Direct comparison
Parametric vs Non-Parametric Tests
How to actually choose: data type, whether sample size lets the CLT rescue you, and the power cost of defaulting to non-parametric. Links to every test guide.
Written and maintained by CASRAI Editorial Board
Last updated
Ask CASRAI · included with Regulatory Radar
Ask about Parametric vs Non-Parametric Tests
Ask CASRAI answers research-administration questions and cites the passages behind every claim — and says so when the corpus does not cover something, instead of guessing. It comes with a Regulatory Radar subscription at $29 a month, alongside the daily digest of regulatory changes and the dashboard of what changed.
150 questions a day, on this site, over the API, or inside your own tools through the CASRAI MCP server.
Everything CASRAI publishes — this page, the dictionary, the guides and the news — stays free to read, with no account and no card.
How do Parametric test, Non-parametric test compare side by side?
The table below compares Parametric test, Non-parametric test across 13 procurement-relevant dimensions, from what it actually tests through what a significant result actually tells you.
Side-by-side comparison
| Dimension | Parametric test | Non-parametric test |
|---|---|---|
| What it actually tests | A population parameter — typically a mean or a mean difference — estimated from the raw values. | The distribution, median, or rank order of the data, without estimating a specific population parameter. |
| Minimum data type | Interval or ratio data (values where the size of the gap between numbers is meaningful). | Works with ordinal data and ranks, and can be used on interval/ratio data too when its parametric counterpart is not appropriate. |
| Distribution assumption | Assumes a specific population distribution — usually that the sampling distribution of the statistic being tested is approximately normal. | Makes no assumption about the population distribution (or, for a few tests such as the Wilcoxon signed-rank test, only a much weaker one, like symmetry). |
| Behavior at small sample sizes | Depends on the raw data itself being reasonably close to the assumed distribution, since there usually isn't enough data for the Central Limit Theorem to compensate. | Remains valid at very small n precisely because it never relied on asymptotic normality. |
| Behavior at large sample sizes | Often valid even against visibly skewed raw data, because the Central Limit Theorem brings the sampling distribution of the mean toward normal as n grows. | Still valid, but the power gap to the parametric alternative (when the parametric assumptions hold) tends to narrow as n grows. |
| Statistical power, when parametric assumptions genuinely hold | Higher — it uses the actual magnitude of every observation. | Lower, commonly cited around a 5-10% efficiency loss for the rank-based alternatives to the t-test and ANOVA, because ranking discards magnitude. |
| Robustness when assumptions are violated (outliers, heavy skew) | Can be distorted by outliers and skew, since both pull directly on the mean. | Resistant to outliers and skew, since ranks compress extreme values down to their rank position. |
| Comparing two independent groups | Independent-samples t-test | Mann-Whitney U test |
| Comparing two paired or matched measurements | Paired-samples t-test | Wilcoxon signed-rank test |
| Comparing three or more independent groups | One-way ANOVA | Kruskal-Wallis test |
| Comparing three or more repeated measurements | Repeated-measures ANOVA | Friedman test |
| Testing association between two continuous variables | Pearson correlation | Spearman's rank correlation |
| What a significant result actually tells you | The group means (or the relationship between means) differ. | The distributions, medians, or rank order differ — not necessarily the means. |
Common questions
Common questions about Parametric test vs Non-parametric test
Is a significant Shapiro-Wilk (or Kolmogorov-Smirnov) test on my raw data enough to decide?
+
Not on its own. Those tests check whether the raw sample looks normal, but the test that actually matters for a t-test or ANOVA is whether the sampling distribution of the mean is approximately normal — which the Central Limit Theorem can deliver even when the raw data is skewed, once the sample is large enough. At large n, a normality test on raw data will flag small, practically irrelevant deviations as statistically significant, which is why it shouldn't be the sole decision rule. A visual check (histogram, Q-Q plot) alongside the sample size is more informative than the p-value alone.
If my sample is large, can I always just ignore non-normal data and run the parametric test?
+
Usually, for a test of the mean — that's the Central Limit Theorem doing its job. It doesn't rescue every situation: severe outliers can still distort a mean regardless of sample size, and the CLT's protection applies specifically to statistics built from averaging, not to every parametric test equally. Check what the specific test you're running actually assumes before treating 'n is large' as a blanket justification.
Does the non-parametric test always cost me power?
+
Only when the parametric test's own assumptions genuinely hold. If the population is meaningfully non-normal, contains outliers, or the data is ordinal to begin with, the non-parametric alternative can match or exceed the parametric test's power, because the parametric test's efficiency advantage depends on its assumptions being true.
Where does ordinal data, like a single Likert-scale item, fit?
+
Ordinal data doesn't meet the interval/ratio assumption most parametric tests rely on, so the non-parametric route (Mann-Whitney, Kruskal-Wallis, Spearman correlation) is the conventional default for a single ordinal item. Practice diverges for a summed multi-item Likert scale treated as roughly continuous — that's a measurement-level judgment call to make explicitly and report, not a case this decision tree resolves for you.
Going deeper
