Outlier / Grubbs' Test Calculator

Detect a single suspected outlier with Grubbs' test.

How Grubbs' test works

Grubbs' test detects one outlier in a univariate dataset by comparing the most extreme value (the one farthest from the mean) against the spread of the data. The test statistic G is that deviation divided by the sample standard deviation.

The p-value and critical value come from the t-distribution with n−2 degrees of freedom. If the p-value is below your significance level, the suspected value is flagged as a statistical outlier.

This test only flags a value — it never removes it. Whether to exclude an outlier is a scientific decision based on measurement error, data quality and domain knowledge, not an automatic rule.

The formulas

G = max|xᵢ − x̄| / s · G_crit = ((n−1)/√n)·√(t²/(n−2+t²))

The critical value uses the t-distribution with n−2 degrees of freedom at significance α/(2n). The p-value is computed from the equivalent t statistic so it is exact at the critical boundary.

Worked example

A dataset with a clear outlier

For values 199.31 … 245.57 (n = 8) the value 245.57 is far from the others. Grubbs' G is about 2.47 with a critical value near 2.13 at α = 0.05, so the value is flagged as an outlier.

Frequently asked questions

What are the assumptions of Grubbs' test?

The data should be approximately normally distributed (the test is sensitive to non-normality), and the test is designed for at most one outlier. For several outliers, use other methods such as the generalized ESD test.

Should I automatically remove an outlier?

No. This calculator deliberately does not remove outliers. Investigate flagged values — a genuine measurement error may justify exclusion, but a valid extreme observation should usually stay.

Why does the test need at least three values?

The critical value uses n−2 degrees of freedom, so the test is only defined for n ≥ 3.

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