Table A
ν2 Denominator | Numerator Degrees of Freedom (ν1) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 39.86 | 49.50 | 53.59 | 55.83 | 57.24 | 58.20 | 58.91 | 59.44 | 59.86 | 60.19 |
2 | 8.53 | 9.00 | 9.16 | 9.24 | 9.29 | 9.33 | 9.35 | 9.37 | 9.38 | 9.39 |
3 | 5.54 | 5.46 | 5.39 | 5.34 | 5.31 | 5.28 | 5.27 | 5.25 | 5.24 | 5.23 |
4 | 4.54 | 4.32 | 4.19 | 4.11 | 4.05 | 4.01 | 3.98 | 3.95 | 3.94 | 3.92 |
5 | 4.06 | 3.78 | 3.62 | 3.52 | 3.45 | 3.40 | 3.37 | 3.34 | 3.32 | 3.30 |
6 | 3.78 | 3.46 | 3.29 | 3.18 | 3.11 | 3.05 | 3.01 | 2.98 | 2.96 | 2.94 |
7 | 3.59 | 3.26 | 3.07 | 2.96 | 2.88 | 2.83 | 2.78 | 2.75 | 2.72 | 2.70 |
8 | 3.46 | 3.11 | 2.92 | 2.81 | 2.73 | 2.67 | 2.62 | 2.59 | 2.56 | 2.54 |
9 | 3.36 | 3.01 | 2.81 | 2.69 | 2.61 | 2.55 | 2.51 | 2.47 | 2.44 | 2.42 |
10 | 3.29 | 2.92 | 2.73 | 2.61 | 2.52 | 2.46 | 2.41 | 2.38 | 2.35 | 2.32 |
11 | 3.23 | 2.86 | 2.66 | 2.54 | 2.45 | 2.39 | 2.34 | 2.30 | 2.27 | 2.25 |
12 | 3.18 | 2.81 | 2.61 | 2.48 | 2.39 | 2.33 | 2.28 | 2.24 | 2.21 | 2.19 |
13 | 3.14 | 2.76 | 2.56 | 2.43 | 2.35 | 2.28 | 2.23 | 2.20 | 2.16 | 2.14 |
14 | 3.10 | 2.73 | 2.52 | 2.39 | 2.31 | 2.24 | 2.19 | 2.15 | 2.12 | 2.10 |
15 | 3.07 | 2.70 | 2.49 | 2.36 | 2.27 | 2.21 | 2.16 | 2.12 | 2.09 | 2.06 |
16 | 3.05 | 2.67 | 2.46 | 2.33 | 2.24 | 2.18 | 2.13 | 2.09 | 2.06 | 2.03 |
17 | 3.03 | 2.64 | 2.44 | 2.31 | 2.22 | 2.15 | 2.10 | 2.06 | 2.03 | 2.00 |
18 | 3.01 | 2.62 | 2.42 | 2.29 | 2.20 | 2.13 | 2.08 | 2.04 | 2.00 | 1.98 |
19 | 2.99 | 2.61 | 2.40 | 2.27 | 2.18 | 2.11 | 2.06 | 2.02 | 1.98 | 1.96 |
20 | 2.97 | 2.59 | 2.38 | 2.25 | 2.16 | 2.09 | 2.04 | 2.00 | 1.96 | 1.94 |
21 | 2.96 | 2.57 | 2.36 | 2.23 | 2.14 | 2.08 | 2.02 | 1.98 | 1.95 | 1.92 |
22 | 2.95 | 2.56 | 2.35 | 2.22 | 2.13 | 2.06 | 2.01 | 1.97 | 1.93 | 1.90 |
23 | 2.94 | 2.55 | 2.34 | 2.21 | 2.11 | 2.05 | 1.99 | 1.95 | 1.92 | 1.89 |
24 | 2.93 | 2.54 | 2.33 | 2.19 | 2.10 | 2.04 | 1.98 | 1.94 | 1.91 | 1.88 |
25 | 2.92 | 2.53 | 2.32 | 2.18 | 2.09 | 2.02 | 1.97 | 1.93 | 1.89 | 1.87 |
26 | 2.91 | 2.52 | 2.31 | 2.17 | 2.08 | 2.01 | 1.96 | 1.92 | 1.88 | 1.86 |
27 | 2.90 | 2.51 | 2.30 | 2.17 | 2.07 | 2.00 | 1.95 | 1.91 | 1.87 | 1.85 |
28 | 2.89 | 2.50 | 2.29 | 2.16 | 2.06 | 2.00 | 1.94 | 1.90 | 1.87 | 1.84 |
29 | 2.89 | 2.50 | 2.28 | 2.15 | 2.06 | 1.99 | 1.93 | 1.89 | 1.86 | 1.83 |
30 | 2.88 | 2.49 | 2.28 | 2.14 | 2.05 | 1.98 | 1.93 | 1.88 | 1.85 | 1.82 |
35 | 2.85 | 2.46 | 2.25 | 2.11 | 2.02 | 1.95 | 1.90 | 1.85 | 1.82 | 1.79 |
40 | 2.84 | 2.44 | 2.23 | 2.09 | 2.00 | 1.93 | 1.87 | 1.83 | 1.79 | 1.76 |
45 | 2.82 | 2.42 | 2.21 | 2.07 | 1.98 | 1.91 | 1.85 | 1.81 | 1.77 | 1.74 |
50 | 2.81 | 2.41 | 2.20 | 2.06 | 1.97 | 1.90 | 1.84 | 1.80 | 1.76 | 1.73 |
100 | 2.76 | 2.36 | 2.14 | 2.00 | 1.91 | 1.83 | 1.78 | 1.73 | 1.69 | 1.66 |
ν2 Denominator | Numerator Degrees of Freedom (ν1) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 161.45 | 199.50 | 215.71 | 224.58 | 230.16 | 233.99 | 236.77 | 238.88 | 240.54 | 241.88 |
2 | 18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.33 | 19.35 | 19.37 | 19.38 | 19.40 |
3 | 10.13 | 9.55 | 9.28 | 9.12 | 9.01 | 8.94 | 8.89 | 8.85 | 8.81 | 8.79 |
4 | 7.71 | 6.94 | 6.59 | 6.39 | 6.26 | 6.16 | 6.09 | 6.04 | 6.00 | 5.96 |
5 | 6.61 | 5.79 | 5.41 | 5.19 | 5.05 | 4.95 | 4.88 | 4.82 | 4.77 | 4.74 |
6 | 5.99 | 5.14 | 4.76 | 4.53 | 4.39 | 4.28 | 4.21 | 4.15 | 4.10 | 4.06 |
7 | 5.59 | 4.74 | 4.35 | 4.12 | 3.97 | 3.87 | 3.79 | 3.73 | 3.68 | 3.64 |
8 | 5.32 | 4.46 | 4.07 | 3.84 | 3.69 | 3.58 | 3.50 | 3.44 | 3.39 | 3.35 |
9 | 5.12 | 4.26 | 3.86 | 3.63 | 3.48 | 3.37 | 3.29 | 3.23 | 3.18 | 3.14 |
10 | 4.96 | 4.10 | 3.71 | 3.48 | 3.33 | 3.22 | 3.14 | 3.07 | 3.02 | 2.98 |
11 | 4.84 | 3.98 | 3.59 | 3.36 | 3.20 | 3.09 | 3.01 | 2.95 | 2.90 | 2.85 |
12 | 4.75 | 3.89 | 3.49 | 3.26 | 3.11 | 3.00 | 2.91 | 2.85 | 2.80 | 2.75 |
13 | 4.67 | 3.81 | 3.41 | 3.18 | 3.03 | 2.92 | 2.83 | 2.77 | 2.71 | 2.67 |
14 | 4.60 | 3.74 | 3.34 | 3.11 | 2.96 | 2.85 | 2.76 | 2.70 | 2.65 | 2.60 |
15 | 4.54 | 3.68 | 3.29 | 3.06 | 2.90 | 2.79 | 2.71 | 2.64 | 2.59 | 2.54 |
16 | 4.49 | 3.63 | 3.24 | 3.01 | 2.85 | 2.74 | 2.66 | 2.59 | 2.54 | 2.49 |
17 | 4.45 | 3.59 | 3.20 | 2.96 | 2.81 | 2.70 | 2.61 | 2.55 | 2.49 | 2.45 |
18 | 4.41 | 3.55 | 3.16 | 2.93 | 2.77 | 2.66 | 2.58 | 2.51 | 2.46 | 2.60 |
19 | 4.38 | 3.52 | 3.13 | 2.90 | 2.74 | 2.63 | 2.54 | 2.48 | 2.42 | 2.38 |
20 | 4.35 | 3.49 | 3.10 | 2.87 | 2.71 | 2.60 | 2.51 | 2.45 | 2.39 | 2.35 |
21 | 4.32 | 3.47 | 3.07 | 2.84 | 2.68 | 2.57 | 2.49 | 2.42 | 2.37 | 2.32 |
22 | 4.30 | 3.44 | 3.05 | 2.82 | 2.66 | 2.55 | 2.46 | 2.40 | 2.34 | 2.30 |
23 | 4.28 | 3.42 | 3.03 | 2.80 | 2.64 | 2.53 | 2.44 | 2.37 | 2.32 | 2.27 |
24 | 4.26 | 3.40 | 3.01 | 2.78 | 2.62 | 2.51 | 2.42 | 2.36 | 2.30 | 2.25 |
25 | 4.24 | 3.39 | 2.99 | 2.76 | 2.00 | 2.49 | 2.40 | 2.34 | 2.28 | 2.24 |
26 | 4.23 | 3.37 | 2.98 | 2.74 | 2.59 | 2.47 | 2.39 | 2.32 | 2.27 | 2.22 |
27 | 4.21 | 3.35 | 2.96 | 2.73 | 2.57 | 2.46 | 2.37 | 2.31 | 2.25 | 2.20 |
28 | 4.20 | 3.34 | 2.95 | 2.71 | 2.56 | 2.45 | 2.36 | 2.29 | 2.24 | 2.19 |
29 | 4.18 | 3.33 | 2.93 | 2.70 | 2.55 | 2.43 | 2.35 | 2.28 | 2.22 | 2.18 |
30 | 4.17 | 3.32 | 2.92 | 2.69 | 2.53 | 2.42 | 2.33 | 2.27 | 2.21 | 2.16 |
35 | 4.12 | 3.27 | 2.87 | 2.64 | 2.49 | 2.37 | 2.29 | 2.22 | 2.16 | 2.11 |
40 | 4.08 | 3.23 | 2.84 | 2.61 | 2.45 | 2.34 | 2.25 | 2.18 | 2.12 | 2.08 |
45 | 4.06 | 3.20 | 2.81 | 2.58 | 2.42 | 2.31 | 2.22 | 2.15 | 2.10 | 2.05 |
50 | 4.03 | 3.18 | 2.79 | 2.56 | 2.40 | 2.29 | 2.20 | 2.13 | 2.07 | 2.03 |
100 | 3.94 | 3.09 | 2.70 | 2.46 | 2.31 | 2.19 | 2.10 | 2.03 | 1.97 | 1.93 |
ν2 Denominator | Numerator Degrees of Freedom (ν1) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 647.8 | 799.5 | 864.2 | 899.6 | 921.8 | 937.1 | 948.2 | 956.7 | 963.3 | 963.3 |
2 | 38.51 | 39.00 | 39.17 | 39.25 | 39.30 | 39.33 | 39.36 | 39.37 | 39.39 | 39.40 |
3 | 17.44 | 16.04 | 15.44 | 15.10 | 14.88 | 14.73 | 14.62 | 14.54 | 14.47 | 14.42 |
4 | 12.22 | 10.65 | 9.98 | 9.60 | 9.36 | 9.20 | 9.07 | 8.98 | 8.90 | 3.84 |
5 | 10.01 | 8.43 | 7.76 | 7.39 | 7.15 | 6.98 | 6.85 | 6.76 | 6.68 | 6.62 |
6 | 8.81 | 7.26 | 6.60 | 6.23 | 5.99 | 5.82 | 5.70 | 5.60 | 5.52 | 5.46 |
7 | 8.07 | 6.54 | 5.89 | 5.52 | 5.29 | 5.12 | 4.99 | 4.90 | 4.82 | 4.76 |
8 | 7.57 | 6.06 | 5.42 | 5.05 | 4.82 | 4.65 | 4.53 | 4.43 | 4.36 | 4.30 |
9 | 7.21 | 5.71 | 5.08 | 4.72 | 4.48 | 4.32 | 4.20 | 4.10 | 4.03 | 3.96 |
10 | 6.94 | 5.46 | 4.83 | 4.47 | 4.24 | 4.07 | 3.95 | 3.85 | 3.78 | 3.72 |
11 | 6.72 | 5.26 | 4.63 | 4.28 | 4.04 | 3.88 | 3.76 | 3.66 | 3.59 | 3.53 |
12 | 6.55 | 5.10 | 4.47 | 4.12 | 3.89 | 3.73 | 3.61 | 3.51 | 3.44 | 3.37 |
13 | 6.41 | 4.97 | 4.35 | 4.00 | 3.77 | 3.60 | 3.48 | 3.39 | 3.31 | 3.25 |
14 | 6.30 | 4.86 | 4.24 | 3.89 | 3.66 | 3.50 | 3.38 | 3.29 | 3.21 | 3.15 |
15 | 6.20 | 4.77 | 4.15 | 3.80 | 3.58 | 3.41 | 3.29 | 3.20 | 3.12 | 3.06 |
16 | 6.12 | 4.69 | 4.08 | 3.73 | 3.50 | 3.34 | 3.22 | 3.12 | 3.05 | 2.99 |
17 | 6.04 | 4.62 | 4.01 | 3.66 | 3.44 | 3.28 | 3.16 | 3.06 | 2.98 | 2.92 |
18 | 5.98 | 4.56 | 3.95 | 3.61 | 3.38 | 3.22 | 3.10 | 3.01 | 2.93 | 2.87 |
19 | 5.92 | 4.51 | 3.90 | 3.56 | 3.33 | 3.17 | 3.05 | 2.96 | 2.88 | 2.82 |
20 | 5.87 | 4.46 | 3.86 | 3.51 | 3.29 | 3.13 | 3.01 | 2.91 | 2.84 | 2.77 |
21 | 5.83 | 4.42 | 3.82 | 3.48 | 3.25 | 3.09 | 2.97 | 2.87 | 2.80 | 2.73 |
