One-Way ANOVA F-Statistic

F = MS_between / MS_within. Test if 3+ group means differ.

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How to use this calculator

  • Enter 2-3 groups of values.

About this calculator

One-way ANOVA tests if 3+ group means differ significantly. F = MS_between / MS_within = ratio of between-group variance to within-group variance. Larger F → groups more different. Compare to F(df_between, df_within) critical value. Assumes normality + equal variances + independence. Source: Fisher (1925) Statistical Methods for Research Workers; NIST Handbook.

Frequently asked

F vs. t?+
t compares 2 groups. F (ANOVA) compares 3+. F = t² for 2 groups (equivalent).
Post-hoc tests?+
ANOVA tells you "at least one differs." Tukey HSD or Bonferroni-corrected pairwise t-tests identify which.
Assumptions?+
Normality (each group), equal variances (Levene's test), independence. Welch's ANOVA relaxes equal variances.
Effect size?+
Eta-squared η² = SSB/SST. 0.01 small, 0.06 medium, 0.14 large.
Two-way ANOVA?+
Tests effects of 2 factors + interaction. Different formula. Used for factorial designs.

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