.12 |
4.26 |
3.86 |
3.63 |
3.48 |
3.37 |
3.29 |
3.23 |
3.18 |
3.13 |
3.10 |
3.07 |
3.02 |
2.98 |
2.93 |
|
10 |
4.96 |
4.10 |
3.71 |
3.48 |
3.33 |
3.22 |
3.14 |
3.07 |
3.02 |
2.97 |
2.94 |
2.91 |
2.86 |
2.82 |
2.77 |
|
11 |
4.84 |
3.98 |
3.59 |
3.36 |
3.20 |
3.09 |
3.01 |
2.95 |
2.90 |
2.86 |
2.82 |
2.79 |
2.74 |
2.70 |
2.65 |
|
12 |
4.75 |
3.88 |
3.49 |
3.26 |
3.11 |
3.00 |
2.92 |
2.85 |
2.80 |
2.76 |
2.72 |
2.69 |
2.64 |
2.60 |
2.54 |
|
13 |
4.67 |
3.80 |
3.41 |
3.18 |
3.02 |
2.92 |
2.84 |
2.77 |
2.72 |
2.67 |
2.63 |
2.60 |
2.55 |
2.51 |
2.46 |
|
14 |
4.60 |
3.74 |
3.34 |
3.11 |
2.96 |
2.85 |
2.77 |
2.70 |
2.65 |
2.60 |
2.56 |
2.53 |
2.48 |
2.44 |
2.39 |
|
15 |
4.54 |
3.68 |
3.29 |
3.06 |
2.90 |
2.79 |
2.70 |
2.64 |
2.59 |
2.55 |
2.51 |
2.48 |
2.43 |
2.39 |
2.33 |
|
16 |
4.49 |
3.63 |
3.24 |
3.01 |
2.85 |
2.74 |
2.66 |
2.59 |
2.54 |
2.49 |
2.45 |
2.42 |
2.37 |
2.33 |
2.28 |
|
17 |
4.45 |
3.59 |
3.20 |
2.96 |
2.81 |
2.70 |
2.62 |
2.55 |
2.50 |
2.45 |
2.41 |
2.38 |
2.33 |
2.29 |
2.23 |
|
18 |
4.41 |
3.55 |
3.16 |
2.93 |
2.77 |
2.66 |
2.58 |
2.51 |
2.46 |
2.41 |
2.37 |
2.34 |
2.29 |
2.25 |
2.19 |
|
19 |
4.38 |
3.52 |
3.13 |
2.90 |
2.74 |
2.63 |
2.55 |
2.48 |
2.43 |
2.38 |
2.34 |
2.31 |
2.26 |
2.21 |
2.15 |
|
20 |
4.35 |
3.49 |
3.10 |
2.87 |
2.71 |
2.60 |
2.52 |
2.45 |
2.40 |
2.35 |
2.31 |
2.28 |
2.23 |
2.18 |
2.12 |
|
21 |
4.32 |
3.47 |
3.07 |
2.84 |
2.68 |
2.57 |
2.49 |
2.42 |
2.37 |
2.32 |
2.28 |
2.25 |
2.20 |
2.15 |
2.09 |
|
22 |
4.30 |
3.44 |
3.05 |
2.82 |
2.66 |
2.55 |
2.47 |
2.40 |
2.35 |
2.30 |
2.26 |
2.23 |
2.18 |
2.13 |
2.07 |
|
23 |
4.28 |
3.42 |
3.03 |
2.80 |
2.64 |
2.53 |
2.45 |
2.38 |
2.32 |
2.28 |
2.24 |
2.20 |
2.14 |
2.10 |
2.04 |
|
24 |
4.26 |
3.40 |
3.01 |
2.78 |
2.62 |
2.51 |
2.43 |
2.36 |
2.30 |
2.26 |
2.22 |
2.18 |
2.13 |
2.09 |
2.02 |
|
25 |
4.24 |
3.38 |
2.99 |
2.76 |
2.60 |
2.49 |
2.41 |
2.34 |
2.28 |
2.24 |
2.20 |
2.15 |
2.11 |
2.06 |
2.00 |
|
26 |
4.22 |
3.37 |
2.98 |
2.74 |
2.59 |
2.47 |
2.39 |
2.32 |
2.27 |
2.22 |
2.18 |
2.15 |
2.10 |
2.05 |
1.99 |
|
27 |
4.21 |
3.35 |
2.96 |
2.73 |
2.57 |
2.46 |
2.37 |
2.30 |
2.25 |
2.20 |
2.16 |
2.13 |
2.08 |
2.03 |
1.97 |
|
28 |
4.20 |
3.34 |
2.95 |
2.71 |
2.56 |
2.44 |
2.36 |
2.29 |
2.24 |
2.19 |
2.15 |
2.12 |
2.06 |
2.02 |
1.96 |
|
29 |
4.18 |
3.33 |
2.93 |
2.70 |
2.54 |
2.43 |
2.35 |
2.28 |
2.22 |
2.18 |
2.14 |
2.10 |
2.05 |
2.00 |
1.94 |
|
30 |
4.17 |
3.32 |
2.92 |
2.69 |
2.53 |
2.42 |
2.34 |
2.27 |
2.21 |
2.16 |
2.12 |
2.09 |
2.04 |
1.99 |
1.93 |
|
32 |
