StatReason

Welch ANOVA Calculator

Compare three or more independent group means without assuming they all share the same variance.

One group per line, comma-separated values. At least 2 groups, each with at least 2 values.

What this answers

Welch ANOVA answers the same question as One-Way ANOVA (do three or more independent group means differ), but without requiring the groups to share the same variance. The classic One-Way ANOVA can become unreliable when group variances differ substantially, especially with unequal group sizes; Welch's correction adjusts for this directly.

When to use it, and when not to

Use Welch ANOVA whenever your groups show meaningfully different spread, which you can check directly with the Levene Variance Test. If your groups show comparable variance, the classic One-Way ANOVA uses slightly more information and remains a reasonable default.

How it is calculated

Each group is weighted by its sample size divided by its own variance, so groups with smaller variance (more precisely estimated means) contribute more to the calculation. The F statistic and its degrees of freedom are both adjusted using the Welch-Satterthwaite approximation, which can produce a non-integer denominator degrees of freedom, unlike the classic ANOVA's clean integer values.

Worked example

For three groups with clearly different spread (a tight low group, a wider middle group, and a very tight high group): Welch ANOVA weights each group's contribution by its own precision rather than assuming they are all equally variable, giving a result that better reflects the actual evidence when variances genuinely differ this much.

Assumption audit

Calculated from your data: each group's mean, variance, and sample size, and the resulting Welch-corrected F statistic and degrees of freedom.
Evidence to review: compare each group's variance directly; if they look reasonably similar, the classic One-Way ANOVA result would likely agree closely with this one anyway.
You must verify: that groups are genuinely independent, and that a significant omnibus result here does not by itself identify which specific groups differ from each other.

What this result does not mean

A significant Welch ANOVA result means at least one group's mean differs from the others at your chosen threshold, not that every group differs from every other, and not which specific groups are responsible for the difference.

Limitations

Welch ANOVA still assumes each group's data is reasonably close to normally distributed; it relaxes the equal-variance assumption specifically, not every assumption behind ANOVA.