Grubbs Single Outlier Test Calculator
Compare the largest standardized deviation with a two-sided single-outlier Grubbs critical value.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Find the one observation farthest from the sample mean and compare its standardized distance with the Student-t-based familywise threshold.
G=max|x−mean|/sample SD; critical=(n−1)/√n × √(t²/(n−2+t²)); t upper-tail=α/(2n)
Worked example
For five values, a single far-separated observation drives G toward its upper limit (n−1)/√n≈1.78885438.
Assumptions and input details
Assumes independent normal data apart from at most one potential outlier. This is one test, not an iterative deletion procedure; multiple outliers can mask each other. Statistical flagging does not justify deleting a valid observation.
References: NIST: Grubbs test
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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