When: α = .025 (one-tailed test) α = .05 (two-tailed test)
Numerator Degrees of Freedom | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
V1 | V2 | 11 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
Denominator Degrees of Freedom | 1 | 973.02 | 976.70 | 984.87 | 993.10 | 996.94 | 1001.2 | 1005.5 | 1009.8 | 1014.0 | 1018.0 |
2 | 39.41 | 39.41 | 39.43 | 39.45 | 39.46 | 39.46 | 39.47 | 39.48 | 39.49 | 39.50 | |
3 | 14.37 | 14.34 | 14.25 | 14.17 | 14.12 | 14.08 | 14.04 | 13.99 | 13.95 | 13.90 | |
4 | 8.79 | 8.75 | 8.66 | 8.56 | 8.51 | 8.46 | 8.41 | 8.36 | 8.31 | 8.26 | |
5 | 6.57 | 6.52 | 6.43 | 6.33 | 6.28 | 6.23 | 6.18 | 6.12 | 6.07 | 6.02 | |
6 | 5.41 | 5.37 | 5.27 | 5.17 | 5.12 | 5.07 | 5.01 | 4.96 | 4.90 | 4.85 | |
7 | 4.71 | 4.67 | 4.57 | 4.47 | 4.42 | 4.36 | 4.31 | 4.25 | 4.20 | 4.14 | |
8 | 4.24 | 4.20 | 4.10 | 4.00 | 3.95 | 3.89 | 3.84 | 3.78 | 3.73 | 3.67 | |
9 | 3.91 | 3.87 | 3.77 | 3.67 | 3.61 | 3.56 | 3.51 | 3.45 | 3.39 | 3.33 | |
10 | 3.67 | 3.62 | 3.52 | 3.42 | 3.37 | 3.31 | 3.26 | 3.20 | 3.14 | 3.08 | |
11 | 3.47 | 3.43 | 3.33 | 3.23 | 3.17 | 3.12 | 3.06 | 3.00 | 2.94 | 2.88 | |
12 | 3.32 | 3.28 | 3.18 | 3.07 | 3.02 | 2.96 | 2.91 | 2.85 | 2.79 | 2.72 | |
13 | 3.20 | 3.15 | 3.05 | 2.95 | 2.89 | 2.84 | 2.78 | 2.72 | 2.66 | 2.60 | |
14 | 3.09 | 3.05 | 2.95 | 2.84 | 2.79 | 2.73 | 2.67 | 2.61 | 2.55 | 2.49 | |
15 | 3.01 | 2.96 | 2.86 | 2.76 | 2.70 | 2.64 | 2.59 | 2.52 | 2.46 | 2.40 | |
16 | 2.93 | 2.89 | 2.79 | 2.68 | 2.63 | 2.57 | 2.51 | 2.45 | 2.38 | 2.32 | |
17 | 2.87 | 2.82 | 2.72 | 2.62 | 2.56 | 2.50 | 2.44 | 2.38 | 2.32 | 2.25 | |
18 | 2.81 | 2.77 | 2.67 | 2.56 | 2.50 | 2.44 | 2.38 | 2.32 | 2.26 | 2.19 | |
19 | 2.77 | 2.72 | 2.62 | 2.51 | 2.45 | 2.39 | 2.33 | 2.27 | 2.20 | 2.13 | |
20 | 2.72 | 2.68 | 2.57 | 2.46 | 2.41 | 2.35 | 2.29 | 2.22 | 2.16 | 2.09 | |
21 | 2.68 | 2.64 | 2.53 | 2.42 | 2.37 | 2.31 | 2.25 | 2.18 | 2.11 | 2.04 | |
22 | 2.65 | 2.60 | 2.50 | 2.39 | 2.33 | 2.27 | 2.21 | 2.14 | 2.08 | 2.00 | |
23 | 2.62 | 2.57 | 2.47 | 2.36 | 2.30 | 2.24 | 2.18 | 2.11 | 2.04 | 1.97 | |
24 | 2.59 | 2.54 | 2.44 | 2.33 | 2.27 | 2.21 | 2.15 | 2.08 | 2.01 | 1.94 | |
25 | 2.56 | 2.51 | 2.41 | 2.30 | 2.24 | 2.18 | 2.12 | 2.05 | 1.98 | 1.91 | |
26 | 2.54 | 2.49 | 2.39 | 2.28 | 2.22 | 2.16 | 2.09 | 2.03 | 1.95 | 1.88 | |
27 | 2.51 | 2.47 | 2.36 | 2.25 | 2.19 | 2.13 | 2.07 | 2.00 | 1.93 | 1.85 | |
28 | 2.49 | 2.45 | 2.34 | 2.23 | 2.17 | 2.11 | 2.05 | 1.98 | 1.91 | 1.83 | |
29 | 2.48 | 2.43 | 2.32 | 2.21 | 2.15 | 2.09 | 2.03 | 1.96 | 1.89 | 1.81 | |
30 | 2.46 | 2.41 | 2.31 | 2.20 | 2.14 | 2.07 | 2.01 | 1.94 | 1.87 | 1.64 | |
40 | 2.33 | 2.29 | 2.18 | 2.07 | 2.01 | 1.94 | 1.88 | 1.80 | 1.72 | 1.56 | |
50 | 2.26 | 2.22 | 2.11 | 1.99 | 1.93 | 1.87 | 1.80 | 1.72 | 1.64 | 1.52 | |
60 | 2.22 | 2.17 | 2.06 | 1.94 | 1.88 | 1.82 | 1.74 | 1.67 | 1.58 | 1.48 | |
70 | 2.18 | 2.14 | 2.03 | 1.91 | 1.85 | 1.78 | 1.71 | 1.63 | 1.54 | 1.44 | |
80 | 2.16 | 2.11 | 2.00 | 1.88 | 1.82 | 1.75 | 1.68 | 1.60 | 1.51 | 1.40 | |
90 | 2.14 | 2.09 | 1.98 | 1.86 | 1.80 | 1.73 | 1.66 | 1.58 | 1.48 | 1.36 | |
100 | 2.12 | 2.08 | 1.97 | 1.85 | 1.78 | 1.72 | 1.64 | 1.56 | 1.46 | 1.32 | |
110 | 2.11 | 2.07 | 1.96 | 1.84 | 1.77 | 1.70 | 1.63 | 1.54 | 1.45 | 1.28 | |
120 | 2.10 | 2.06 | 1.95 | 1.83 | 1.76 | 1.69 | 1.61 | 1.53 | 1.43 | 1.24 | |
∞ | 2.02 | 1.94 | 1.83 | 1.71 | 1.64 | 1.57 | 1.48 | 1.39 | 1.27 | 1.00 | |
Critical values computed by John Timko. Used by permission. |