Non-parametric tests

Learning objectives

Explain that a non-parametric test is used when the assumption of a normal population cannot be justified, and state the weaker assumptions each test still requires, such as a symmetric distribution for the Wilcoxon signed-rank test

Carry out a single-sample sign test for a population median by counting how many observations lie above and below the hypothesised median, discarding ties, and using the binomial distribution with p = ½

Carry out a Wilcoxon signed-rank test for a median, or for paired data, by ranking the absolute differences, attaching the original signs, summing the positive and the negative ranks and comparing the smaller sum with the tabulated critical value, rejecting the null hypothesis when the statistic is small enough

Carry out a Wilcoxon rank-sum test to compare two independent samples by ranking the combined data, summing the ranks of the smaller sample and comparing that total with the tabulated critical value, noting that the syllabus does not set questions with tied ranks or zero differences

Apply a normal approximation to the test statistic when the sample is large, using the appropriate mean and variance for the signed-rank or rank-sum statistic, and state the conclusion in context

Choose the appropriate test for a given situation by deciding whether the data are paired or independent and whether a normal model can reasonably be assumed