ANOVA Family
Welch ANOVA Calculator
Welch ANOVA Calculator compare group means with unequal variances.
ANOVA Family
Welch ANOVA Calculator
Compare group means with unequal variances.
Formula
Welch ANOVA weights each group by n/s^2 and uses Welch-Satterthwaite denominator degrees of freedom for unequal variances.
About the Welch ANOVA Calculator
Compare group means with unequal variances. ANOVA calculators partition variation among named factors, conditions, subjects, interactions, and residual error for the selected experimental design.
How the Welch ANOVA Calculator Works
Welch ANOVA weights each group by n/s^2 and uses Welch-Satterthwaite denominator degrees of freedom for unequal variances.
The calculation runs in your browser. Submitted values are validated for the required numeric range, data shape, units, and method-specific restrictions before a result is shown.
Required Inputs
- Groups (required)
- Alpha (required)
Results Reported
The result panel shows the final answer together with the intermediate quantities needed to audit the calculation. Depending on this method, reported values include:
weighted_meancorrectiondf_betweendf_withinf_statisticp_valuedecision
Welch ANOVA Calculator Example
Use the example data button to load a known sample, then calculate and review the statistic, p-value or estimate, and interpretation.
| Input | Example value |
|---|---|
| Groups | A: 8, 9, 6, 7
B: 10, 12, 9, 11
C: 14, 13, 15, 16 |
| Matrix | 1, 2, 1
2, 3, 2
1, 2, 2
2, 4, 3 |
| Alpha | 0.05 |
How to Use the Calculator
- Confirm that the calculator title and method match the quantity, test, conversion, or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date, or option format.
- Select Example Data to inspect a valid input layout, or enter your own values and select Calculate.
- Review the result table, formula, worked substitutions, warnings, and interpretation rather than using only the headline number.
- Use Copy Result or Download CSV when you need a reusable record of the displayed calculation.
Understanding the Result
Match the calculator to replication, repeated measures, factor structure, and variance assumptions before interpreting an F test.
Keep the entered values, units, selected options, and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size, and decision. For an estimate or conversion, report the formula convention and final unit.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods, or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Welch ANOVA Calculator calculate?
Compare group means with unequal variances.
Which formula does the Welch ANOVA Calculator use?
Welch ANOVA weights each group by n/s^2 and uses Welch-Satterthwaite denominator degrees of freedom for unequal variances.
What input does this calculator need?
The calculator form shows the required values and validates them before calculating.
Are the formulas visible?
Yes. Each calculator displays its method, assumptions, and interpretation unless disabled by the site administrator.