One-Way ANOVA F-Statistic
F = MS_between / MS_within. Test if 3+ group means differ.
Result
F-statistic
36.9744
df = (2, 12). Compare to F-table.
- Groups (k)3
- Total N15
- Grand mean9.4667
- SSB (between)96.1333
- SSW (within)15.6000
- MSB48.0667
- MSW1.3000
- F36.974359
- df (between, within)(2, 12)
Step-by-step
- Grand mean = 9.467.
- SS_between = Σ nⱼ(meanⱼ − grand)² = 96.133.
- SS_within = Σ Σ (xᵢⱼ − meanⱼ)² = 15.600.
- F = MSB/MSW = 36.9744.
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
t compares 2 groups. F (ANOVA) compares 3+. F = t² for 2 groups (equivalent).
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