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.
Related research methods
- Descriptive Statistics
- Outlier Detection
When to use this tool
Use Grubbs' test to check whether a single extreme value is an outlier under an approximately normal assumption.
Assumptions
- Approximately normal data (Grubbs' test is sensitive to departures).
- At most a few suspected outliers.
Limitations
- Outliers may be genuine or erroneous; a test does not tell you which.
- Do not remove outliers solely because a test flags them — decide based on data quality and context.
How to interpret the result
A significant Grubbs' test suggests the flagged value is unlikely to have come from the same normal distribution as the rest of the sample.
How to report the result
Report the test statistic, critical value (or p-value), and the decision, together with how outliers were handled.
Next steps in your analysis
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