Appendix 2. Student’s t distribution
This table gives percentage points of the t distribution of n degrees of freedom. These are the values of t for which a given percentage, P, of the t distribution lies outside the range -t to +t. As the number of degrees of freedom increases, the distribution becomes closer to the standard normal distribution.
One-tailed |
Two-tailed |
|||
Percentage (P) |
||||
Degree of freedom (v) |
5% |
1% |
5% |
1% |
1 |
6.31 |
31.8 |
12.7 |
63.7 |
2 |
2.92 |
6.96 |
4.30 |
9.92 |
3 |
2.35 |
4.54 |
3.18 |
5.84 |
4 |
2.13 |
3.75 |
2.78 |
4.60 |
5 |
2.02 |
3.36 |
2.57 |
4.03 |
6 |
1.94 |
3.14 |
2.45 |
3.71 |
7 |
1.89 |
3.00 |
2.36 |
3.50 |
8 |
1.86 |
2.90 |
2.31 |
3.36 |
9 |
1.83 |
2.82 |
2.26 |
3.25 |
10 |
1.81 |
2.76 |
2.23 |
3.17 |
11 |
1.80 |
2.72 |
2.20 |
3.11 |
12 |
1.78 |
2.68 |
2.18 |
3.05 |
13 |
1.77 |
2.65 |
2.16 |
3.01 |
14 |
1.76 |
2.62 |
2.14 |
2.98 |
15 |
1.75 |
2.60 |
2.13 |
2.95 |
16 |
1.75 |
2.58 |
2.12 |
2.92 |
17 |
1.74 |
2.57 |
2.11 |
2.90 |
18 |
1.73 |
2.55 |
2.10 |
2.88 |
19 |
1.73 |
2.44 |
2.09 |
2.86 |
20 |
1.72 |
2.53 |
2.09 |
2.85 |
22 |
1.72 |
2.51 |
2.07 |
2.82 |
24 |
1.72 |
2.49 |
2.06 |
2.80 |
26 |
1.71 |
2.48 |
2.06 |
2.78 |
28 |
1.70 |
2.47 |
2.05 |
2.76 |
30 |
1.70 |
2.46 |
2.04 |
2.75 |
35 |
1.69 |
2.44 |
2.03 |
2.72 |
40 |
1.68 |
2.42 |
2.02 |
2.70 |
45 |
1.68 |
2.41 |
2.01 |
2.69 |
50 |
1.68 |
2.40 |
2.01 |
2.68 |
55 |
1.67 |
2.40 |
2.00 |
2.67 |
60 |
1.67 |
2.39 |
2.00 |
2.66 |
¥ |
1.64 |
2.33 |
1.96 |
2.58 |