Welch ANOVA Calculator
Compare means of three or more independent groups with unequal sample variances using Welch’s omnibus F.
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Result
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Calculation steps
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How to calculate
Calculate inverse-variance group weights, a weighted grand mean and the unequal-variance F approximation.
Weights=ni/si²; use weighted between-mean variation and Welch denominator/df correction
Worked example
If every group mean is identical and each sample variance is positive, the Welch statistic is zero and the upper-tail probability is one.
Assumptions and input details
3–10 independent groups with at least two observations and positive sample variance each. Approximate F inference requires the usual distribution assumptions, especially for small groups. No pairwise post-hoc tests, repeated-subject model or automatic significance decision.
References: SciPy: Welch ANOVA and distribution assumptions
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.
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The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Partition variation across three or more groups into between-group and within-group sums of squares.
Compare independent sample means using unequal-variance standard errors, Welch degrees of freedom and a two-sided interval.
Compare group variances using median-centered Brown–Forsythe and normal-theory Bartlett calculations.
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