Parametric vs Non-Parametric Tests

Before picking a specific test you choose a family. Parametric tests (t-test, ANOVA, Pearson correlation) assume the outcome is continuous and roughly normally distributed, and some assume equal variances. When those assumptions hold, parametric tests are more powerful: they use the actual values and are more likely to detect a real effect. Non-parametric tests (Mann-Whitney, Kruskal-Wallis, Wilcoxon, Spearman) make far fewer assumptions; instead of the raw values they convert data to ranks (order positions) and compare those. This makes them robust to skew, outliers, and ordinal data, at the cost of a little power. How to decide: look at the outcome. Is it continuous and approximately normal? A quick histogram or Q-Q plot, or a formal Shapiro-Wilk test, answers this. If yes, and the sample is not tiny, use parametric. If the data are skewed, ordinal (like pain 0 to 10 or a Likert scale), have influential outliers, or the sample is very small, lean non-parametric. With large samples, parametric tests are fairly forgiving of mild non-normality thanks to the central limit theorem, so do not reflexively switch on a borderline check. Two common misconceptions. Non-parametric does not mean 'no assumptions at all' (for example, Mann-Whitney assumes similar distribution shapes when you interpret it as comparing medians). And a 'significant' Shapiro-Wilk test in a very large sample can flag trivial non-normality that does not matter in practice. The judgment is clinical and practical, not mechanical. Why it matters: using a parametric test on badly skewed data (length of stay, biomarker levels) can give misleading p-values; using a non-parametric test needlessly on clean normal data slightly weakens your study. Whatever you choose, state which test you used and why, and match your descriptive statistics to it.