22 | 5.79 | 4.38 | 3.78 | 3.44 | 3.22 | 3.05 | 2.93 | 2.84 | 2.76 | 2.70 |
23 | 5.75 | 4.35 | 3.75 | 3.41 | 3.18 | 3.02 | 2.90 | 2.81 | 2.73 | 2.67 |
24 | 5.72 | 4.32 | 3.72 | 3.38 | 3.15 | 2.99 | 2.87 | 2.78 | 2.70 | 2.64 |
25 | 5.69 | 4.29 | 3.69 | 3.35 | 3.13 | 2.97 | 2.85 | 2.75 | 2.68 | 2.61 |
26 | 5.66 | 4.27 | 3.67 | 3.33 | 3.10 | 2.94 | 2.82 | 2.73 | 2.65 | 2.59 |
27 | 5.63 | 4.24 | 3.65 | 3.31 | 3.08 | 2.92 | 2.80 | 2.71 | 2.63 | 2.57 |
28 | 5.61 | 4.22 | 3.63 | 3.29 | 3.06 | 2.90 | 2.78 | 2.69 | 2.61 | 2.55 |
29 | 5.59 | 4.20 | 3.61 | 3.27 | 3.04 | 2.88 | 2.76 | 2.67 | 2.59 | 2.53 |
30 | 5.57 | 4.18 | 3.59 | 3.25 | 3.03 | 2.87 | 2.75 | 2.65 | 2.57 | 2.51 |
40 | 5.42 | 4.05 | 3.46 | 3.13 | 2.90 | 2.74 | 2.62 | 2.53 | 2.45 | 2.39 |
60 | 5.29 | 3.93 | 3.34 | 3.01 | 2.79 | 2.63 | 2.51 | 2.41 | 2.33 | 2.27 |
120 | 5.15 | 3.80 | 3.23 | 2.89 | 2.67 | 2.52 | 2.39 | 2.30 | 2.22 | 2.16 |
ν2 Denominator | Numerator Degrees of Freedom (ν1) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
1 | 4,052.2 | 4,999.3 | 5,403.5 | 5,624.3 | 5,764.0 | 5,859.0 | 5,928.3 | 5,981.0 | 6,022.4 | 6,055.9 |
2 | 98.50 | 99.00 | 99.16 | 99.25 | 99.30 | 99.33 | 99.36 | 99.38 | 99.39 | 99.40 |
3 | 34.12 | 30.82 | 29.46 | 28.71 | 28.24 | 27.91 | 27.67 | 27.49 | 27.34 | 27.23 |
4 | 21.20 | 18.00 | 16.69 | 15.98 | 15.52 | 15.21 | 14.98 | 14.80 | 14.66 | 14.55 |
5 | 16.26 | 13.27 | 12.06 | 11.39 | 10.97 | 10.67 | 10.46 | 10.29 | 10.16 | 10.05 |
6 | 13.75 | 10.92 | 9.78 | 9.15 | 8.75 | 8.47 | 8.26 | 8.10 | 7.98 | 7.87 |
7 | 12.25 | 9.55 | 8.45 | 7.85 | 7.46 | 7.19 | 6.99 | 6.84 | 6.72 | 6.62 |
8 | 11.26 | 8.65 | 7.59 | 7.01 | 6.63 | 6.37 | 6.18 | 6.03 | 5.91 | 5.81 |
9 | 10.56 | 8.02 | 6.99 | 6.42 | 6.06 | 5.80 | 5.61 | 5.47 | 5.35 | 5.26 |
10 | 10.04 | 7.56 | 6.55 | 5.99 | 5.64 | 5.39 | 5.20 | 5.06 | 4.94 | 4.85 |
11 | 9.65 | 7.21 | 6.22 | 5.67 | 5.32 | 5.07 | 4.89 | 4.74 | 4.63 | 4.54 |
12 | 9.33 | 6.93 | 5.95 | 5.41 | 5.06 | 4.82 | 4.64 | 4.50 | 4.39 | 4.30 |
13 | 9.07 | 6.70 | 5.74 | 5.21 | 4.86 | 4.62 | 4.44 | 4.30 | 4.19 | 4.10 |
14 | 8.86 | 6.51 | 5.56 | 5.04 | 4.69 | 4.46 | 4.28 | 4.14 | 4.03 | 3.94 |
15 | 8.68 | 6.36 | 5.42 | 4.89 | 4.56 | 4.32 | 4.14 | 4.00 | 3.89 | 3.80 |
16 | 8.53 | 6.23 | 5.29 | 4.77 | 4.44 | 4.20 | 4.03 | 3.89 | 3.78 | 3.69 |
17 | 8.40 | 6.11 | 5.19 | 4.67 | 4.34 | 4.10 | 3.93 | 3.79 | 3.68 | 3.59 |
18 | 8.29 | 6.01 | 5.09 | 4.58 | 4.25 | 4.01 | 3.84 | 3.71 | 3.60 | 3.51 |
19 | 8.18 | 5.93 | 5.01 | 4.50 | 4.17 | 3.94 | 3.77 | 3.63 | 3.52 | 3.43 |
20 | 8.10 | 5.85 | 4.94 | 4.43 | 4.10 | 3.87 | 3.70 | 3.56 | 3.46 | 3.37 |
21 | 8.02 | 5.78 | 4.87 | 4.37 | 4.04 | 3.81 | 3.64 | 3.51 | 3.40 | 3.31 |
22 | 7.95 | 5.72 | 4.82 | 4.31 | 3.99 | 3.76 | 3.59 | 3.45 | 3.35 | 3.26 |
23 | 7.88 | 5.66 | 4.76 | 4.26 | 3.94 | 3.71 | 3.54 | 3.41 | 3.30 | 3.21 |
24 | 7.82 | 5.61 | 4.72 | 4.22 | 3.90 | 3.67 | 3.50 | 3.36 | 3.26 | 3.17 |
25 | 7.77 | 5.57 | 4.68 | 4.18 | 3.85 | 3.63 | 3.46 | 3.32 | 3.22 | 3.13 |
26 | 7.72 | 5.53 | 4.64 | 4.14 | 3.82 | 3.59 | 3.42 | 3.29 | 3.18 | 3.09 |
27 | 7.68 | 5.49 | 4.60 | 4.11 | 3.78 | 3.56 | 3.39 | 3.26 | 3.15 | 3.06 |
28 | 7.64 | 5.45 | 4.57 | 4.07 | 3.75 | 3.53 | 3.36 | 3.23 | 3.12 | 3.03 |
29 | 7.60 | 5.42 | 4.54 | 4.04 | 3.73 | 3.50 | 3.33 | 3.20 | 3.09 | 3.00 |
30 | 7.56 | 5.39 | 4.51 | 4.02 | 3.70 | 3.47 | 3.30 | 3.17 | 3.07 | 2.98 |
35 | 7.42 | 5.27 | 4.40 | 3.91 | 3.59 | 3.37 | 3.20 | 3.07 | 2.96 | 2.88 |
40 | 7.31 | 5.18 | 4.31 | 3.83 | 3.51 | 3.29 | 3.12 | 2.99 | 2.89 | 2.80 |
45 | 7.23 | 5.11 | 4.25 | 3.77 | 3.45 | 3.23 | 3.07 | 2.94 | 2.83 | 2.74 |
50 | 7.17 | 5.06 | 4.20 | 3.72 | 3.41 | 3.19 | 3.02 | 2.89 | 2.78 | 2.70 |
100 | 6.90 | 4.82 | 3.98 | 3.51 | 3.21 | 2.99 | 2.82 | 2.69 | 2.59 | 2.50 |
Critical values of the Snedecor’s F-distribution.
Table B
Degrees of Freedom ν | Associated Probability for a Right-Tailed Test | ||||||||
---|---|---|---|---|---|---|---|---|---|
0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 | 0.0005 | |
1 | 1.000 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 | 127.3 | 318.309 | 636.619 |
2 | 0.816 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 | 14.09 | 22.33 | 31.60 |
3 | 0.765 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 | 7.453 | 10.21 | 12.92 |
4 | 0.741 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 | 5.598 | 7.173 | 8.610 |
5 | 0.727 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 | 4.773 | 5.894 | 6.869 |
6 | 0.718 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 | 4.317 | 5.208 | 5.959 |
7 | 0.711 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 | 4.029 | 4.785 | 5.408 |
8 | 0.706 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 | 3.833 | 4.501 | 5.041 |
9 | 0.703 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 | 3.690 | 4.297 | 4.781 |
10 | 0.700 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 | 3.581 | 4.144 | 4.587 |
11 | 0.697 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 | 3.497 | 4.025 | 4.437 |
12 | 0.695 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 | 3.428 | 3.930 | 4.318 |
13 | 0.694 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 | 3.372 | 3.852 | 4.221 |
14 | 0.692 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 | 3.326 | 3.787 | 4.140 |
15 | 0.691 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 | 3.286 | 3.733 | 4.073 |
16 | 0.690 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 | 3.252 | 3.686 | 4.015 |
17 | 0.689 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 | 3.222 | 3.646 | 3.965 |
18 | 0.688 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 | 3.197 | 3.610 | 3.922 |
19 | 0.688 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 | 3.174 | 3.579 | 3.883 |
20 | 0.687 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 | 3.153 | 3.552 | 3.850 |
21 | 0.686 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 | 3.135 | 3.527 | 3.819 |
22 | 0.686 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 | 3.119 | 3.505 | 3.792 |
23 | 0.685 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 | 3.104 | 3.485 | 3.768 |
24 | 0.685 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 | 3.091 | 3.467 | 3.745 |
25 | 0.684 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 | 3.078 | 3.450 | 3.725 |
26 | 0.684 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 | 3.067 | 3.435 | 3.707 |
27 | 0.684 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 | 3.057 | 3.421 | 3.689 |
28 | 0.683 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 | 3.047 | 3.408 | 3.674 |
29 | 0.683 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 | 3.038 | 3.396 | 3.660 |
30 | 0.683 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 | 3.030 | 3.385 | 3.646 |
35 | 0.682 | 1.306 | 1.690 | 2.030 | 2.438 | 2.724 | 2.996 | 3.340 | 3.591 |
40 | 0.681 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 | 2.971 | 3.307 | 3.551 |
45 | 0.680 | 1.301 | 1.679 | 2.014 | 2.412 | 2.690 | 2.952 | 3.281 | 3.520 |
50 | 0.679 | 1.299 | 1.676 | 2.009 | 2.403 | 2.678 | 2.937 | 3.261 | 3.496 |
z | 0.674 | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 | 2.807 | 3.090 | 3.291 |
Critical values of the Student’s t-distribution.
