Shapiro-Wilk Normality Test
Shapiro-Wilk normality test · Also known as: Shapiro-Wilk W test, W test for normality, Shapiro-Wilk normallik testi
The Shapiro-Wilk test is a hypothesis test that checks whether a continuous variable was drawn from a normal distribution. It was introduced by Samuel Shapiro and Martin Wilk in 1965 and is regarded as one of the most powerful normality tests, recommended for sample sizes below 5000.
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When to use it
Use it to test the normality of a single continuous variable, typically as an assumption check before applying parametric tests. It requires a continuous variable and at least a handful of observations (the StatWise implementation expects a minimum of about eight). It is recommended for samples under 5000; for very large samples the Kolmogorov-Smirnov test is generally preferred.
Strengths & limitations
- Considered one of the most powerful tests for detecting departures from normality.
- Works well across a wide range of sample sizes, especially small to moderate ones.
- Simple to apply and reported by every major statistical package.
- Requires a continuous variable and is not meant for discrete or categorical data.
- Loses reliability on very large samples, where it flags trivial deviations as significant; it is recommended only for n below 5000.
- Only assesses normality — it says nothing about which specific way the data depart from it.
Frequently asked
Should I prefer Shapiro-Wilk or Kolmogorov-Smirnov?
Shapiro-Wilk is generally more powerful and is the recommended choice for samples below 5000. For very large samples the Kolmogorov-Smirnov test is often preferred, since Shapiro-Wilk tends to flag even trivial deviations as significant at large n.
What does a non-significant result mean?
A p-value above 0.05 means there is no significant evidence against normality, so you may proceed with methods that assume normality. It does not prove the data are exactly normal — failure to reject the null is not positive proof.
How many observations do I need?
The test needs a continuous variable and at least a small sample to be meaningful; the StatWise implementation expects roughly eight observations or more. With too few points the test has little power to detect non-normality.
My data fail the test — what should I do?
Consider the sample size and inspect a histogram or Q-Q plot before deciding. If non-normality is genuine, you can transform the variable or switch to a nonparametric method instead of forcing a parametric test.
Sources
- Shapiro, S. S. & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3-4), 591–611. DOI: 10.1093/biomet/52.3-4.591 ↗
How to cite this page
ScholarGate. (2026, June 1). Shapiro-Wilk normality test. ScholarGate. https://scholargate.app/en/statistics/shapiro-wilk-test
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