Parametric vs Nonparametric Tests
Parametric Tests vs Nonparametric Tests
Two broad families of statistical tests. Parametric tests assume the data follow a specific distribution (usually normal) and operate on parameters like means. Nonparametric tests make fewer distributional assumptions and often use ranks.
Comparison Table
| Feature | Parametric Tests | Nonparametric Tests |
|---|---|---|
| Distribution Assumption | Assumes normal distribution | No specific distribution assumed |
| Data Type | Continuous (interval/ratio) | Ordinal, ranked, or non-normal continuous |
| Central Tendency | Compares means | Compares medians or ranks |
| Statistical Power | Higher when assumptions met | Lower but more robust |
| Examples | t-test, ANOVA, Pearson r | Mann-Whitney U, Kruskal-Wallis, Spearman rho |
Key Differences
- →Parametric tests require normally distributed data (or large samples for CLT); nonparametric tests do not.
- →Parametric tests are generally more powerful when their assumptions are satisfied, meaning they are better at detecting true effects.
- →Nonparametric tests convert data to ranks, making them resistant to outliers and skewed distributions.
- →Parametric tests estimate population parameters (means, variances); nonparametric tests focus on distribution-free comparisons.
When to Use Parametric Tests
- ✓Your data are continuous and approximately normally distributed.
- ✓Sample sizes are large enough for the Central Limit Theorem to apply.
- ✓You need maximum statistical power to detect small effects.
When to Use Nonparametric Tests
- ✓Your data are ordinal (e.g., Likert scale ratings) or heavily skewed.
- ✓Sample sizes are very small and normality cannot be verified.
- ✓Outliers are present and you want a test robust to extreme values.
Common Confusions
- !Thinking nonparametric tests have no assumptions at all (they still assume independence and identically shaped distributions in some cases).
- !Automatically choosing nonparametric tests for small samples without first checking if the data are approximately normal.
- !Believing parametric tests always fail with non-normal data (they are quite robust with moderate sample sizes).
FAQs
Common questions about this comparison
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is the nonparametric alternative to the independent-samples t-test. For paired data, the Wilcoxon signed-rank test replaces the paired t-test. These tests compare rank sums rather than means.
Not necessarily. If your data meet parametric assumptions, using a parametric test gives you more statistical power. Nonparametric tests are a good fallback when assumptions are violated, but they are less efficient when the data truly are normal.