What is the difference between parametric and non-parametric tests?

Example Answer

Parametric tests specify a statistical model with a finite set of parameters. That does not always mean normal data: a binomial model for conversion is parametric too. Nonparametric tests avoid some particular distributional forms, often using ranks or the empirical distribution, but they still have assumptions about the sampling design and the hypothesis being tested.

For example, a two-sample Mann–Whitney test can compare independent groups without a normality assumption. Its basic null concerns the distributions, so I would not automatically describe it as a test of medians. A location-shift interpretation needs additional conditions, such as similarly shaped distributions. I would choose the test based on the estimand, pairing or clustering, sample size, and the type of difference that matters. Switching to a rank test does not fix dependent observations or biased sampling.

Why this works

It explains what distribution-free methods relax while retaining the conditions needed for a valid interpretation.

Follow-up to prepare for

If the business question specifically concerns a difference in means, does a rank-based test answer that question?