Table C
n | k (Number of Parameters – Includes Intercept) | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||||||||||
dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | dL | dU | |
6 | 0.610 | 1.400 | – | – | – | – | – | – | – | – | – | – | – | – | – | – | – | – |
7 | 0.700 | 1.356 | 0.467 | 1.896 | – | – | – | – | – | – | – | – | – | – | – | – | – | – |
8 | 0.763 | 1.332 | 0.559 | 1.777 | 0.367 | 2.287 | – | – | – | – | – | – | – | – | – | – | – | – |
9 | 0.824 | 1.320 | 0.629 | 1.699 | 0.455 | 2.128 | 0.296 | 2.588 | – | – | – | – | – | – | – | – | – | – |
10 | 0.879 | 1.320 | 0.697 | 1.641 | 0.525 | 2.016 | 0.376 | 2.414 | 0.243 | 2.822 | – | – | – | – | – | – | – | – |
11 | 0.927 | 1.324 | 0.758 | 1.604 | 0.595 | 1.928 | 0.444 | 2.283 | 0.315 | 2.645 | 0.203 | 3.004 | – | – | – | – | – | – |
12 | 0.971 | 1.331 | 0.812 | 1.579 | 0.658 | 1.864 | 0.512 | 2.177 | 0.380 | 2.506 | 0.268 | 2.832 | 0.171 | 3.149 | – | – | – | – |
13 | 1.010 | 0.861 | 0.861 | 1.562 | 0.715 | 1.816 | 0.574 | 2.094 | 0.444 | 2.390 | 0.328 | 2.692 | 0.230 | 2.985 | 0.147 | 3.266 | – | – |
14 | 1.045 | 1.350 | 0.905 | 1.551 | 0.767 | 1.779 | 0.632 | 2.030 | 0.505 | 2.296 | 0.389 | 2.572 | 0.286 | 2.848 | 0.200 | 3.111 | 0.127 | 3.360 |
15 | 1.077 | 1.361 | 0.946 | 1.543 | 0.814 | 1.750 | 0.685 | 1.977 | 0.562 | 2.220 | 0.447 | 2.471 | 0.343 | 2.727 | 0.251 | 2.979 | 0.175 | 3.216 |
16 | 1.106 | 1.371 | 0.982 | 1.539 | 0.857 | 1.728 | 0.734 | 1.935 | 0.615 | 2.157 | 0.502 | 2.388 | 0.398 | 2.624 | 0.304 | 2.860 | 0.222 | 3.090 |
17 | 1.133 | 1.381 | 1.015 | 1.536 | 0.897 | 1.710 | 0.779 | 1.900 | 0.664 | 2.104 | 0.554 | 2.318 | 0.451 | 2.537 | 0.356 | 2.757 | 0.272 | 2.975 |
18 | 1.158 | 1.391 | 1.046 | 1.535 | 0.933 | 1.696 | 0.820 | 1.872 | 0.710 | 2.060 | 0.603 | 2.258 | 0.502 | 2.461 | 0.407 | 2.668 | 0.321 | 2.873 |
19 | 1.180 | 1.401 | 1.074 | 1.536 | 0.967 | 1.685 | 0.859 | 1.848 | 0.752 | 2.023 | 0.649 | 2.206 | 0.549 | 2.396 | 0.456 | 2.589 | 0.369 | 2.783 |
20 | 1.201 | 1.411 | 1.100 | 1.537 | 0.998 | 1.676 | 0.894 | 1.828 | 0.792 | 1.991 | 0.691 | 2.162 | 0.595 | 2.339 | 0.502 | 2.521 | 0.416 | 2.704 |
21 | 1.221 | 1.420 | 1.125 | 1.538 | 1.026 | 1.669 | 0.927 | 1.812 | 0.829 | 1.964 | 0.731 | 2.124 | 0.637 | 2.290 | 0.546 | 2.461 | 0.461 | 2.633 |
22 | 1.239 | 1.429 | 1.147 | 1.541 | 1.053 | 1.664 | 0.958 | 1.797 | 0.863 | 1.940 | 0.769 | 2.090 | 0.677 | 1.246 | 0.588 | 2.407 | 0.504 | 2.571 |
23 | 1.257 | 1.437 | 1.168 | 1.543 | 1.078 | 1.660 | 0.986 | 1.785 | 0.895 | 1.920 | 0.804 | 2.061 | 0.715 | 2.208 | 0.628 | 2.360 | 0.545 | 2.514 |
24 | 1.273 | 1.446 | 1.188 | 1.546 | 1.101 | 1.656 | 1.013 | 1.775 | 0.925 | 1.902 | 0.837 | 2.035 | 0.750 | 2.174 | 0.666 | 2.318 | 0.584 | 2.464 |
25 | 1.288 | 1.454 | 1.206 | 1.550 | 1.123 | 1.654 | 1.038 | 1.767 | 0.953 | 1.886 | 0.868 | 2.013 | 0.784 | 2.144 | 0.702 | 2.280 | 0.621 | 2.419 |
26 | 1.302 | 1.461 | 1.224 | 1.553 | 1.143 | 1.652 | 1.062 | 1.759 | 0.979 | 1.873 | 0.897 | 1.992 | 0.816 | 2.117 | 0.735 | 2.246 | 0.657 | 2.379 |
27 | 1.316 | 1.469 | 1.240 | 1.556 | 1.162 | 1.651 | 1.084 | 1.753 | 1.004 | 1.861 | 0.925 | 1.974 | 0.845 | 2.093 | 0.767 | 2.216 | 0.691 | 2.342 |
28 | 1.328 | 1.476 | 1.255 | 1.560 | 1.1181 | 1.650 | 1.104 | 1.747 | 1.028 | 1.850 | 0.951 | 1.959 | 0.874 | 2.071 | 0.798 | 2.188 | 0.723 | 2.309 |
29 | 1.341 | 1.483 | 1.270 | 1.563 | 1.198 | 1.650 | 1.124 | 1.743 | 1.050 | 1.841 | 0.975 | 1.944 | 0.900 | 2.052 | 0.826 | 2.164 | 0.753 | 2.278 |
30 | 1.352 | 1.489 | 1.284 | 1.567 | 1.214 | 1.650 | 1.143 | 1.739 | 1.071 | 1.833 | 0.998 | 1.931 | 0.926 | 2.034 | 0.854 | 2.141 | 0.782 | 2.251 |
31 | 1.363 | 1.496 | 1.297 | 1.570 | 1.229 | 1.650 | 1.160 | 1.735 | 1.090 | 1.825 | 1.020 | 1.920 | 0.950 | 2.018 | 0.879 | 2.120 | 0.810 | 2.226 |
32 | 1.373 | 1.502 | 1.309 | 1.574 | 1.244 | 1.650 | 1.177 | 1.732 | 1.109 | 1.819 | 1.041 | 1.909 | 0.972 | 2.004 | 0.904 | 2.102 | 0.836 | 2.203 |
33 | 1.383 | 1.508 | 1.321 | 1.577 | 1.258 | 1.651 | 1.193 | 1.730 | 1.127 | 1.813 | 1.061 | 1.900 | 0.994 | 1.991 | 0.927 | 20.85 | 0.861 | 2.181 |
34 | 1.393 | 1.514 | 1.333 | 1.580 | 1.271 | 1.652 | 1.208 | 1.728 | 1.144 | 1.808 | 1.079 | 1.891 | 1.015 | 1.978 | 0.950 | 2.069 | 0.885 | 2.162 |
35 | 1.402 | 1.519 | 1.343 | 1.584 | 1.283 | 1.653 | 1.222 | 1.726 | 1.160 | 1.803 | 1.097 | 1.884 | 1.034 | 1.967 | 0.971 | 2.054 | 0.908 | 2.144 |
36 | 1.411 | 1.525 | 1.354 | 1.587 | 1.295 | 1.654 | 1.236 | 1.724 | 1.175 | 1.799 | 1.114 | 1.876 | 1.053 | 1.957 | 0.991 | 2.041 | 0.930 | 2.127 |
37 | 1.419 | 1.530 | 1.364 | 1.590 | 1.307 | 1.655 | 1.249 | 1.723 | 1.190 | 1.795 | 1.131 | 1.870 | 1.071 | 1.948 | 1.011 | 2.029 | 0.951 | 2.112 |
38 | 1.427 | 1.535 | 1.373 | 1.594 | 1.318 | 1.656 | 1.261 | 1.722 | 1.204 | 1.792 | 1.146 | 1.864 | 1.088 | 1.939 | 1.029 | 2.017 | 0.970 | 2.098 |
39 | 1.435 | 1.540 | 1.382 | 1.597 | 1.328 | 1.658 | 1.273 | 1.722 | 1.218 | 1.789 | 1.161 | 1.859 | 1.104 | 1.932 | 1.047 | 2.007 | 0.990 | 2.085 |
40 | 1.442 | 1.544 | 1.391 | 1.600 | 1.338 | 1.659 | 1.285 | 1.721 | 1.230 | 1.786 | 1.175 | 1.854 | 1.120 | 1.924 | 1.064 | 1.997 | 1.008 | 2.072 |
45 | 1.475 | 1.566 | 1.430 | 1.615 | 1.383 | 1.666 | 1.336 | 1.720 | 1.287 | 1.776 | 1.238 | 1.835 | 1.189 | 1.895 | 1.139 | 1.958 | 1.089 | 2.022 |
50 | 1.503 | 1.585 | 1.462 | 1.628 | 1.421 | 1.674 | 1.378 | 1.721 | 1.335 | 1.771 | 1.291 | 1.822 | 1.246 | 1.875 | 1.201 | 1.930 | 1.156 | 1.986 |
55 | 1.528 | 1.601 | 1.490 | 1.641 | 1.452 | 1.611 | 1.414 | 1.724 | 1.374 | 1.768 | 1.334 | 1.814 | 1.294 | 1.861 | 1.253 | 1.909 | 1.212 | 1.959 |
60 | 1.549 | 1.616 | 1.514 | 1.652 | 1.480 | 1.689 | 1.444 | 1.727 | 1.408 | 1.767 | 1.372 | 1.808 | 1.335 | 1.850 | 1.298 | 1.894 | 1.260 | 1.939 |
65 | 1.567 | 1.629 | 1.536 | 1.662 | 1.503 | 1.696 | 1.471 | 1.731 | 1.438 | 1.767 | 1.404 | 1.805 | 1.170 | 1.843 | 1.336 | 1.882 | 1.301 | 1.923 |
