Wilcoxon Rank Test
The Wilcoxon Rank Test is used to test whether there is a significant difference between two repeated (paired) sample medians when your data cannot be assumed to be normally distributed.
- You want to compare two repeated (paired) samples (that is, each subject has been tested under the two conditions).
- Your data cannot be assumed to be normally distributed.
NOTES:
(a) You can use a Shapiro-Wilk (for data sets with up to 2,000 values) OR Kolmogorov-Smirnov Test (for very large data sets with over 2,000 values) Collecting Your Data to check for the assumption of “normality”.
(b) If your data is continuous and can be assumed to be normally distributed, you should use a Paired t-Test.
(c) If your data samples are independent, you should use a Mann-Whitney U-Test.
This test looks at the medians of the two samples.
A Wilcoxon Rank Test uses the following hypotheses:
H0: the medians of the two samples are equal.
H1: the medians of the two samples are not equal.
To do a Wilcoxon Rank Test, the following conditions must be met:
- Matched data: Each of the subjects in group A has also been tested in group B. The data must be entered into the online calculator in matched pairs.
- Shape: The shapes of the distributions for the two groups must be roughly the same. Comparing graphs of the data can be useful to confirm this condition is met.
An online calculator for this test can be found HERE.
You want to know if a certain information campaign increases the frequency with which people recycle their cans at school. To test this, you ask 20 people to keep track of how many cans they recycle during the week before and the week after they experience the campaign. Since each person can be “paired” with themselves, you plan on using a paired t-test to determine if there was a significant difference between the mean number of recycled cans before and after the campaign. However, the distribution turns out to be non-normal, so you decide to use a Wilcoxon Signed Rank Test. Your data is as shown on the right. Use the online calculator HERE. |  |
Match the fields with their values.
Treatment 1 | "Cans after" data |
Treatment 2 | One-tailed |
Significance level | Two-tailed |
One or two tailed hypothesis? | 0.05 |
| "Cans before" data |
This test produces a lot of data, but if you scroll down you should see:
"The result is significant at p < .05."
This means that we can reasonably assume that the information campaign helped people recycle more cans.
BUT can you identify factors outside your control which may have influenced this study? Tick all that could apply.
It should be clear that this isn't a well-designed study ... But it did allow you to practice doing a Wilcoxon Rank Test!