Shapiro-Wilk Normality Test
Normality tests online with Q-Q plot. Shapiro Wilk for small to medium samples.
When to use it
Use to test whether a sample comes from a normal distribution before running a parametric test (t-test, ANOVA, regression). Shapiro-Wilk has the best power for small to medium samples (n up to about 5000) and is the most widely cited normality test in agronomy and biology journals.
When NOT to use it
Do not use as the only check; pair with a Q-Q plot. Do not use on very large samples (n > 5000) where the test rejects trivial deviations of no practical importance. For tail-sensitivity prefer Anderson-Darling. For checking normality of regression residuals, run the test on residuals not on raw Y.
What you get
The W statistic, the p-value, sample size, mean and SD, plus a normal Q-Q plot of the data with the reference line. Output flags when n is outside the test's recommended range.
How to interpret the output
Reject normality when p is below alpha. A non-rejection is not proof of normality, only that the test could not detect deviation. For ANOVA practical guidance: mild non-normality is tolerable when groups are balanced and n is moderate; severe right-skew suggests a log transform. Always read the Q-Q plot in addition to the p (Royston 1995 recommends visual checks as primary, formal tests as confirmation).
Common pitfalls
- Treating a non-significant p as proof the data are normal.
- Running the test on raw Y instead of residuals when checking ANOVA assumptions.
- Rejecting normality on a tiny deviation in a very large sample.
- Skipping the Q-Q plot.
Try it in StatVeda
The Shapiro-Wilk Normality engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Shapiro-Wilk NormalityReferences
- Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3-4), 591 to 611.
- Royston, P. (1995). A remark on Algorithm AS 181: The W test for normality. Applied Statistics, 44(4), 547 to 551.