70 | 1.583 | 1.641 | 1.554 | 1.672 | 1.525 | 1.703 | 1.494 | 1.735 | 1.464 | 1.768 | 1.433 | 1.802 | 1.401 | 1.838 | 1.369 | 1.874 | 1.337 | 1.910 |
75 | 1.598 | 1.652 | 1.571 | 1.680 | 1.543 | 1.709 | 1.515 | 1.739 | 1.487 | 1.770 | 1.458 | 1.801 | 1.428 | 1.834 | 1.399 | 1.867 | 1.369 | 1.901 |
80 | 1.611 | 1.662 | 1.586 | 1.688 | 1.560 | 1.715 | 1.534 | 1.743 | 1.507 | 1.772 | 1.480 | 1.801 | 1.453 | 1.831 | 1.425 | 1.861 | 1.397 | 1.893 |
85 | 1.624 | 1.671 | 1.600 | 1.696 | 1.575 | 1.721 | 1.550 | 1.747 | 1.525 | 1.774 | 1.500 | 1.801 | 1.474 | 1.829 | 1.448 | 1.857 | 1.422 | 1.886 |
90 | 1.635 | 1.679 | 1.612 | 1.703 | 1.589 | 1.726 | 1.566 | 1.751 | 1.542 | 1.776 | 1.518 | 1.801 | 1.494 | 1.827 | 1.469 | 1.854 | 1.445 | 1.881 |
95 | 1.645 | 1.687 | 1.623 | 1.709 | 1.602 | 1.732 | 1.579 | 1.755 | 1.557 | 1.778 | 1.535 | 1.802 | 1.512 | 1.827 | 1.489 | 1.852 | 1.465 | 1.877 |
100 | 1.654 | 1.694 | 1.634 | 1.715 | 1.613 | 1.736 | 1.592 | 1.758 | 1.571 | 1.780 | 1.550 | 1.803 | 1.528 | 1.827 | 1.489 | 1.852 | 1.465 | 1.877 |
150 | 1.720 | 1.747 | 1.706 | 1.760 | 1.693 | 1.774 | 1.679 | 1.788 | 1.665 | 1.802 | 1.651 | 1.817 | 1.637 | 1.832 | 1.622 | 1.846 | 1.608 | 1.862 |
200 | 1.758 | 1.779 | 1.748 | 1.789 | 1.738 | 1.799 | 1.728 | 1.809 | 1.718 | 1.820 | 1.707 | 1.831 | 1.697 | 1.841 | 1.686 | 1.852 | 1.675 | 1.863 |
Table D
Degrees of Freedom ν | 0.99 | 0.975 | 0.95 | 0.9 | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 |
---|---|---|---|---|---|---|---|---|---|
1 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
2 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 |
3 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 |
4 | 0.297 | 0.484 | 0.711 | 1.064 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 |
5 | 0.554 | 0.831 | 1.145 | 1.610 | 9.236 | 11.070 | 12.832 | 15.086 | 16.750 |
6 | 0.872 | 1.237 | 1.635 | 2.204 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 |
7 | 1.239 | 1.690 | 2.167 | 2.833 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 |
8 | 1.647 | 2.180 | 2.733 | 3.490 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 |
9 | 2.088 | 2.700 | 3.325 | 4.168 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 |
10 | 2.558 | 3.247 | 3.940 | 4.865 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 |
11 | 3.053 | 3.816 | 4.575 | 5.578 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 |
12 | 3.571 | 4.404 | 5.226 | 6.304 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 |
13 | 4.107 | 5.009 | 5.892 | 7.041 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 |
14 | 4.660 | 5.629 | 6.571 | 7.790 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 |
15 | 5.229 | 6.262 | 7.261 | 8.547 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 |
16 | 5.812 | 6.908 | 7.962 | 9.312 | 23.542 | 26.296 | 28.845 | 32.000 | 34.267 |
17 | 6.408 | 7.564 | 8.672 | 10.085 | 24.769 | 27.587 | 30.191 | 33.409 | 35.718 |
18 | 7.015 | 8.231 | 9.390 | 10.865 | 25.989 | 28.869 | 31.526 | 34.805 | 37.156 |
19 | 7.633 | 8.907 | 10.117 | 11.651 | 27.204 | 30.144 | 32.852 | 36.191 | 38.582 |
20 | 8.260 | 9.591 | 10.851 | 12.443 | 28.412 | 31.410 | 34.170 | 37.566 | 39.997 |
21 | 8.897 | 10.283 | 11.591 | 13.240 | 29.615 | 32.671 | 35.479 | 38.932 | 41.401 |
22 | 9.542 | 10.982 | 12.338 | 14.041 | 30.813 | 33.924 | 36.781 | 40.289 | 42.796 |
23 | 10.196 | 11.689 | 13.091 | 14.848 | 32.007 | 35.172 | 38.076 | 41.638 | 44.181 |
24 | 10.856 | 12.401 | 13.848 | 15.659 | 33.196 | 36.415 | 39.364 | 42.980 | 45.558 |
25 | 11.524 | 13.120 | 14.611 | 16.473 | 34.382 | 37.652 | 40.646 | 44.314 | 46.928 |
26 | 12.198 | 13.844 | 15.379 | 17.292 | 35.563 | 38.885 | 41.923 | 45.642 | 48.290 |
27 | 12.878 | 14.573 | 16.151 | 18.114 | 36.741 | 40.113 | 43.195 | 46.963 | 49.645 |
28 | 13.565 | 15.308 | 16.928 | 18.939 | 37.916 | 41.337 | 44.461 | 48.278 | 50.994 |
29 | 14.256 | 16.047 | 17.708 | 19.768 | 39.087 | 42.557 | 45.722 | 49.588 | 52.335 |
30 | 14.953 | 16.791 | 18.493 | 20.599 | 40.256 | 43.773 | 46.979 | 50.892 | 53.672 |
31 | 15.655 | 17.539 | 19.281 | 21.434 | 41.422 | 44.985 | 48.232 | 52.191 | 55.002 |
32 | 16.362 | 18.291 | 20.072 | 22.271 | 42.585 | 46.194 | 49.480 | 53.486 | 56.328 |
33 | 17.073 | 19.047 | 20.867 | 23.110 | 43.745 | 47.400 | 50.725 | 54.775 | 57.648 |
34 | 17.789 | 19.806 | 21.664 | 23.952 | 44.903 | 48.602 | 51.966 | 56.061 | 58.964 |
35 | 18.509 | 20.569 | 22.465 | 24.797 | 46.059 | 49.802 | 53.203 | 57.342 | 60.275 |
36 | 19.233 | 21.336 | 23.269 | 25.643 | 47.212 | 50.998 | 54.437 | 58.619 | 61.581 |
37 | 19.960 | 22.106 | 24.075 | 26.492 | 48.363 | 52.192 | 55.668 | 59.893 | 62.883 |
38 | 20.691 | 22.878 | 24.884 | 27.343 | 49.513 | 53.384 | 56.895 | 61.162 | 64.181 |
39 | 21.426 | 23.654 | 25.695 | 28.196 | 50.660 | 54.572 | 58.120 | 62.428 | 65.475 |
40 | 22.164 | 24.433 | 26.509 | 29.051 | 51.805 | 55.758 | 59.342 | 63.691 | 66.766 |
41 | 22.906 | 25.215 | 27.326 | 29.907 | 52.949 | 56.942 | 60.561 | 64.950 | 68.053 |
42 | 23.650 | 25.999 | 28.144 | 30.765 | 54.090 | 58.124 | 61.777 | 66.206 | 69.336 |
43 | 24.398 | 26.785 | 28.965 | 31.625 | 55.230 | 59.304 | 62.990 | 67.459 | 70.616 |
44 | 25.148 | 27.575 | 29.787 | 32.487 | 56.369 | 60.481 | 64.201 | 68.710 | 71.892 |
45 | 25.901 | 28.366 | 30.612 | 33.350 | 57.505 | 61.656 | 65.410 | 69.957 | 73.166 |
46 | 26.657 | 29.160 | 31.439 | 34.215 | 58.641 | 62.830 | 66.616 | 71.201 | 74.437 |
47 | 27.416 | 29.956 | 32.268 | 35.081 | 59.774 | 64.001 | 67.821 | 72.443 | 75.704 |
48 | 28.177 | 30.754 | 33.098 | 35.949 | 60.907 | 65.171 | 69.023 | 73.683 | 76.969 |
49 | 28.941 | 31.555 | 33.930 | 36.818 | 62.038 | 66.339 | 70.222 | 74.919 | 78.231 |
50 | 29.707 | 32.357 | 34.764 | 37.689 | 63.167 | 67.505 | 71.420 | 76.154 | 79.490 |
Critical values (for a right-tailed unilateral test) of the chi-square distribution.
