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.
Key highlights
- 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.
Intuition
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How it works
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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.
Common pitfalls
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Applications
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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
- 1.Shapiro, S. S. & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3-4), 591–611.
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Cite this page
ScholarGate. (2026, June 1). Shapiro-Wilk test. ScholarGate. https://scholargate.app/statistics/shapiro-wilk-test