Describe the process of hypothesis testing with non-parametric tests.

Instruction: Explain when non-parametric tests are used and describe the general process of conducting one.

Context: This question gauges the candidate's knowledge of non-parametric tests, highlighting their flexibility in hypothesis testing without normal distribution assumptions.

Updated

Official answer

Specify the outcome, estimand and sampling or assignment design first. Nonparametric methods relax particular distributional forms; they are not assumption-free and are not all rank tests.

For independent groups, Mann–Whitney can test a distributional null under suitable sampling assumptions. A median-shift interpretation needs additional restrictions. For paired data, Wilcoxon signed-rank concerns the distribution of within-pair differences and uses symmetry assumptions for its usual location interpretation; the sign test asks a different question. Kruskal–Wallis extends a rank comparison to multiple independent groups.

Choose the method before inspecting which yields significance. Check ties, zeros, dependence and the applicability of exact or asymptotic calibration. A permutation test must preserve the design and relevant exchangeability, rather than freely shuffling clustered records.

Report the statistic, uncertainty or effect summary suited to the estimand, and multiplicity handling. A significant result does not by itself justify rollout; practical value, measurement validity and guardrails still matter.

Related Questions