ANOVA Calculator
Perform one-way ANOVA: compute SSB, SSW, F statistic and p-value for group means comparison.
Inputs
F Statistic
18.7500
P-value
0.002624
SS Between (SSB)
150.0000
SS Within (SSW)
24.0000
df Between
2
df Within
6
Step by step
Values used
Group 1 (comma separated) = 23, 25, 27; Group 2 (comma separated) = 30, 32, 28; Group 3 (comma separated) = 35, 33, 37
F Statistic
F = MSB / MSW = (SSB/dfB) / (SSW/dfW)
F Statistic
= 18.7500
P-value
= 0.002624
SS Between (SSB)
= 150.0000
SS Within (SSW)
= 24.0000
df Between
= 2
df Within
= 6
How it works
One-way ANOVA tests whether the means of multiple groups differ significantly. It partitions total variance into between-group (SSB) and within-group (SSW) components and computes an F ratio. A small p-value suggests at least one group mean differs.
Formula
F Statistic
F = MSB / MSW = (SSB/dfB) / (SSW/dfW)
- MSB
- Mean square between
- MSW
- Mean square within
- dfB
- k − 1
- dfW
- N − k
Frequently Asked Questions
What does a significant ANOVA tell you?
It tells you that at least one group mean differs from the others, but not which specific groups differ. Post-hoc tests (e.g., Tukey HSD) are needed for pairwise comparisons.
What assumptions does one-way ANOVA make?
Independence of observations, normality within groups, and approximately equal variances (homoscedasticity).