9231 · 4.4
Non-parametric tests — FAQ
Frequently asked questions for 9231 Non-parametric tests. Direct answers first, then deeper explanation — then practise with marking.
What's the main difference between the Wilcoxon signed-rank test and the Wilcoxon rank-sum test?
The signed-rank test is for a single sample (or paired data, where you test the median of the differences). It tests if the population median is a specific value. The rank-sum test is for two independent samples, and it tests whether the two populations they come from have the same median.
Why do we use the median in these tests instead of the mean?
The median is a more 'robust' measure of central tendency than the mean. This means it is less affected by extreme values (outliers) or skewed data. Since non-parametric tests are designed for situations where the data might not be normally distributed, using the median is a more reliable approach.
What happens if there are ties in the data for a rank-sum test?
If two or more observations are identical, they are each assigned the average of the ranks they would have occupied. For example, if two values are tied for the 5th and 6th positions, they both receive a rank of (5+6)/2 = 5.5. The next value then receives rank 7. The formulae for the variance in the large sample approximations should be adjusted for ties, but this is not typically required in the 9231 syllabus unless the formula is given.