Table E
zc | Second Decimal of zc | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | |
0.0 | 0.5000 | 0.4960 | 0.4920 | 0.4880 | 0.4840 | 0.4801 | 0.4761 | 0.4721 | 0.4681 | 0.4641 |
0.1 | 0.4602 | 0.4562 | 0.4522 | 0.4483 | 0.4443 | 0.4404 | 0.4364 | 0.4325 | 0.4286 | 0.4247 |
0.2 | 0.4207 | 0.4168 | 0.4129 | 0.4090 | 0.4052 | 0.4013 | 0.3974 | 0.3936 | 0.3897 | 0.3859 |
0.3 | 0.3821 | 0.3783 | 0.3745 | 0.3707 | 0.3669 | 0.3632 | 0.3594 | 0.3557 | 0.3520 | 0.3483 |
0.4 | 0.3446 | 0.3409 | 0.3372 | 0.3336 | 0.3300 | 0.3264 | 0.3228 | 0.3192 | 0.3156 | 0.3121 |
0.5 | 0.3085 | 0.3050 | 0.3015 | 0.2981 | 0.2946 | 0.2912 | 0.2877 | 0.2842 | 0.2810 | 0.2776 |
0.6 | 0.2743 | 0.2709 | 0.2676 | 0.2643 | 0.2611 | 0.2578 | 0.2546 | 0.2514 | 0.2483 | 0.2451 |
0.7 | 0.2420 | 0.2389 | 0.2358 | 0.2327 | 0.2296 | 0.2266 | 0.2236 | 0.2206 | 0.2177 | 0.2148 |
0.8 | 0.2119 | 0.2090 | 0.2061 | 0.2033 | 0.2005 | 0.1977 | 0.1949 | 0.1922 | 0.1894 | 0.1867 |
0.9 | 0.1841 | 0.1814 | 0.1788 | 0.1762 | 0.1736 | 0.1711 | 0.1685 | 0.1660 | 0.1635 | 0.1611 |
1.0 | 0.1587 | 0.1562 | 0.1539 | 0.1515 | 0.1492 | 0.1469 | 0.1446 | 0.1423 | 0.1401 | 0.1379 |
1.1 | 0.1357 | 0.1335 | 0.1314 | 0.1292 | 0.1271 | 0.1251 | 0.1230 | 0.1210 | 0.1190 | 0.1170 |
1.2 | 0.1151 | 0.1131 | 0.1112 | 0.1093 | 0.1075 | 0.1056 | 0.1038 | 0.1020 | 0.1003 | 0.0985 |
1.3 | 0.0968 | 0.0951 | 0.0934 | 0.0918 | 0.0901 | 0.0885 | 0.0869 | 0.0853 | 0.0838 | 0.0823 |
1.4 | 0.0808 | 0.0793 | 0.0778 | 0.0764 | 0.0749 | 0.0735 | 0.0722 | 0.0708 | 0.0694 | 0.0681 |
1.5 | 0.0668 | 0.0655 | 0.0643 | 0.0630 | 0.0618 | 0.0606 | 0.0594 | 0.0582 | 0.0571 | 0.0559 |
1.6 | 0.0548 | 0.0537 | 0.0526 | 0.0516 | 0.0505 | 0.0495 | 0.0485 | 0.0475 | 0.0465 | 0.0455 |
1.7 | 0.0446 | 0.0436 | 0.0427 | 0.0418 | 0.0409 | 0.0401 | 0.0392 | 0.0384 | 0.0375 | 0.0367 |
1.8 | 0.0359 | 0.0352 | 0.0344 | 0.0336 | 0.0329 | 0.0322 | 0.0314 | 0.0307 | 0.0301 | 0.0294 |
1.9 | 0.0287 | 0.0281 | 0.0274 | 0.0268 | 0.0262 | 0.0256 | 0.0250 | 0.0244 | 0.0239 | 0.0233 |
2.0 | 0.0228 | 0.0222 | 0.0217 | 0.0212 | 0.0207 | 0.0202 | 0.0197 | 0.0192 | 0.0188 | 0.0183 |
2.1 | 0.0179 | 0.0174 | 0.0170 | 0.0166 | 0.0162 | 0.0158 | 0.0154 | 0.0150 | 0.0146 | 0.0143 |
2.2 | 0.0139 | 0.0136 | 0.0132 | 0.0129 | 0.0125 | 0.0122 | 0.0119 | 0.0116 | 0.0113 | 0.0110 |
2.3 | 0.0107 | 0.0104 | 0.0102 | 0.0099 | 0.0096 | 0.0094 | 0.0091 | 0.0089 | 0.0087 | 0.0084 |
2.4 | 0.0082 | 0.0080 | 0.0078 | 0.0075 | 0.0073 | 0.0071 | 0.0069 | 0.0068 | 0.0066 | 0.0064 |
2.5 | 0.0062 | 0.0060 | 0.0059 | 0.0057 | 0.0055 | 0.0054 | 0.0052 | 0.0051 | 0.0049 | 0.0048 |
2.6 | 0.0047 | 0.0045 | 0.0044 | 0.0043 | 0.0041 | 0.0040 | 0.0039 | 0.0038 | 0.0037 | 0.0036 |
2.7 | 0.0035 | 0.0034 | 0.0033 | 0.0032 | 0.0031 | 0.0030 | 0.0029 | 0.0028 | 0.0027 | 0.0026 |
2.8 | 0.0026 | 0.0025 | 0.0024 | 0.0023 | 0.0023 | 0.0022 | 0.0021 | 0.0021 | 0.0020 | 0.0019 |
2.9 | 0.0019 | 0.0018 | 0.0017 | 0.0017 | 0.0016 | 0.0016 | 0.0015 | 0.0015 | 0.0014 | 0.0014 |
3.0 | 0.0013 | 0.0013 | 0.0013 | 0.0012 | 0.0012 | 0.0011 | 0.0011 | 0.0011 | 0.0010 | 0.0010 |
3.1 | 0.0010 | 0.0009 | 0.0009 | 0.0009 | 0.008 | 0.0008 | 0.0008 | 0.0008 | 0.007 | 0.007 |
3.2 | 0.0007 | |||||||||
3.3 | 0.0005 | |||||||||
3.4 | 0.0003 | |||||||||
3.5 | 0.00023 | |||||||||
3.6 | 0.00016 | |||||||||
3.7 | 0.00011 | |||||||||
3.8 | 0.00007 | |||||||||
3.9 | 0.00005 | |||||||||
4.0 | 0.00003 |
Associated probability for a right-tailed test.
Table F1
p | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | k | 0.01 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 1/3 | 0.40 | 0.45 | 0.50 | ||
2 | 0 | 9801 | 9025 | 8100 | 7225 | 6400 | 5625 | 4900 | 4444 | 3600 | 3025 | 2500 | 2 | 2 |
1 | 198 | 950 | 1800 | 2550 | 3200 | 3750 | 4200 | 4444 | 4800 | 4950 | 5000 | 1 | ||
2 | 1 | 25 | 100 | 225 | 400 | 625 | 900 | 1111 | 1600 | 2025 | 2500 | 0 | ||
3 | 0 | 9703 | 8574 | 7290 | 6141 | 5120 | 4219 | 3430 | 2963 | 2160 | 1664 | 1250 | 3 | 3 |
1 | 294 | 1354 | 2430 | 3251 | 3840 | 4219 | 4410 | 4444 | 4320 | 4084 | 3750 | 2 | ||
2 | 3 | 71 | 270 | 574 | 960 | 1406 | 1890 | 2222 | 2880 | 3341 | 3750 | 1 | ||
3 | 0 | 1 | 10 | 34 | 80 | 156 | 270 | 370 | 640 | 911 | 1250 | 0 | ||
4 | 0 | 9606 | 8145 | 6561 | 5220 | 4096 | 3164 | 2401 | 1975 | 1296 | 915 | 625 | 4 | 4 |
1 | 388 | 1715 | 2916 | 3685 | 4096 | 4219 | 4116 | 3951 | 3456 | 2995 | 2500 | 3 | ||
2 | 6 | 135 | 486 | 975 | 1536 | 2109 | 2646 | 2963 | 3456 | 3675 | 3750 | 2 | ||
3 | 0 | 5 | 36 | 115 | 256 | 469 | 756 | 988 | 1536 | 2005 | 2500 | 1 | ||
4 | 0 | 0 | 1 | 5 | 16 | 39 | 81 | 123 | 256 | 410 | 625 | 0 | ||
5 | 0 | 9510 | 7738 | 5905 | 4437 | 3277 | 2373 | 1681 | 1317 | 778 | 503 | 312 | 5 | 5 |
1 | 480 | 2036 | 3280 | 3915 | 4096 | 3955 | 3602 | 3292 | 2592 | 2059 | 1562 | 4 | ||
2 | 10 | 214 | 729 | 1382 | 2048 | 2637 | 3087 | 3292 | 3456 | 3369 | 3125 | 3 | ||
3 | 0 | 11 | 81 | 244 | 512 | 879 | 1323 | 1646 | 2304 | 2757 | 3125 | 2 | ||
4 | 0 | 0 | 4 | 22 | 64 | 146 | 283 | 412 | 768 | 1128 | 1562 | 1 | ||
5 | 0 | 0 | 0 | 1 | 3 | 10 | 24 | 41 | 102 | 185 | 312 | 0 | ||
6 | 0 | 9415 | 7351 | 5314 | 3771 | 2621 | 1780 | 1176 | 878 | 467 | 277 | 156 | 6 | 6 |
1 | 571 | 2321 | 3543 | 3993 | 3932 | 3560 | 3025 | 2634 | 1866 | 1359 | 938 | 5 | ||
2 | 14 | 305 | 984 | 1762 | 2458 | 2966 | 3241 | 3292 | 3110 | 2780 | 2344 | 4 | ||
3 | 0 | 21 | 146 | 415 | 819 | 1318 | 1852 | 2195 | 2765 | 3032 | 3125 | 3 | ||
4 | 0 | 1 | 12 | 55 | 154 | 330 | 595 | 823 | 1382 | 1861 | 2344 | 2 | ||
5 | 0 | 0 | 1 | 4 | 15 | 44 | 102 | 165 | 369 | 609 | 938 | 1 | ||
6 | 0 | 0 | 0 | 0 | 1 | 2 | 7 | 14 | 41 | 83 | 156 | 0 | ||
7 | 0 | 9321 | 6983 | 4783 | 3206 | 2097 | 1335 | 824 | 585 | 280 | 152 | 78 | 7 | 7 |
1 | 659 | 2573 | 3720 | 3960 | 3670 | 3115 | 2471 | 2048 | 1306 | 872 | 547 | 6 | ||
2 | 20 | 406 | 1240 | 2097 | 2753 | 3115 | 3177 | 3073 | 2613 | 2140 | 1641 | 5 | ||
3 | 0 | 36 | 230 | 617 | 1147 | 1730 | 2269 | 2561 | 2903 | 2918 | 2734 | 4 | ||
4 | 0 | 2 | 26 | 109 | 287 | 577 | 972 | 1280 | 1935 | 2388 | 2734 | 3 | ||
5 | 0 | 0 | 2 | 12 | 43 | 115 | 250 | 384 | 774 | 1172 | 1641 | 2 | ||
6 | 0 | 0 | 0 | 1 | 4 | 13 | 36 | 64 | 172 | 320 | 547 | 1 | ||
7 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 5 | 16 | 37 | 78 | 0 | ||
0.99 | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 2/3 | 0.60 | 0.55 | 0.50 | k | N | ||
p | ||||||||||||||
p | ||||||||||||||
N | k | 0.01 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 1/3 | 0.40 | 0.45 | 0.50 | ||
8 | 0 | 9227 | 6634 | 4305 | 2725 | 1678 | 1001 | 576 | 390 | 168 | 84 | 39 | 8 | 8 |
1 | 746 | 2793 | 3826 | 3847 | 3355 | 2670 | 1977 | 1561 | 896 | 548 | 312 | 7 | ||
2 | 26 | 515 | 1488 | 2376 | 2936 | 3115 | 2965 | 2731 | 2090 | 1569 | 1094 | 6 | ||
3 | 1 | 54 | 331 | 839 | 1468 | 2076 | 2541 | 2731 | 2787 | 2568 | 2188 | 5 | ||
4 | 0 | 4 | 46 | 185 | 459 | 865 | 1361 | 1707 | 2322 | 2627 | 2734 | 4 | ||
5 | 0 | 0 | 4 | 26 | 92 | 231 | 467 | 683 | 1239 | 1719 | 2188 | 3 | ||
6 | 0 | 0 | 0 | 2 | 11 | 38 | 100 | 171 | 413 | 703 | 1094 | 2 | ||
7 | 0 | 0 | 0 | 0 | 1 | 4 | 12 | 24 | 79 | 164 | 312 | 1 | ||
8 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 7 | 17 | 39 | 0 | ||
9 | 0 | 9135 | 6302 | 3874 | 2316 | 1342 | 751 | 404 | 260 | 101 | 46 | 20 | 9 | 9 |
1 | 830 | 2985 | 3874 | 3679 | 3020 | 2253 | 1556 | 1171 | 605 | 339 | 176 | 8 | ||
2 | 34 | 629 | 1722 | 2597 | 3020 | 3003 | 2668 | 2341 | 1612 | 1110 | 703 | 7 | ||
3 | 1 | 77 | 446 | 1069 | 1762 | 2336 | 2668 | 2731 | 2508 | 2119 | 1641 | 6 | ||
4 | 0 | 6 | 74 | 283 | 661 | 1168 | 1715 | 2048 | 2508 | 2600 | 2461 | 5 | ||
5 | 0 | 0 | 8 | 50 | 165 | 389 | 735 | 1024 | 1672 | 2128 | 2461 | 4 | ||
6 | 0 | 0 | 1 | 6 | 28 | 87 | 210 | 341 | 743 | 1160 | 1641 | 3 | ||
7 | 0 | 0 | 0 | 0 | 3 | 12 | 39 | 73 | 212 | 407 | 703 | 2 | ||
8 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 9 | 35 | 83 | 176 | 1 | ||
9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 8 | 20 | 0 | ||
10 | 0 | 9044 | 5987 | 3487 | 1969 | 1074 | 563 | 282 | 173 | 60 | 25 | 10 | 10 | 10 |
1 | 914 | 3151 | 3874 | 3474 | 2684 | 1877 | 1211 | 867 | 403 | 207 | 98 | 9 | ||
2 | 42 | 746 | 1937 | 2759 | 3020 | 2816 | 2335 | 1951 | 1209 | 763 | 439 | 5 | ||
