🧪 One-Way ANOVA Calculator

Compare group means with the classic one-way ANOVA. Paste raw data for two or more groups and obtain the ANOVA table, F statistic, p-value, critical value, effect sizes (η², ω²), and a step-by-step explanation aligned with Montgomery’s design-of-experiments guidelines.

1. Enter Group Data

Provide raw numeric observations for each treatment group. Use commas, spaces, or newlines as separators. Add or remove groups as needed.

Significance Level (α)

Custom α must be between 0.001 and 0.25.

Formula Reference

Core ANOVA

\\[ F = \frac{MS_{\text{treatment}}}{MS_{\text{error}}} = \frac{SS_{\text{between}}/df_{\text{between}}}{SS_{\text{within}}/df_{\text{within}}} \\]

Effect Sizes

\\[ \eta^2 = \frac{SS_{\text{between}}}{SS_{\text{total}}}, \qquad \omega^2 = \frac{SS_{\text{between}} - df_{\text{between}} MS_{\text{within}}}{SS_{\text{total}} + MS_{\text{within}}} \\]

How to Use This Calculator

  1. Enter raw numeric data for each treatment group (minimum two groups, total N > groups).
  2. Confirm the significance level α (defaults to 0.05).
  3. Click “Run ANOVA” to compute sums of squares, mean squares, the F test, and effect sizes.
  4. If F is significant, consider post-hoc comparisons (Tukey HSD, Bonferroni) using the reported MS error and df.
  5. Review residual diagnostics (not included) for normality and homogeneity assumptions (e.g., residual plots, Levene’s test).

References

  • Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley.
  • Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver & Boyd.
  • Keppel, G., & Wickens, T. D. (2004). Design and Analysis (4th ed.). Pearson.

Disclaimer

ANOVA assumes independence, approximate normality within groups, and homogeneity of variances. Investigate these conditions with diagnostic plots before relying on the conclusions for critical decisions.