When: α = .05 (one-tailed test) α = .10 (two-tailed test)
Numerator Degrees of Freedom | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
V1 | V2 | 11 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
Denominator Degrees of Freedom | 1 | 242.98 | 243.86 | 245.93 | 248.01 | 249.05 | 250.09 | 251.14 | 252.17 | 253.25 | 254.33 |
2 | 19.41 | 19.41 | 19.43 | 19.45 | 19.45 | 19.46 | 19.47 | 19.48 | 19.49 | 19.50 | |
3 | 8.76 | 8.74 | 8.70 | 8.66 | 8.64 | 8.62 | 8.59 | 8.57 | 8.55 | 8.53 | |
4 | 5.94 | 5.91 | 5.86 | 5.80 | 5.77 | 5.75 | 5.72 | 5.69 | 5.66 | 5.63 | |
5 | 4.70 | 4.68 | 4.62 | 4.56 | 4.53 | 4.50 | 4.46 | 4.43 | 4.40 | 4.36 | |
6 | 4.03 | 4.00 | 3.94 | 3.87 | 3.84 | 3.81 | 3.77 | 3.74 | 3.70 | 3.67 | |
7 | 3.60 | 3.57 | 3.51 | 3.44 | 3.41 | 3.38 | 3.34 | 3.30 | 3.27 | 3.23 | |
8 | 3.31 | 3.28 | 3.22 | 3.15 | 3.12 | 3.08 | 3.04 | 3.01 | 2.97 | 2.93 | |
9 | 3.10 | 3.07 | 3.01 | 2.94 | 2.90 | 2.86 | 2.83 | 2.79 | 2.75 | 2.71 | |
10 | 2.94 | 2.91 | 2.85 | 2.77 | 2.74 | 2.70 | 2.66 | 2.62 | 2.58 | 2.54 | |
11 | 2.82 | 2.79 | 2.72 | 2.65 | 2.61 | 2.57 | 2.53 | 2.49 | 2.45 | 2.40 | |
12 | 2.72 | 2.69 | 2.62 | 2.54 | 2.51 | 2.47 | 2.43 | 2.38 | 2.34 | 2.30 | |
13 | 2.64 | 2.60 | 2.53 | 2.46 | 2.42 | 2.38 | 2.34 | 2.30 | 2.25 | 2.21 | |
14 | 2.57 | 2.53 | 2.46 | 2.39 | 2.35 | 2.31 | 2.27 | 2.22 | 2.18 | 2.13 | |
15 | 2.51 | 2.48 | 2.40 | 2.33 | 2.29 | 2.25 | 2.20 | 2.16 | 2.11 | 2.07 | |
16 | 2.46 | 2.42 | 2.35 | 2.28 | 2.24 | 2.19 | 2.15 | 2.11 | 2.06 | 2.01 | |
17 | 2.41 | 2.38 | 2.31 | 2.23 | 2.19 | 2.15 | 2.10 | 2.06 | 2.01 | 1.96 | |
18 | 2.37 | 2.34 | 2.27 | 2.19 | 2.15 | 2.11 | 2.06 | 2.02 | 1.97 | 1.92 | |
19 | 2.34 | 2.31 | 2.23 | 2.16 | 2.11 | 2.07 | 2.03 | 1.98 | 1.93 | 1.88 | |
20 | 2.31 | 2.28 | 2.20 | 2.12 | 2.08 | 2.04 | 1.99 | 1.95 | 1.90 | 1.84 | |
21 | 2.28 | 2.25 | 2.18 | 2.10 | 2.05 | 2.01 | 1.96 | 1.92 | 1.87 | 1.81 | |
22 | 2.26 | 2.23 | 2.15 | 2.07 | 2.03 | 1.98 | 1.94 | 1.89 | 1.84 | 1.78 | |
23 | 2.24 | 2.20 | 2.13 | 2.05 | 2.01 | 1.96 | 1.91 | 1.86 | 1.81 | 1.76 | |
24 | 2.22 | 2.18 | 2.11 | 2.03 | 1.98 | 1.94 | 1.89 | 1.84 | 1.79 | 1.73 | |
25 | 2.20 | 2.16 | 2.09 | 2.01 | 1.96 | 1.92 | 1.87 | 1.82 | 1.77 | 1.71 | |
26 | 2.18 | 2.15 | 2.07 | 1.99 | 1.95 | 1.90 | 1.85 | 1.80 | 1.75 | 1.69 | |
27 | 2.17 | 2.13 | 2.06 | 1.97 | 1.93 | 1.88 | 1.84 | 1.79 | 1.73 | 1.67 | |
28 | 2.15 | 2.12 | 2.04 | 1.96 | 1.91 | 1.87 | 1.82 | 1.77 | 1.71 | 1.65 | |
29 | 2.14 | 2.10 | 2.03 | 1.94 | 1.90 | 1.85 | 1.81 | 1.75 | 1.70 | 1.64 | |
30 | 2.13 | 2.09 | 2.01 | 1.93 | 1.89 | 1.84 | 1.79 | 1.74 | 1.68 | 1.62 | |
40 | 2.04 | 2.00 | 1.92 | 1.84 | 1.79 | 1.74 | 1.69 | 1.64 | 1.58 | 1.52 | |
50 | 1.99 | 1.95 | 1.87 | 1.78 | 1.74 | 1.69 | 1.63 | 1.58 | 1.51 | 1.46 | |
60 | 1.95 | 1.92 | 1.84 | 1.75 | 1.70 | 1.65 | 1.59 | 1.53 | 1.47 | 1.42 | |
70 | 1.93 | 1.89 | 1.81 | 1.72 | 1.67 | 1.62 | 1.57 | 1.51 | 1.44 | 1.39 | |
80 | 1.91 | 1.88 | 1.79 | 1.70 | 1.65 | 1.60 | 1.55 | 1.48 | 1.41 | 1.36 | |
90 | 1.90 | 1.86 | 1.78 | 1.69 | 1.64 | 1.59 | 1.53 | 1.47 | 1.39 | 1.33 | |
100 | 1.89 | 1.85 | 1.77 | 1.68 | 1.63 | 1.57 | 1.52 | 1.45 | 1.38 | 1.30 | |
110 | 1.88 | 1.84 | 1.76 | 1.67 | 1.62 | 1.56 | 1.50 | 1.44 | 1.36 | 1.27 | |
120 | 1.87 | 1.83 | 1.75 | 1.66 | 1.61 | 1.55 | 1.50 | 1.43 | 1.35 | 1.25 | |
∞ | 1.79 | 1.75 | 1.67 | 1.57 | 1.52 | 1.46 | 1.39 | 1.32 | 1.22 | 1.00 | |
Critical values computed by John Timko. Used by permission. |