4.15 |
3.30 |
2.90 |
2.67 |
2.51 |
2.40 |
2.32 |
2.25 |
2.19 |
2.14 |
2.10 |
2.07 |
2.02 |
1.97 |
1.91 |
|
34 |
4.13 |
3.28 |
2.88 |
2.65 |
2.49 |
2.38 |
2.30 |
2.23 |
2.17 |
2.12 |
2.08 |
2.05 |
2.00 |
1.95 |
1.89 |
|
36 |
4.11 |
3.26 |
2.86 |
2.63 |
2.48 |
2.36 |
2.28 |
2.21 |
2.15 |
2.10 |
2.06 |
2.03 |
1.98 |
1.93 |
1.87 |
|
38 |
4.10 |
3.25 |
2.85 |
2.62 |
2.46 |
2.35 |
2.26 |
2.19 |
2.14 |
2.09 |
2.05 |
2.02 |
1.96 |
1.92 |
1.85 |
|
40 |
4.08 |
3.23 |
2.84 |
2.61 |
2.45 |
2.34 |
2.25 |
2.18 |
2.12 |
2.07 |
2.04 |
2.00 |
1.95 |
1.90 |
1.84 |
|
42 |
4.07 |
3.22 |
2.83 |
2.59 |
2.44 |
2.32 |
2.24 |
2.17 |
2.11 |
2.06 |
2.02 |
1.99 |
1.94 |
1.89 |
1.82 |
|
44 |
4.06 |
3.21 |
2.82 |
2.58 |
2.43 |
2.31 |
2.23 |
2.16 |
2.10 |
2.05 |
2.01 |
1.98 |
1.92 |
1.88 |
1.81 |
|
46 |
4.05 |
3.20 |
2.81 |
2.57 |
2.42 |
2.30 |
2.22 |
2.14 |
2.09 |
2.04 |
2.00 |
1.97 |
1.91 |
1.87 |
1.80 |
|
48 |
4.04 |
3.19 |
2.80 |
2.56 |
2.41 |
2.30 |
2.21 |
2.14 |
2.08 |
2.03 |
1.99 |
1.96 |
1.90 |
1.86 |
1.79 |
|
50 |
4.03 |
3.18 |
2.79 |
2.56 |
2.40 |
2.29 |
2.20 |
2.13 |
2.07 |
2.02 |
1.98 |
1.95 |
1.90 |
1.85 |
1.78 |
|
55 |
4.02 |
3.17 |
2.78 |
2.54 |
2.38 |
2.27 |
2.18 |
2.11 |
2.05 |
2.00 |
1.97 |
1.93 |
1.88 |
1.83 |
1.76 |
|
60 |
4.00 |
3.15 |
2.76 |
2.52 |
2.37 |
2.25 |
2.17 |
2.10 |
2.04 |
1.99 |
1.95 |
1.92 |
1.86 |
1.81 |
1.75 |
|
65 |
3.99 |
3.14 |
2.75 |
2.51 |
2.36 |
2.24 |
2.15 |
2.08 |
2.02 |
1.98 |
1.94 |
1.90 |
1.85 |
1.80 |
1.73 |
|
70 |
3.98 |
3.13 |
2.74 |
2.50 |
2.35 |
2.23 |
2.14 |
2.07 |
2.01 |
1.97 |
1.93 |
1.89 |
1.84 |
1.79 |
1.72 |
|
80 |
3.96 |
3.11 |
2.72 |
2.48 |
2.33 |
2.21 |
2.12 |
2.05 |
1.99 |
1.95 |
1.91 |
1.88 |
1.82 |
1.77 |
1.70 |
|
100 |
3.94 |
3.09 |
2.70 |
2.46 |
2.30 |
2.19 |
2.10 |
2.03 |
1.97 |
1.92 |
1.88 |
1.85 |
1.79 |
1.75 |
1.68 |
|
125 |
3.92 |
3.07 |
2.68 |
2.44 |
2.29 |
2.17 |
2.08 |
2.01 |
1.95 |
1.90 |
1.86 |
1.83 |
1.77 |
1.72 |
1.65 |
|
150 |
3.91 |
3.06 |
2.67 |
2.43 |
2.27 |
2.16 |
2.07 |
2.00 |
1.94 |
1.89 |
1.85 |
1.82 |
1.76 |
1.71 |
1.64 |
|
200 |
3.89 |
3.04 |
2.65 |
2.41 |
2.26 |
2.14 |
2.05 |
1.98 |
1.92 |
1.87 |
1.83 |
1.80 |
1.74 |
1.69 |
1.62 |
|
400 |
3.86 |
3.02 |
2.62 |
2.39 |
2.23 |
2.12 |
2.03 |
1.96 |
1.90 |
1.85 |
1.81 |
1.78 |
1.72 |
1.67 |
1.60 |
|
1,000 |
3.85 |
3.00 |
2.61 |
2.38 |
2.22 |
2.10 |
2.02 |
1.95 |
1.89 |
1.84 |
1.80 |
1.76 |
1.70 |
1.65 |
1.58 |
|
∞ |
3.84 |
2.99 |
2.60 |
2.37 |
2.21 |
2.09 |
2.01 |
1.94 |
1.88 |
1.83 |
1.79 |
1.75 |
1.69 |
1.64 |
1.57 |