Degrees of freedom ν | Fraction p in percent | |||||
---|---|---|---|---|---|---|
68.27 (a) | 90 | 95 | 95.45 (a) | 99 | 99.73 (a) | |
1 | 1.84 | 6.31 | 12.71 | 13.97 | 63.66 | 235.80 |
2 | 1.32 | 2.92 | 4.30 | 4.53 | 9.92 | 19.21 |
3 | 1.20 | 2.35 | 3.18 | 3.31 | 5.84 | 9.22 |
4 | 1.14 | 2.13 | 2.78 | 2.87 | 4.60 | 6.62 |
5 | 1.11 | 2.02 | 2.57 | 2.65 | 4.03 | 5.51 |
6 | 1.09 | 1.94 | 2.45 | 2.52 | 3.71 | 4.90 |
7 | 1.08 | 1.89 | 2.36 | 2.43 | 3.50 | 4.53 |
8 | 1.07 | 1.86 | 2.31 | 2.37 | 3.36 | 4.28 |
9 | 1.06 | 1.83 | 2.26 | 2.32 | 3.25 | 4.09 |
10 | 1.05 | 1.81 | 2.23 | 2.28 | 3.17 | 3.96 |
11 | 1.05 | 1.80 | 2.20 | 2.25 | 3.11 | 3.85 |
12 | 1.04 | 1.78 | 2.18 | 2.23 | 3.05 | 3.76 |
13 | 1.04 | 1.77 | 2.16 | 2.21 | 3.01 | 3.69 |
14 | 1.04 | 1.76 | 2.14 | 2.20 | 2.98 | 3.64 |
15 | 1.03 | 1.75 | 2.13 | 2.18 | 2.95 | 3.59 |
16 | 1.03 | 1.75 | 2.12 | 2.17 | 2.92 | 3.54 |
17 | 1.03 | 1.74 | 2.11 | 2.16 | 2.90 | 3.51 |
18 | 1.03 | 1.73 | 2.10 | 2.15 | 2.88 | 3.48 |
19 | 1.03 | 1.73 | 2.09 | 2.14 | 2.86 | 3.45 |
20 | 1.03 | 1.72 | 2.09 | 2.13 | 2.85 | 3.42 |
25 | 1.02 | 1.71 | 2.06 | 2.11 | 2.79 | 3.33 |
30 | 1.02 | 1.70 | 2.04 | 2.09 | 2.75 | 3.27 |
35 | 1.01 | 1.70 | 2.03 | 2.07 | 2.72 | 3.23 |
40 | 1.01 | 1.68 | 2.02 | 2.06 | 2.70 | 3.20 |
45 | 1.01 | 1.68 | 2.01 | 2.06 | 2.69 | 3.18 |
50 | 1.01 | 1.68 | 2.01 | 2.05 | 2.68 | 3.16 |
100 | 1.005 | 1.660 | 1.984 | 2.025 | 2.626 | 3.077 |
∞ | 1.000 | 1.645 | 1.960 | 2.000 | 2.576 | 3.000 |
(a)For a quantity z described by a normal distribution with expectation µz and standard deviation σ, the interval µz ± kσ encompasses p = 68.27, 95.45, and 99.73 percent of the distribution for k = 1, 2, and 3, respectively.