Shapiro-Wilk Normality Test calculator

Test if your sample data is normally distributed. Run Shapiro-Wilk online and plot corresponding Q-Q plots.

What it does

Tests whether a sample is consistent with having come from a normal distribution.

When to use it

As one input to judging distributional shape — best read alongside a histogram or Q-Q plot rather than on its own.

Cautions

• It answers "is there evidence of non-normality?", which depends mostly on sample size. At n = 2,000 almost everything fails; at n = 15 almost nothing does.
• Most tests assume normality of the sampling distribution, not the raw data, and the Central Limit Theorem covers that in reasonably sized samples. A failed test is not automatically a reason to switch tests.
• For regression, the assumption is about residuals, not the outcome variable.

Alternatives

• A Q-Q plot — you want to see how it departs from normal, which matters more than whether it does

How to read the output

The p-value is about SAMPLE SIZE as much as normality

It tests whether the data could have come from a normal distribution. Power scales with n, so the same mild skew passes at n = 20 and fails at n = 2,000. A significant result on a large sample usually means a harmless departure that the test can now detect, and a non-significant one on a small sample means the test could not see anything — not that the data are normal.

Do not use it to choose your test

Testing normality and then picking a t-test or a rank test on the result is a two-stage procedure. The final p-value no longer means what it claims, because the choice of test depended on the same data. Decide from the design and a histogram, and remember the t-test assumes normality of the SAMPLING DISTRIBUTION, which the central limit theorem delivers at moderate n regardless.

Look at the plot

A histogram or Q-Q plot shows the shape and size of any departure. The test reduces that to one number and answers a question — "exactly normal?" — whose answer is always no. What matters is whether the departure is big enough to affect the analysis, which only the plot shows.

How this calculator is validated · Which statistical test should I use?