Direct comparison
Parametric vs Non-Parametric Tests: When to Use Each | CASRAI
Parametric tests assume normally distributed interval/ratio data; non-parametric tests make no distributional assumptions and suit ordinal data, small samples, or non-normal distributions.
Side-by-side comparison
| Dimension | Parametric Tests | Non-Parametric Tests |
|---|---|---|
| Key assumption | Data approximately normally distributed; interval or ratio scale | No distributional assumption; works with any distribution or ordinal scale |
| Common examples | t-test, ANOVA, Pearson correlation, linear regression | Mann-Whitney U, Kruskal-Wallis, Spearman rho, Wilcoxon signed-rank |
| Statistical power | Higher when assumptions are met | Lower — require a larger sample for the same power |
| Data type | Continuous, normally distributed; interval or ratio scale | Ordinal, skewed, or continuous with outliers; small N |
| Sample size | Generally perform well with N ≥ 30 (central limit theorem helps) | Preferred when N is small or normality cannot be confirmed |
| Robustness to violations | Some robustness to mild non-normality with large samples | Inherently robust — no normality assumption to violate |
| When to choose | Large samples, interval/ratio data, normality confirmed | Small samples, ordinal data, non-normal or unknown distribution, outliers |
| Tests for normality | Shapiro-Wilk, Kolmogorov-Smirnov — check before applying | Not required — the test is assumption-free |
Common questions
FAQ
Should I always use non-parametric tests to be safe?+
Not necessarily. Non-parametric tests are less statistically powerful than parametric equivalents when parametric assumptions are met — they require a larger sample to detect the same effect. If your data are approximately normally distributed and measured on an interval or ratio scale, parametric tests are more efficient and appropriate. Use non-parametric tests when assumptions are genuinely violated.
What is the non-parametric equivalent of a t-test?+
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is the non-parametric equivalent of the independent samples t-test. The Wilcoxon signed-rank test is the equivalent of the paired t-test. Both rank the data rather than using raw values, removing the normality assumption.
Does a large sample size remove the need for non-parametric tests?+
With large samples, the central limit theorem means the sampling distribution of the mean approaches normality regardless of the underlying distribution, making parametric tests more robust. However, if the underlying data are ordinal (e.g. Likert scales), parametric tests remain conceptually inappropriate because arithmetic operations on ordinal data are not meaningful, regardless of sample size.
Going deeper