3 | 1 | 105 | 574 | 1298 | 2013 | 2503 | 2668 | 2601 | 2150 | 1665 | 1172 | 7 | ||
4 | 0 | 10 | 112 | 401 | 881 | 1460 | 2001 | 2276 | 2508 | 2384 | 2051 | 6 | ||
5 | 0 | 1 | 15 | 85 | 264 | 584 | 1029 | 1366 | 2007 | 2340 | 2461 | 5 | ||
6 | 0 | 0 | 1 | 12 | 55 | 162 | 368 | 569 | 1115 | 1596 | 2051 | 4 | ||
7 | 0 | 0 | 0 | 1 | 8 | 31 | 90 | 163 | 425 | 746 | 1172 | 3 | ||
8 | 0 | 0 | 0 | 0 | 1 | 4 | 14 | 30 | 106 | 229 | 439 | 2 | ||
9 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 16 | 42 | 98 | 1 | ||
10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 10 | 0 | ||
15 | 0 | 8601 | 4633 | 2059 | 874 | 352 | 134 | 47 | 23 | 5 | 1 | 0 | 15 | 15 |
1 | 1303 | 3658 | 3432 | 2312 | 1319 | 668 | 305 | 171 | 47 | 16 | 5 | 14 | ||
2 | 92 | 1348 | 2669 | 2856 | 2309 | 1559 | 916 | 599 | 219 | 90 | 32 | 13 | ||
3 | 4 | 307 | 1285 | 2184 | 2501 | 2252 | 1700 | 1299 | 634 | 318 | 139 | 12 | ||
4 | 0 | 49 | 428 | 1156 | 1876 | 2252 | 2186 | 1948 | 1268 | 780 | 417 | 11 | ||
5 | 0 | 6 | 105 | 449 | 1032 | 1651 | 2061 | 2143 | 1859 | 1404 | 916 | 10 | ||
6 | 0 | 0 | 19 | 132 | 430 | 917 | 1472 | 1786 | 2066 | 1914 | 1527 | 9 | ||
7 | 0 | 0 | 3 | 30 | 138 | 393 | 811 | 1148 | 1771 | 2013 | 1964 | 8 | ||
8 | 0 | 0 | 0 | 5 | 35 | 131 | 348 | 574 | 1181 | 1647 | 1964 | 7 | ||
9 | 0 | 0 | 0 | 1 | 7 | 34 | 116 | 223 | 612 | 1048 | 1527 | 6 | ||
10 | 0 | 0 | 0 | 0 | 1 | 7 | 30 | 67 | 245 | 515 | 916 | 5 | ||
11 | 0 | 0 | 0 | 0 | 0 | 1 | 6 | 15 | 74 | 191 | 417 | 4 | ||
12 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 16 | 52 | 139 | 3 | ||
13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 10 | 32 | 2 | ||
14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 5 | 1 | ||
15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
0.99 | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 2/3 | 0.60 | 0.55 | 0.50 | k | N | ||
p | ||||||||||||||
p | ||||||||||||||
N | k | 0.01 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 1/3 | 0.40 | 0.45 | 0.50 | ||
20 | 0 | 8179 | 3585 | 1216 | 388 | 115 | 32 | 8 | 3 | 0 | 0 | 0 | 20 | 20 |
1 | 1652 | 3774 | 2702 | 1368 | 576 | 211 | 68 | 30 | 5 | 1 | 0 | 19 | ||
2 | 159 | 1887 | 2852 | 2293 | 1369 | 669 | 278 | 143 | 31 | 8 | 2 | 18 | ||
3 | 10 | 596 | 1901 | 2428 | 2054 | 1339 | 716 | 429 | 123 | 40 | 11 | 17 | ||
4 | 0 | 133 | 898 | 1821 | 2182 | 1897 | 1304 | 911 | 350 | 139 | 46 | 16 | ||
5 | 0 | 22 | 319 | 1028 | 1746 | 2023 | 1789 | 1457 | 746 | 365 | 148 | 15 | ||
6 | 0 | 3 | 89 | 454 | 1091 | 1686 | 1916 | 1821 | 1244 | 746 | 370 | 14 | ||
7 | 0 | 0 | 20 | 160 | 545 | 1124 | 1643 | 1821 | 1659 | 1221 | 739 | 13 | ||
8 | 0 | 0 | 4 | 46 | 222 | 609 | 1144 | 1480 | 1797 | 1623 | 1201 | 12 | ||
9 | 0 | 0 | 1 | 11 | 74 | 271 | 654 | 987 | 1597 | 1771 | 1602 | 11 | ||
10 | 0 | 0 | 0 | 2 | 20 | 99 | 308 | 543 | 1171 | 1593 | 1762 | 10 | ||
11 | 0 | 0 | 0 | 0 | 5 | 30 | 120 | 247 | 710 | 1185 | 1602 | 9 | ||
12 | 0 | 0 | 0 | 0 | 1 | 8 | 39 | 92 | 355 | 727 | 1201 | 8 | ||
13 | 0 | 0 | 0 | 0 | 0 | 2 | 10 | 28 | 146 | 366 | 739 | 7 | ||
14 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 7 | 49 | 150 | 370 | 6 | ||
15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 13 | 49 | 148 | 5 | ||
16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 13 | 46 | 4 | ||
17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 11 | 3 | ||
18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | ||
19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ||
20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
25 | 0 | 7778 | 2774 | 718 | 172 | 38 | 8 | 1 | 0 | 0 | 0 | 0 | 25 | 25 |
1 | 1964 | 3650 | 1994 | 759 | 236 | 63 | 14 | 5 | 0 | 0 | 0 | 24 | ||
2 | 238 | 2305 | 2659 | 1607 | 708 | 251 | 74 | 30 | 4 | 1 | 0 | 23 | ||
3 | 18 | 930 | 2265 | 2174 | 1358 | 641 | 243 | 114 | 19 | 4 | 1 | 22 | ||
4 | 1 | 269 | 1384 | 2110 | 1867 | 1175 | 572 | 313 | 71 | 18 | 4 | 21 | ||
5 | 0 | 60 | 646 | 1564 | 1960 | 1645 | 1030 | 658 | 199 | 63 | 16 | 20 | ||
6 | 0 | 10 | 239 | 920 | 1633 | 1828 | 1472 | 1096 | 442 | 172 | 53 | 19 | ||
7 | 0 | 1 | 72 | 441 | 1108 | 1654 | 1712 | 1487 | 800 | 381 | 143 | 18 | ||
8 | 0 | 0 | 18 | 175 | 623 | 1241 | 1651 | 1673 | 1200 | 701 | 322 | 17 | ||
9 | 0 | 0 | 4 | 58 | 294 | 781 | 1336 | 1580 | 1511 | 1084 | 609 | 16 | ||
10 | 0 | 0 | 1 | 16 | 118 | 417 | 916 | 1264 | 1612 | 1419 | 974 | 15 | ||
11 | 0 | 0 | 0 | 4 | 40 | 189 | 536 | 862 | 1465 | 1583 | 1328 | 14 | ||
12 | 0 | 0 | 0 | 1 | 12 | 74 | 268 | 503 | 1140 | 1511 | 1550 | 13 | ||
13 | 0 | 0 | 0 | 0 | 3 | 25 | 115 | 251 | 760 | 1236 | 1550 | 12 | ||
14 | 0 | 0 | 0 | 0 | 1 | 7 | 42 | 108 | 434 | 867 | 1328 | 11 | ||
15 | 0 | 0 | 0 | 0 | 0 | 2 | 13 | 40 | 212 | 520 | 974 | 10 | ||
16 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 12 | 88 | 266 | 609 | 9 | ||
17 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 31 | 115 | 322 | 8 | ||
18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 9 | 42 | 143 | 7 | ||
19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 13 | 53 | 6 | ||
20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 16 | 5 | ||
21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 4 | ||
22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | ||
23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | ||
24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ||
25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
0.99 | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 2/3 | 0.60 | 0.55 | 0.50 | k | N | ||
p | ||||||||||||||
p | ||||||||||||||
N | k | 0.01 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 1/3 | 0.40 | 0.45 | 0.50 | ||
30 | 0 | 7397 | 2146 | 424 | 76 | 12 | 2 | 0 | 0 | 0 | 0 | 0 | 30 | 30 |
1 | 2242 | 3389 | 1413 | 404 | 93 | 18 | 3 | 1 | 0 | 0 | 0 | 29 | ||
2 | 328 | 2586 | 2277 | 1034 | 337 | 86 | 18 | 6 | 0 | 0 | 0 | 28 | ||
3 | 31 | 1270 | 2361 | 1703 | 785 | 269 | 72 | 26 | 3 | 0 | 0 | 27 | ||
4 | 2 | 451 | 1771 | 2028 | 1325 | 604 | 208 | 89 | 12 | 2 | 0 | 26 | ||
5 | 0 | 124 | 1023 | 1861 | 1723 | 1047 | 464 | 232 | 41 | 8 | 1 | 25 | ||
6 | 0 | 27 | 474 | 1368 | 1795 | 1455 | 829 | 484 | 115 | 29 | 6 | 24 | ||
7 | 0 | 5 | 180 | 828 | 1538 | 1662 | 1219 | 829 | 263 | 81 | 19 | 23 | ||
8 | 0 | 1 | 58 | 420 | 1106 | 1593 | 1501 | 1192 | 505 | 191 | 55 | 22 | ||
9 | 0 | 0 | 16 | 181 | 676 | 1298 | 1573 | 1457 | 823 | 382 | 133 | 21 | ||
10 | 0 | 0 | 4 | 67 | 355 | 909 | 1416 | 1530 | 1152 | 656 | 280 | 20 | ||
11 | 0 | 0 | 1 | 22 | 161 | 551 | 1103 | 1391 | 1396 | 976 | 509 | 19 | ||
12 | 0 | 0 | 0 | 6 | 64 | 291 | 749 | 1101 | 1474 | 1265 | 805 | 18 | ||
13 | 0 | 0 | 0 | 1 | 22 | 134 | 444 | 762 | 1360 | 1433 | 1115 | 17 | ||
14 | 0 | 0 | 0 | 0 | 7 | 54 | 231 | 436 | 1101 | 1424 | 1354 | 16 | ||
15 | 0 | 0 | 0 | 0 | 2 | 19 | 106 | 247 | 783 | 1242 | 1445 | 15 | ||
16 | 0 | 0 | 0 | 0 | 0 | 6 | 42 | 116 | 489 | 953 | 1354 | 14 | ||
17 | 0 | 0 | 0 | 0 | 0 | 2 | 15 | 48 | 269 | 642 | 1115 | 13 | ||
18 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 17 | 129 | 379 | 805 | 12 | ||
19 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 5 | 54 | 196 | 509 | 11 | ||
20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 20 | 88 | 280 | 10 | ||
21 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 34 | 133 | 9 | ||
22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 12 | 55 | 8 | ||
23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 19 | 7 | ||
24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 6 | 6 | ||
25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 5 | ||
26. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | ||
27 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | ||
28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | ||
29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ||
30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
0.99 | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 2/3 | 0.60 | 0.55 | 0.50 | k | N |
The decimal point was omitted. All entries should be read as .nnn.
For p ≤ .5, use the upper line for p and the left column for k.
For p > .5, use the bottom line for p and the right column for k.
