<<<back to statistical tests

The related t-test is a:

Whereas the unrelated t-test is a:

To find the correct critical value when calculating whether results are statistically significant using the related or unrelated t-test, you need to know:

  • Whether your experimental hypothesis is one-tailed or two-tailed
  • The degrees of freedom (df)
    • For related t-test, this is (sample size – 1)
    • For unrelated t-test, this is ((sample size of group A + sample size of group B) – 2)
  • The level of significance (p)
    • This will be given to you in the exam

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Note: Tables like the ones below will be provided in the exam – you don’t have to memorise all these critical values!

One-tailed t-test

One-tailed: The experimental hypothesis predicts a change in only one direction (also called a directional hypothesis).

The following are critical values of the related t-test and the unrelated t-test for one-tailed experiments where the degrees of freedom (df) range between 1-20 and for p values of 0.1, 0.05 and 0.025.

df p = 0.1 p = 0.05 p = 0.025
1 2 6.314 12.706
2 1.895 2.92 4.303
3 1.644 2.353 3.182
4 1.533 2.132 2.776
5 1.487 2.015 2.571
6 1.446 1.943 2.447
7 1.41 1.895 2.365
8 1.4 1.86 2.306
9 1.389 1.833 2.262
10 1.376 1.812 2.228
11 1.368 1.796 2.201
12 1.364 1.782 2.179
13 1.358 1.771 2.16
14 1.355 1.761 2.145
15 1.349 1.753 2.131
16 1.343 1.746 2.12
17 1.338 1.74 2.11
18 1.336 1.734 2.101
19 1.334 1.729 2.093
20 1.332 1.724 2.086

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Two-tailed t-test

Two-tailed: The experimental hypothesis predicts a change in either direction (also called a non-directional hypothesis).

The following are critical values of related t-test and the unrelated t-test for two-tailed experiments where the degrees of freedom (df) range between 1-20 and for p values of 0.1, 0.05 and 0.025.

df p = 0.1 p = 0.05 p = 0.025
1 6.314 12.707 25.452
2 2.92 4.303 6.206
3 2.353 3.182 4.177
4 2.132 2.776 3.496
5 2.015 2.571 3.164
6 1.943 2.447 2.969
7 1.895 2.365 2.842
8 1.86 2.306 2.752
9 1.833 2.262 2.686
10 1.812 2.228 2.634
11 1.796 2.201 2.594
12 1.782 2.179 2.561
13 1.771 2.16 2.533
14 1.761 2.145 2.51
15 1.753 2.131 2.490
16 1.746 2.12 2.473
17 1.74 2.11 2.459
18 1.734 2.101 2.446
19 1.729 2.093 2.434
20 1.724 2.086 2.424

Your results are statistically significant if the observed value is equal to or greater than the critical value.

<<<back to statistical tests