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Statistical assumptions checker

Paste one numeric sample to inspect normality, shape and possible outliers in one report.

Approximate normality p-value: —

Fill in the fields above — the result is computed on this page.

Observations
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Shapiro–Francia W′
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Approximate p
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Anderson–Darling A²*
—
Anderson–Darling p
—
QQ correlation
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IQR outliers
—
Skewness
—
Excess kurtosis
—

Normal QQ plot

Points close to the reference line are consistent with a normal shape.

Diagnostic tests

Test Statistic p-value
Fill in the fields above — the result is computed on this page.
What these numbers mean
  • Interpret tests together with the QQ plot.
  • A small p-value flags evidence against normality.
  • Outliers should be investigated rather than removed automatically.

The Shapiro result is a documented Shapiro–Francia large-sample approximation. Results can be unstable for very small samples and overly sensitive for large samples.

How to use this page
  1. Paste the observations.
  2. Inspect the QQ plot and outliers.
  3. Use the test selector if assumptions are doubtful.

What this page does not do: The Shapiro result is a documented Shapiro–Francia large-sample approximation. Results can be unstable for very small samples and overly sensitive for large samples.

Further reading

Assumption checks support a decision about a model; they do not replace inspection of the data and study design. The report combines a normal-score approximation, Anderson–Darling, a QQ plot, skewness, kurtosis and the IQR rule.

Frequently asked questions

Does p > 0.05 prove normality?

No. It means the sample did not provide strong evidence against the model.

Should every outlier be removed?

No. Verify measurement and context first.

See also

← All calculators

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