When: α = .01 (one-tailed test) α = .02 (two-tailed test)
Numerator Degrees of Freedom | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
V1 | V2 | 11 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | α |
Denominator Degrees of Freedom | 1 | 6,083 | 6,106 | 6,157 | 6,209 | 6,235 | 6,261 | 6,287 | 6,313 | 6,339 | 6,366 |
2 | 99.41 | 99.42 | 99.43 | 99.45 | 99.46 | 99.47 | 99.47 | 99.48 | 99.49 | 99.50 | |
3 | 27.13 | 27.05 | 26.87 | 26.69 | 26.60 | 26.50 | 26.41 | 26.32 | 26.22 | 26.13 | |
4 | 14.45 | 14.37 | 14.20 | 14.02 | 13.93 | 13.84 | 13.75 | 13.65 | 13.56 | 13.46 | |
5 | 9.96 | 9.89 | 9.72 | 9.55 | 9.47 | 9.38 | 9.29 | 9.20 | 9.11 | 9.02 | |
6 | 7.79 | 7.72 | 7.56 | 7.40 | 7.31 | 7.23 | 7.14 | 7.06 | 6.97 | 6.88 | |
7 | 6.54 | 6.47 | 6.31 | 6.16 | 6.07 | 5.99 | 5.91 | 5.82 | 5.74 | 5.65 | |
8 | 5.73 | 5.67 | 5.52 | 5.36 | 5.28 | 5.20 | 5.12 | 5.03 | 4.95 | 4.86 | |
9 | 5.18 | 5.11 | 4.96 | 4.81 | 4.73 | 4.65 | 4.57 | 4.48 | 4.40 | 4.31 | |
10 | 4.77 | 4.71 | 4.56 | 4.41 | 4.33 | 4.25 | 4.17 | 4.08 | 4.00 | 3.91 | |
11 | 4.46 | 4.40 | 4.25 | 4.10 | 4.02 | 3.94 | 3.86 | 3.78 | 3.69 | 3.60 | |
12 | 4.22 | 4.16 | 4.01 | 3.86 | 3.78 | 3.70 | 3.62 | 3.54 | 3.45 | 3.36 | |
13 | 4.02 | 3.96 | 3.82 | 3.66 | 3.59 | 3.51 | 3.43 | 3.34 | 3.25 | 3.17 | |
14 | 3.86 | 3.80 | 3.66 | 3.51 | 3.43 | 3.35 | 3.27 | 3.18 | 3.09 | 3.00 | |
15 | 3.73 | 3.67 | 3.52 | 3.37 | 3.29 | 3.21 | 3.13 | 3.05 | 2.96 | 2.87 | |
16 | 3.62 | 3.55 | 3.41 | 3.26 | 3.18 | 3.10 | 3.02 | 2.93 | 2.84 | 2.75 | |
17 | 3.52 | 3.46 | 3.31 | 3.16 | 3.08 | 3.00 | 2.92 | 2.83 | 2.75 | 2.65 | |
18 | 3.43 | 3.37 | 3.23 | 3.08 | 3.00 | 2.92 | 2.84 | 2.75 | 2.66 | 2.57 | |
19 | 3.36 | 3.30 | 3.15 | 3.00 | 2.92 | 2.84 | 2.76 | 2.67 | 2.58 | 2.49 | |
20 | 3.29 | 3.23 | 3.09 | 2.94 | 2.86 | 2.78 | 2.69 | 2.61 | 2.52 | 2.42 | |
21 | 3.24 | 3.17 | 3.03 | 2.88 | 2.80 | 2.72 | 2.64 | 2.55 | 2.46 | 2.36 | |
22 | 3.18 | 3.12 | 2.98 | 2.83 | 2.75 | 2.67 | 2.58 | 2.50 | 2.40 | 2.31 | |
23 | 3.14 | 3.07 | 2.93 | 2.78 | 2.70 | 2.62 | 2.54 | 2.45 | 2.35 | 2.26 | |
24 | 3.09 | 3.03 | 2.89 | 2.74 | 2.66 | 2.58 | 2.49 | 2.40 | 2.31 | 2.21 | |
25 | 3.06 | 2.99 | 2.85 | 2.70 | 2.62 | 2.54 | 2.45 | 2.36 | 2.27 | 2.17 | |
26 | 3.02 | 2.96 | 2.81 | 2.66 | 2.58 | 2.50 | 2.42 | 2.33 | 2.23 | 2.13 | |
27 | 2.99 | 2.93 | 2.78 | 2.63 | 2.55 | 2.47 | 2.38 | 2.29 | 2.20 | 2.10 | |
28 | 2.96 | 2.90 | 2.75 | 2.60 | 2.52 | 2.44 | 2.35 | 2.26 | 2.17 | 2.06 | |
29 | 2.93 | 2.87 | 2.73 | 2.57 | 2.49 | 2.41 | 2.33 | 2.23 | 2.14 | 2.03 | |
30 | 2.91 | 2.84 | 2.70 | 2.55 | 2.47 | 2.39 | 2.30 | 2.21 | 2.11 | 2.01 | |
40 | 2.73 | 2.66 | 2.52 | 2.37 | 2.29 | 2.20 | 2.11 | 2.02 | 1.92 | 1.80 | |
50 | 2.63 | 2.56 | 2.42 | 2.27 | 2.18 | 2.10 | 2.01 | 1.91 | 1.80 | 1.70 | |
60 | 2.56 | 2.50 | 2.35 | 2.20 | 2.12 | 2.03 | 1.94 | 1.84 | 1.73 | 1.60 | |
70 | 2.51 | 2.45 | 2.31 | 2.15 | 2.07 | 1.98 | 1.89 | 1.79 | 1.67 | 1.52 | |
80 | 2.48 | 2.42 | 2.27 | 2.12 | 2.03 | 1.94 | 1.85 | 1.75 | 1.63 | 1.44 | |
90 | 2.45 | 2.39 | 2.24 | 2.09 | 2.00 | 1.92 | 1.82 | 1.72 | 1.60 | 1.36 | |
100 | 2.43 | 2.37 | 2.22 | 2.07 | 1.98 | 1.89 | 1.80 | 1.69 | 1.57 | 1.28 | |
110 | 2.41 | 2.35 | 2.21 | 2.05 | 1.97 | 1.88 | 1.78 | 1.67 | 1.55 | 1.20 | |
120 | 2.40 | 2.34 | 2.19 | 2.04 | 1.95 | 1.86 | 1.76 | 1.66 | 1.53 | 1.10 | |
∞ | 2.39 | 2.18 | 2.04 | 1.88 | 1.79 | 1.70 | 1.59 | 1.47 | 1.32 | 1.00 | |
Critical values computed by John Timko. Used by permission. |