Tests that make no assumption about the shape of the underlying distribution. Useful precisely when the data is not normal.
Syllabus points covered
- Use the sign test for a population median
- Use the Wilcoxon signed-rank test for a population median and for paired samples
- Use the Wilcoxon rank-sum test for two independent samples
- Determine critical values and state conclusions in context
Common mistakes
- Keeping a zero difference in the sample. Any value equal to the hypothesised median is discarded, and n must be reduced to match before you look up the critical value.
- Assigning ranks to the raw values rather than to the absolute differences in a signed-rank test.
- Forgetting to take the smaller of T+ and T− as the test statistic.
- Comparing the test statistic to the critical value in the wrong direction — for these tests you reject the null hypothesis when the statistic is small, not large.
- Stating the conclusion as a bare inequality. The marks are for the sentence about the situation in the question.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Further Mathematics past papers