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The sign test can be used to test for:
- Differences
- In related data (e.g. repeated measures)
- In the nominal format
To find the correct critical value when calculating whether results are statistically significant using the sign test, you need to know:
- Whether your experimental hypothesis is one-tailed or two-tailed
- Your sample size (n) – e.g. the number of participants in your trial
- The level of significance (p)
Your results are statistically significant if the observed value is equal to or less 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
One-tailed: The experimental hypothesis predicts a change in only one direction (also called a directional hypothesis).
The following are critical values for one-tailed experiments with sample sizes (n) between 5-20 and p values of 0.1, 0.05, and 0.02.
| n | p = 0.1 | p = 0.05 | p = 0.02 |
| 5 | 0 | 0 | – |
| 6 | 1 | 0 | 0 |
| 7 | 1 | 0 | 0 |
| 8 | 1 | 1 | 0 |
| 9 | 2 | 1 | 1 |
| 10 | 2 | 1 | 1 |
| 11 | 3 | 2 | 1 |
| 12 | 3 | 2 | 2 |
| 13 | 3 | 3 | 2 |
| 14 | 4 | 3 | 2 |
| 15 | 4 | 3 | 3 |
| 16 | 5 | 4 | 3 |
| 17 | 5 | 4 | 4 |
| 18 | 6 | 5 | 4 |
| 19 | 6 | 5 | 4 |
| 20 | 6 | 5 | 5 |
Your results are statistically significant if the observed value is equal to or less than the critical value.
Two-tailed
Two-tailed: The experimental hypothesis predicts a change in either direction (also called a non-directional hypothesis).
The following are critical values for two-tailed experiments with sample sizes (n) between 5-20 and p values of 0.1, 0.05 and 0.02.
| n | p = 0.1 | p = 0.05 | p = 0.02 |
| 5 | 0 | – | – |
| 6 | 0 | 0 | – |
| 7 | 0 | 0 | 0 |
| 8 | 1 | 0 | 0 |
| 9 | 1 | 1 | 0 |
| 10 | 1 | 1 | 0 |
| 11 | 2 | 1 | 1 |
| 12 | 2 | 2 | 1 |
| 13 | 3 | 2 | 1 |
| 14 | 3 | 2 | 2 |
| 15 | 3 | 3 | 2 |
| 16 | 4 | 3 | 2 |
| 17 | 4 | 4 | 3 |
| 18 | 5 | 4 | 3 |
| 19 | 5 | 4 | 4 |
| 20 | 5 | 5 | 4 |
Your results are statistically significant if the observed value is equal to or less than the critical value.