Table F2
k | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
4 | 062 | 312 | 688 | 938 | 1.0 | |||||||||||||
5 | 031 | 188 | 500 | 812 | 969 | 1.0 | ||||||||||||
6 | 016 | 109 | 344 | 656 | 891 | 984 | 1.0 | |||||||||||
7 | 008 | 062 | 227 | 500 | 773 | 938 | 992 | 1.0 | ||||||||||
8 | 004 | 035 | 145 | 363 | 637 | 855 | 965 | 996 | 1.0 | |||||||||
9 | 002 | 020 | 090 | 254 | 500 | 746 | 910 | 980 | 998 | 1.0 | ||||||||
10 | 001 | 011 | 055 | 172 | 377 | 623 | 828 | 945 | 989 | 999 | 1.0 | |||||||
11 | 006 | 033 | 113 | 274 | 500 | 726 | 887 | 967 | 994 | 999 + | 1.0 | |||||||
12 | 003 | 019 | 073 | 194 | 387 | 613 | 806 | 927 | 981 | 997 | 999 + | 1.0 | ||||||
13 | 002 | 011 | 046 | 133 | 291 | 500 | 709 | 867 | 954 | 989 | 998 | 999 + | 1.0 | |||||
14 | 001 | 006 | 029 | 090 | 212 | 395 | 605 | 788 | 910 | 971 | 994 | 999 + | 999 + | 1.0 | ||||
15 | 004 | 018 | 059 | 151 | 304 | 500 | 696 | 849 | 941 | 982 | 996 | 999 + | 999 + | 1.0 | ||||
16 | 002 | 011 | 038 | 105 | 227 | 402 | 598 | 773 | 895 | 962 | 989 | 998 | 999 + | 999 + | 1.0 | |||
17 | 001 | 006 | 025 | 072 | 166 | 315 | 500 | 685 | 834 | 928 | 975 | 994 | 999 | 999 + | 999 + | 1.0 | ||
18 | 001 | 004 | 015 | 048 | 119 | 240 | 407 | 593 | 760 | 881 | 952 | 985 | 996 | 999 | 999 + | 999 + | ||
19 | 002 | 010 | 032 | 084 | 180 | 324 | 500 | 676 | 820 | 916 | 968 | 990 | 998 | 999 + | 999 + | |||
20 | 001 | 006 | 021 | 058 | 132 | 252 | 412 | 588 | 748 | 868 | 942 | 979 | 994 | 999 | 999 + | |||
21 | 001 | 004 | 013 | 039 | 095 | 192 | 332 | 500 | 668 | 808 | 905 | 961 | 987 | 996 | 999 | |||
22 | 002 | 008 | 026 | 067 | 143 | 262 | 416 | 584 | 738 | 857 | 933 | 974 | 992 | 998 | ||||
23 | 001 | 005 | 017 | 047 | 105 | 202 | 339 | 500 | 661 | 798 | 895 | 953 | 983 | 995 | ||||
24 | 001 | 003 | 011 | 032 | 076 | 154 | 271 | 419 | 581 | 729 | 846 | 924 | 968 | 989 | ||||
25 | 002 | 007 | 022 | 054 | 115 | 212 | 345 | 500 | 655 | 788 | 885 | 946 | 978 | |||||
26 | 001 | 005 | 014 | 038 | 084 | 163 | 279 | 423 | 577 | 721 | 837 | 916 | 962 | |||||
27 | 001 | 003 | 010 | 026 | 061 | 124 | 221 | 351 | 500 | 649 | 779 | 876 | 939 | |||||
28 | 002 | 006 | 018 | 044 | 092 | 172 | 286 | 425 | 575 | 714 | 828 | 908 | ||||||
29 | 001 | 004 | 012 | 031 | 068 | 132 | 229 | 356 | 500 | 644 | 771 | 868 | ||||||
30 | 001 | 003 | 008 | 021 | 049 | 100 | 181 | 292 | 428 | 572 | 708 | 819 | ||||||
31 | 002 | 005 | 015 | 035 | 075 | 141 | 237 | 360 | 500 | 640 | 763 | |||||||
32 | 001 | 004 | 010 | 025 | 055 | 108 | 189 | 298 | 430 | 570 | 702 | |||||||
33 | 001 | 002 | 007 | 018 | 040 | 081 | 148 | 243 | 364 | 500 | 636 | |||||||
34 | 001 | 005 | 012 | 029 | 061 | 115 | 196 | 304 | 432 | 568 | ||||||||
35 | 001 | 003 | 008 | 020 | 045 | 088 | 155 | 250 | 368 | 500 |
Unilateral probabilities for the binomial test when p = q = 1/2.
Note: Decimal points and values less than 0.0005 were omitted.
Table G
Sample Size (N) | Significance Level α | ||||
---|---|---|---|---|---|
0.20 | 0.15 | 0.10 | 0.05 | 0.01 | |
1 | 0.900 | 0.925 | 0.950 | 0.975 | 0.995 |
2 | 0.684 | 0.726 | 0.776 | 0.842 | 0.929 |
3 | 0.565 | 0.597 | 0.642 | 0.708 | 0.828 |
4 | 0.494 | 0.525 | 0.564 | 0.624 | 0.733 |
5 | 0.446 | 0.474 | 0.510 | 0.565 | 0.669 |
6 | 0.410 | 0.436 | 0.470 | 0.521 | 0.618 |
7 | 0.381 | 0.405 | 0.438 | 0.486 | 0.577 |
8 | 0.358 | 0.381 | 0.411 | 0.457 | 0.543 |
9 | 0.339 | 0.360 | 0.388 | 0.432 | 0.514 |
10 | 0.322 | 0.342 | 0.368 | 0.410 | 0.490 |
11 | 0.307 | 0.326 | 0.352 | 0.391 | 0.468 |
12 | 0.295 | 0.313 | 0.338 | 0.375 | 0.450 |
13 | 0.284 | 0.302 | 0.325 | 0.361 | 0.433 |
14 | 0.274 | 0.292 | 0.314 | 0.349 | 0.418 |
15 | 0.266 | 0.283 | 0.304 | 0.338 | 0.404 |
16 | 0.258 | 0.274 | 0.295 | 0.328 | 0.392 |
17 | 0.250 | 0.266 | 0.286 | 0.318 | 0.381 |
18 | 0.244 | 0.259 | 0.278 | 0.309 | 0.371 |
19 | 0.237 | 0.252 | 0.272 | 0.301 | 0.363 |
20 | 0.231 | 0.246 | 0.264 | 0.294 | 0.356 |
25 | 0.21 | 0.22 | 0.24 | 0.27 | 0.32 |
30 | 0.19 | 0.20 | 0.22 | 0.24 | 0.29 |
35 | 0.18 | 0.19 | 0.21 | 0.23 | 0.27 |
Greater than 50 |
Table H1
Sample Size N | Significance Level α | ||||||||
---|---|---|---|---|---|---|---|---|---|
0.01 | 0.02 | 0.05 | 0.10 | 0.50 | 0.90 | 0.95 | 0.98 | 0.99 | |
3 | 0.753 | 0.758 | 0.767 | 0.789 | 0.959 | 0.998 | 0.999 | 1.000 | 1.000 |
4 | 0.687 | 0.707 | 0.748 | 0.792 | 0.935 | 0.987 | 0.992 | 0.996 | 0.997 |
5 | 0.686 | 0.715 | 0.762 | 0.806 | 0.927 | 0.979 | 0.986 | 0.991 | 0.993 |
6 | 0.713 | 0.743 | 0.788 | 0.826 | 0.927 | 0.974 | 0.981 | 0.936 | 0.989 |
7 | 0.730 | 0.760 | 0.803 | 0.838 | 0.928 | 0.972 | 0.979 | 0.985 | 0.988 |
8 | 0.749 | 0.778 | 0.818 | 0.851 | 0.932 | 0.972 | 0.978 | 0.984 | 0.987 |
9 | 0.764 | 0.791 | 0.829 | 0.859 | 0.935 | 0.972 | 0.978 | 0.984 | 0.986 |
10 | 0.781 | 0.806 | 0.842 | 0.869 | 0.938 | 0.972 | 0.978 | 0.983 | 0.986 |
11 | 0.792 | 0.817 | 0.850 | 0.876 | 0.940 | 0.973 | 0.979 | 0.984 | 0.986 |
12 | 0.805 | 0.828 | 0.859 | 0.883 | 0.943 | 0.973 | 0.979 | 0.984 | 0.986 |
13 | 0.814 | 0.837 | 0.866 | 0.889 | 0.945 | 0.974 | 0.979 | 0.984 | 0.986 |
14 | 0.825 | 0.846 | 0.874 | 0.895 | 0.947 | 0.975 | 0.980 | 0.984 | 0.986 |
15 | 0.835 | 0.855 | 0.881 | 0.901 | 0.950 | 0.976 | 0.980 | 0.984 | 0.987 |
16 | 0.844 | 0.863 | 0.887 | 0.906 | 0.952 | 0.975 | 0.981 | 0.985 | 0.987 |
17 | 0.851 | 0.869 | 0.892 | 0.910 | 0.954 | 0.977 | 0.981 | 0.985 | 0.987 |
18 | 0.858 | 0.874 | 0.897 | 0.914 | 0.956 | 0.978 | 0.982 | 0.986 | 0.988 |
19 | 0.863 | 0.879 | 0.901 | 0.917 | 0.957 | 0.978 | 0.982 | 0.986 | 0.988 |
20 | 0.868 | 0.884 | 0.905 | 0.920 | 0.959 | 0.979 | 0.983 | 0.986 | 0.988 |
21 | 0.873 | 0.888 | 0.908 | 0.823 | 0.960 | 0.980 | 0.983 | 0.987 | 0.989 |
22 | 0.878 | 0.892 | 0.911 | 0.926 | 0.961 | 0.980 | 0.984 | 0.987 | 0.989 |
23 | 0.881 | 0.895 | 0.914 | 0.928 | 0.962 | 0.981 | 0.984 | 0.987 | 0.989 |
24 | 0.884 | 0.898 | 0.916 | 0.930 | 0.963 | 0.981 | 0.984 | 0.987 | 0.989 |
25 | 0.888 | 0.901 | 0.918 | 0.931 | 0.964 | 0.981 | 0.985 | 0.988 | 0.989 |
26 | 0.891 | 0.904 | 0.920 | 0.933 | 0.965 | 0.982 | 0.985 | 0.988 | 0.989 |
27 | 0.894 | 0.906 | 0.923 | 0.935 | 0.965 | 0.982 | 0.985 | 0.988 | 0.990 |
28 | 0.896 | 0.908 | 0.924 | 0.936 | 0.966 | 0.982 | 0.985 | 0.988 | 0.990 |
29 | 0.898 | 0.910 | 0.926 | 0.937 | 0.966 | 0.982 | 0.985 | 0.988 | 0.990 |
30 | 0.900 | 0.912 | 0.927 | 0.939 | 0.967 | 0.983 | 0.985 | 0.988 | 0.900 |
Table H2
i / n | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0.7071 | 0.7071 | 0.6872 | 0.6646 | 0.6431 | 0.6233 | 0.6052 | 0.5888 | 0.5739 | |
2 | 0.0000 | 0.1677 | 0.2413 | 0.2806 | 0.3031 | 0.3164 | 0.3244 | 0.3291 | ||
3 | 0.0000 | 0.0875 | 0.1401 | 0.1743 | 0.1976 | 0.2141 | ||||
4 | 0.0000 | 0.0561 | 0.0947 | 0.1224 | ||||||
5 | 0.0000 | 0.0399 | ||||||||
i / n | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 0.5601 | 0.5475 | 0.5359 | 0.5251 | 0.5150 | 0.5056 | 0.4968 | 0.4886 | 0.4808 | 0.4734 |
2 | 0.3315 | 0.3325 | 0.3325 | 0.3318 | 0.3306 | 0.3290 | 0.3273 | 0.3253 | 0.3232 | 0.3211 |
3 | 0.2260 | 0.2347 | 0.2412 | 0.2460 | 0.2495 | 0.2521 | 0.2540 | 0.2553 | 0.2561 | 0.2565 |
