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The Wilcoxon test is a:
- Test of difference
- On related data (e.g. repeated measures)
- In the ordinal format
To find the correct critical value when calculating whether results are statistically significant using the Wilcoxon test, you need to know:
- Whether your experimental hypothesis is one-tailed or two-tailed
- The level of significance (p)
- This will be given to you in the exam
- Your sample size (n)
- This is calculated by counting the number of participants in your trial who showed a difference (i.e. you don’t include participants whose results were the same both times)
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 Wilcoxon test
One-tailed: The experimental hypothesis predicts a change in only one direction (also called a directional hypothesis).
The following are critical values for the Wilcoxon test for one-tailed experiments where the sample size (n) ranges between 5-20 and for p values of 0.1, 0.05 and 0.025.
| n | p = 0.1 | p = 0.05 | p = 0.025 |
| 5 | 2 | 0 | – |
| 6 | 3 | 2 | 0 |
| 7 | 5 | 3 | 2 |
| 8 | 8 | 5 | 3 |
| 9 | 10 | 8 | 5 |
| 10 | 14 | 10 | 8 |
| 11 | 17 | 13 | 10 |
| 12 | 21 | 17 | 13 |
| 13 | 26 | 21 | 17 |
| 14 | 31 | 25 | 21 |
| 15 | 36 | 30 | 25 |
| 16 | 42 | 35 | 29 |
| 17 | 48 | 41 | 34 |
| 18 | 55 | 47 | 40 |
| 19 | 62 | 53 | 46 |
| 20 | 69 | 60 | 52 |
Your results are statistically significant if the observed value is equal to or less than the critical value.
Two-tailed Wilcoxon test
Two-tailed: The experimental hypothesis predicts a change in either direction (also called a non-directional hypothesis).
The following are critical values for the Wilcoxon test for two-tailed experiments where the sample size (n) ranges between 5-20 and for p values of 0.1, 0.05 and 0.025.
| n | p = 0.1 | p = 0.05 | p = 0.025 |
| 5 | 0 | – | – |
| 6 | 2 | 0 | – |
| 7 | 3 | 2 | 0 |
| 8 | 5 | 3 | 2 |
| 9 | 8 | 5 | 3 |
| 10 | 10 | 8 | 5 |
| 11 | 13 | 10 | 8 |
| 12 | 17 | 13 | 10 |
| 13 | 21 | 17 | 13 |
| 14 | 25 | 21 | 17 |
| 15 | 30 | 25 | 20 |
| 16 | 35 | 29 | 25 |
| 17 | 41 | 34 | 29 |
| 18 | 47 | 40 | 34 |
| 19 | 53 | 46 | 39 |
| 20 | 60 | 52 | 45 |
Your results are statistically significant if the observed value is equal to or less than the critical value.