Degrees of freedom count the independent values available when estimating a statistical quantity. In a t-test, they help determine which critical t-value to use; the t-statistic alone does not establish whether a result meets a chosen significance threshold. section 4.2.1
The calculation depends on the test:
- For a one-sample example with 200 observations, use 200 − 1 = 199 degrees of freedom. section 4.2.1
- For the independent two-group t-test described here, use n₁ + n₂ − 2. Two groups of 31 observations each therefore have 60 degrees of freedom. section 4.2.1
Table 4.1 Abbreviated t-distribution table showing that increasing the degrees of freedom has diminishing returns on the t-critical values at each alpha level (p-value threshold).
|
degrees of freedom
|
alpha level
|
||||
|---|---|---|---|---|---|
|
0.1
|
0.05
|
0.01
|
0.005
|
0.001
|
|
|
10
|
1.81
|
2.23
|
3.17
|
3.58
|
4.59
|
|
20
|
1.72
|
2.09
|
2.85
|
3.15
|
3.85
|
|
30
|
1.70
|
2.04
|
2.75
|
3.03
|
3.65
|
|
40
|
1.68
|
2.02
|
2.70
|
2.97
|
3.55
|
|
50
|
1.68
|
2.01
|
2.68
|
2.94
|
3.50
|
|
60
|
1.67
|
2.00
|
2.66
|
2.91
|
3.46
|
|
70
|
1.67
|
1.99
|
2.65
|
2.90
|
3.44
|
|
80
|
1.66
|
1.99
|
2.64
|
2.89
|
3.42
|
|
90
|
1.66
|
1.99
|
2.63
|
2.88
|
3.40
|
|
100
|
1.66
|
1.98
|
2.63
|
2.87
|
3.39
|
|
150
|
1.66
|
1.98
|
2.61
|
2.85
|
3.36
|
|
200
|
1.65
|
1.97
|
2.60
|
2.84
|
3.34
|
The t-distribution table pairs degrees of freedom with an alpha level to select a critical value. At alpha 0.05, the listed value falls from 2.00 at 60 degrees of freedom to 1.97 at 200: increasing the sample size brings diminishing changes to this cutoff. section 4.2.1
Select the calculation for the test before consulting a critical-value table. A statistically significant result still needs careful interpretation: sample size and the assumptions of a parametric test matter. section 4.2.1