4 | 0.1429 | 0.1586 | 0.1707 | 0.1802 | 0.1878 | 0.1939 | 0.1988 | 0.2027 | 0.2059 | 0.2085 |
5 | 0.0695 | 0.0922 | 0.1099 | 0.1240 | 0.1353 | 0.1447 | 0.1524 | 0.1587 | 0.1641 | 0.1686 |
6 | 0.0000 | 0.0303 | 0.0539 | 0.0727 | 0.0880 | 0.1005 | 0.1109 | 0.1197 | 0.1271 | 0.1334 |
7 | 0.0000 | 0.0240 | 0.0433 | 0.0593 | 0.0725 | 0.0837 | 0.0932 | 0.1013 | ||
8 | 0.0000 | 0.0196 | 0.0359 | 0.0496 | 0.0612 | 0.0711 | ||||
9 | 0.0000 | 0.0163 | 0.0303 | 0.0422 | ||||||
10 | 0.0000 | 0.0140 | ||||||||
i / n | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
1 | 0.4643 | 0.4590 | 0.4542 | 0.4493 | 0.4450 | 0.4407 | 0.4366 | 0.4328 | 0.4291 | 0.4254 |
2 | 0.3185 | 0.3156 | 0.3126 | 0.3098 | 0.3069 | 0.3043 | 0.3018 | 0.2992 | 0.2968 | 0.2944 |
3 | 0.2578 | 0.2571 | 0.2563 | 0.2554 | 0.2543 | 0.2533 | 0.2522 | 0.2510 | 0.2499 | 0.2487 |
4 | 0.2119 | 0.2131 | 0.2139 | 0.2145 | 0.2148 | 0.2151 | 0.2152 | 0.2151 | 0.2150 | 0.2148 |
5 | 0.1736 | 0.1764 | 0.1787 | 0.1807 | 0.1822 | 0.1836 | 0.1848 | 0.1857 | 0.1864 | 0.1870 |
6 | 0.1399 | 0.1443 | 0.1480 | 0.1512 | 0.1539 | 0.1563 | 0.1584 | 0.1601 | 0.1616 | 0.1630 |
7 | 0.1092 | 0.1150 | 0.1201 | 0.1245 | 0.1283 | 0.1316 | 0.1346 | 0.1372 | 0.1395 | 0.1415 |
8 | 0.0804 | 0.0878 | 0.0941 | 0.0997 | 0.1046 | 0.1089 | 0.1128 | 0.1162 | 0.1192 | 0.1219 |
9 | 0.0530 | 0.0618 | 0.0696 | 0.0764 | 0.0823 | 0.0876 | 0.0923 | 0.0965 | 0.1002 | 0.1036 |
10 | 0.0263 | 0.0368 | 0.0459 | 0.0539 | 0.0610 | 0.0672 | 0.0728 | 0.0778 | 0.0822 | 0.0862 |
11 | 0.0000 | 0.0122 | 0.0228 | 0.0321 | 0.0403 | 0.0476 | 0.0540 | 0.0598 | 0.0650 | 0.0697 |
12 | 0.0000 | 0.0107 | 0.0200 | 0.0284 | 0.0358 | 0.0424 | 0.0483 | 0.0537 | ||
13 | 0.0000 | 0.0094 | 0.0178 | 0.0253 | 0.0320 | 0.0381 | ||||
14 | 0.0000 | 0.0084 | 0.0159 | 0.0227 | ||||||
15 | 0.0000 | 0.0076 |
Table I
Sc | N | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
3 | 0.6250 | ||||||||||||
4 | 0.3750 | ||||||||||||
5 | 0.2500 | 0.5625 | |||||||||||
6 | 0.1250 | 0.4375 | |||||||||||
7 | 0.3125 | ||||||||||||
8 | 0.1875 | 0.5000 | |||||||||||
9 | 0.1250 | 0.4063 | |||||||||||
10 | 0.0625 | 0.3125 | |||||||||||
11 | 0.2188 | 0.5000 | |||||||||||
12 | 0.1563 | 0.4219 | |||||||||||
13 | 0.0938 | 0.3438 | |||||||||||
14 | 0.0625 | 0.2813 | 0.5313 | ||||||||||
15 | 0.0313 | 0.2188 | 0.4688 | ||||||||||
16 | 0.1563 | 0.4063 | |||||||||||
17 | 0.1094 | 0.3438 | |||||||||||
18 | 0.0781 | 0.2891 | 0.5273 | ||||||||||
19 | 0.0469 | 0.2344 | 0.4727 | ||||||||||
20 | 0.0313 | 0.1875 | 0.4219 | ||||||||||
21 | 0.0156 | 0.1484 | 0.3711 | ||||||||||
22 | 0.1094 | 0.3203 | |||||||||||
23 | 0.0781 | 0.2734 | 0.5000 | ||||||||||
24 | 0.0547 | 0.2305 | 0.4551 | ||||||||||
25 | 0.0391 | 0.1914 | 0.4102 | ||||||||||
26 | 0.0234 | 0.1563 | 0.3672 | ||||||||||
27 | 0.0156 | 0.1250 | 0.3262 | ||||||||||
28 | 0.0078 | 0.0977 | 0.2852 | 0.5000 | |||||||||
29 | 0.0742 | 0.2480 | 0.4609 | ||||||||||
30 | 0.0547 | 0.2129 | 0.4229 | ||||||||||
31 | 0.0391 | 0.1797 | 0.3848 | ||||||||||
32 | 0.0273 | 0.1504 | 0.3477 | ||||||||||
33 | 0.0195 | 0.1250 | 0.3125 | 0.5171 | |||||||||
34 | 0.0117 | 0.1016 | 0.2783 | 0.4829 | |||||||||
35 | 0.0078 | 0.0820 | 0.2461 | 0.4492 | |||||||||
36 | 0.0039 | 0.0645 | 0.2158 | 0.4155 | |||||||||
37 | 0.0488 | 0.1875 | 0.3823 | ||||||||||
38 | 0.0371 | 0.1611 | 0.3501 | ||||||||||
39 | 0.0273 | 0.1377 | 0.3188 | 0.5151 | |||||||||
40 | 0.0195 | 0.1162 | 0.2886 | 0.4849 | |||||||||
41 | 0.0137 | 0.0967 | 0.2598 | 0.4548 | |||||||||
42 | 0.0098 | 0.0801 | 0.2324 | 0.4250 | |||||||||
43 | 0.0059 | 0.0654 | 0.2065 | 0.3955 | |||||||||
44 | 0.0039 | 0.0527 | 0.1826 | 0.3667 | |||||||||
45 | 0.0020 | 0.0420 | 0.1602 | 0.3386 | |||||||||
46 | 0.0322 | 0.1392 | 0.3110 | 0.5000 | |||||||||
47 | 0.0244 | 0.1201 | 0.2847 | 0.4730 | |||||||||
48 | 0.0186 | 0.1030 | 0.2593 | 0.4463 | |||||||||
49 | 0.0137 | 0.0874 | 0.2349 | 0.4197 | |||||||||
50 | 0.0098 | 0.0737 | 0.2119 | 0.3934 | |||||||||
51 | 0.0068 | 0.0615 | 0.1902 | 0.3677 | |||||||||
52 | 0.0049 | 0.0508 | 0.1697 | 0.3424 | |||||||||
53 | 0.0029 | 0.0415 | 0.1506 | 0.3177 | 0.5000 | ||||||||
54 | 0.0020 | 0.0337 | 0.1331 | 0.2939 | 0.4758 | ||||||||
55 | 0.0010 | 0.0269 | 0.1167 | 0.2709 | 0.4516 | ||||||||
56 | 0.0210 | 0.1018 | 0.2487 | 0.4276 | |||||||||
57 | 0.0161 | 0.0881 | 0.2274 | 0.4039 | |||||||||
58 | 0.0122 | 0.0757 | 0.2072 | 0.3804 | |||||||||
59 | 0.0093 | 0.0647 | 0.1879 | 0.3574 | |||||||||
60 | 0.0068 | 0.0549 | 0.1698 | 0.3349 | 0.5110 | ||||||||
61 | 0.0049 | 0.0461 | 0.1527 | 0.3129 | 0.4890 | ||||||||
62 | 0.0034 | 0.0386 | 0.1367 | 0.2915 | 0.4670 | ||||||||
63 | 0.0024 | 0.0320 | 0.1219 | 0.2708 | 0.4452 | ||||||||
64 | 0.0015 | 0.0261 | 0.1082 | 0.2508 | 0.4235 | ||||||||
65 | 0.0010 | 0.0212 | 0.0955 | 0.2316 | 0.4020 | ||||||||
66 | 0.0005 | 0.0171 | 0.0839 | 0.2131 | 0.3808 | ||||||||
67 | 0.0134 | 0.0732 | 0.1955 | 0.3599 | |||||||||
68 | 0.0105 | 0.0636 | 0.1788 | 0.3394 | |||||||||
69 | 0.0081 | 0.0549 | 0.1629 | 0.3193 | |||||||||
70 | 0.0061 | 0.0471 | 0.1479 | 0.2997 | |||||||||
71 | 0.0046 | 0.0402 | 0.1338 | 0.2807 | |||||||||
72 | 0.0034 | 0.0341 | 0.1206 | 0.2622 | |||||||||
73 | 0.0024 | 0.0287 | 0.1083 | 0.2444 | |||||||||
74 | 0.0017 | 0.0239 | 0.0969 | 0.2271 | |||||||||
75 | 0.0012 | 0.0199 | 0.0863 | 0.2106 | |||||||||
76 | 0.0007 | 0.0164 | 0.0765 | 0.1947 | |||||||||
77 | 0.0005 | 0.0133 | 0.0676 | 0.1796 | |||||||||
78 | 0.0002 | 0.0107 | 0.0594 | 0.1651 | |||||||||
79 | 0.0085 | 0.0520 | 0.1514 | ||||||||||
80 | 0.0067 | 0.0453 | 0.1384 | ||||||||||
81 | 0.0052 | 0.0392 | 0.1262 | ||||||||||
82 | 0.0040 | 0.0338 | 0.1147 | ||||||||||
83 | 0.0031 | 0.0290 | 0.1039 | ||||||||||
84 | 0.0023 | 0.0247 | 0.0938 | ||||||||||
85 | 0.0017 | 0.0209 | 0.0844 | ||||||||||
86 | 0.0012 | 0.0176 | 0.0757 | ||||||||||
87 | 0.0009 | 0.0148 | 0.0677 | ||||||||||
88 | 0.0006 | 0.0123 | 0.0603 | ||||||||||
89 | 0.0004 | 0.0101 | 0.0535 | ||||||||||
90 | 0.0002 | 0.0083 | 0.0473 | ||||||||||
91 | 0.0001 | 0.0067 | 0.0416 | ||||||||||
92 | 0.0054 | 0.0365 | |||||||||||
93 | 0.0043 | 0.0319 | |||||||||||
94 | 0.0034 | 0.0277 | |||||||||||
95 | 0.0026 | 0.0240 | |||||||||||
96 | 0.0020 | 0.0206 | |||||||||||
97 | 0.0015 | 0.0177 | |||||||||||
98 | 0.0012 | 0.0151 | |||||||||||
99 | 0.0009 | 0.0128 | |||||||||||
100 | 0.0006 | 0.0108 | |||||||||||
101 | 0.0004 | 0.0090 | |||||||||||
102 | 0.0003 | 0.0075 | |||||||||||
103 | 0.0002 | 0.0062 | |||||||||||
104 | 0.0001 | 0.0051 | |||||||||||
105 | 0.0042 | ||||||||||||
106 | 0.0034 | ||||||||||||
107 | 0.0027 | ||||||||||||
108 | 0.0021 | ||||||||||||
109 | 0.0017 | ||||||||||||
110 | 0.0013 | ||||||||||||
111 | 0.0010 | ||||||||||||
112 | 0.0008 | ||||||||||||
113 | 0.0006 | ||||||||||||
114 | 0.0004 | ||||||||||||
115 | 0.0003 | ||||||||||||
116 | 0.0002 | ||||||||||||
117 | 0.0002 | ||||||||||||
118 | 0.0001 | ||||||||||||
119 | 0.0001 | ||||||||||||
120 | 0.0000 |
Right-tailed unilateral probabilities for the Wilcoxon test.