ANOVA calculator

Welch's ANOVA calculator

Compare multiple group means when group variances are unequal using Welch's ANOVA, adjusted F-statistic, Welch degrees of freedom, and Games-Howell post-hoc test.

Run this test live in StatLab npm i @statlab/core

When to use it

Use for multi-group mean comparisons when Levene’s test indicates unequal variances.

Required Inputs

  • Groups of numeric values
  • Alpha level
  • Post-hoc method (Games-Howell)

Mathematical Formula

F_W = [ Σ w_i(X̄_i - X̄')² / (k - 1) ] / [ 1 + 2(k - 2)/(k² - 1) * Σ ((1 - w_i/W)² / (n_i - 1)) ]

Reporting Cautions

  • Use Games-Howell for post-hoc comparisons instead of Tukey HSD when variances differ.
  • Degrees of freedom are non-integer due to Welch adjustment.

Code Snippets (Python, R, TypeScript)

Python (SciPy / Statsmodels) 
import pingouin as pg
res = pg.welch_anova(dv='value', between='group', data=df)
print(res)
R Language 
oneway.test(value ~ group, data = df, var.equal = FALSE)
TypeScript (@statlab/core) 
import { welchAnova } from '@statlab/core';
const result = welchAnova([groupA, groupB, groupC]);

Developer Use Cases & Production Integrations

  • Comparing API response time distributions across microservices with heterogeneous traffic variances.
  • Benchmarking system load tests where high-load variants exhibit much higher variance.

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