Paired tests — Edexcel A-Level Statistics
Test yourself on Paired tests with PEARSON EDEXCEL A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
Paired tests explained
This criterion covers three paired tests: the sign test, the Wilcoxon signed-rank test and the paired t-test.
Read the full explanation
You must choose the appropriate test from the data's features and interpret the outcome. The paired t-test assumes differences are approximately normally distributed; the Wilcoxon signed-rank test uses ranks of absolute differences and suits symmetric non-normal differences; the sign test uses only the direction of each difference and is the most robust but least powerful. For example, with paired measurements of a pollutant before and after treatment, if differences are clearly skewed you use the sign test. If differences are symmetric but not normal, the Wilcoxon signed-rank test is appropriate. In an MCQ you may be asked which test is suitable, or to interpret a given p-value for the chosen test.
Your focus
- Identify paired data and form the within-pair differences before selecting a test.
- Choose between the sign test, the Wilcoxon signed-rank test and the paired t-test using the distributional features of the differences.
- Interpret the result of the chosen paired test in the context of the original variables and population.
Paired tests exam tips
Marking Points
- Selects the paired t-test when the differences can reasonably be treated as approximately normally distributed, and interprets its result for the mean difference.
- Selects the Wilcoxon signed-rank test when the differences are not approximately normal but are roughly symmetric, and interprets its result for the median difference.
- Selects the sign test when only the direction of the differences is used or when differences are clearly skewed, and interprets its result for the median difference.
- Recognises that all three tests are for paired data, so the analysis is based on the differences within each pair rather than on two independent samples.
- Interprets the outcome in context, stating whether there is sufficient evidence of a change or difference in the named variable for the population concerned.
Examiner Tips
- 💡Check the data structure first: if each observation in one sample is matched with one in the other, the test must be paired.
- 💡Look for clues about the distribution of the differences, such as skewness or outliers, to decide between the paired t-test and the rank-based tests.
- 💡When interpreting, name the test, the parameter and the context, and state the conclusion in terms of evidence rather than proof.
Common Mistakes
- Using an independent two-sample test on paired data; the correction is to form the differences within each pair and apply a paired test.
- Choosing the Wilcoxon signed-rank test when the differences are strongly skewed; the correction is to use the sign test instead, as Wilcoxon assumes symmetry.
- Confusing the parameter being tested, for example claiming the Wilcoxon signed-rank test compares means; the correction is that it is used to test the median difference.
- Ignoring the direction of the alternative hypothesis when interpreting the result; the correction is to match the conclusion to the one- or two-tailed alternative stated.