One-Way Analysis of Variance
Use this tool to test if three or more groups have different means using one-way ANOVA.
What is ANOVA?
ANOVA (Analysis of Variance) is a statistical method used to compare means of three or more groups to determine if at least one group mean is significantly different from the others.
Common uses:
- Comparing treatment effects
- Marketing campaign performance
- Product testing across regions
- Educational studies with multiple methods
Understanding Results
F-statistic: Ratio of between-group variability to within-group variability. Higher values indicate more significant differences.
p-value: Probability of observing the results if the null hypothesis (no difference) is true. Compare to α (significance level).
Interpretation: If p-value ≤ α, reject the null hypothesis - at least one group mean is different.
Data Groups
Group 1
Group 2
Group 3
ANOVA Results
ANOVA Summary Table
| Source | SS | df | MS | F | p-value |
|---|
Interpretation
Assumptions Check
Group Means Visualization
ANOVA Formulas
Total Sum of Squares (SST)
SSTotal = ΣΣ(Xij - X̄grand)²
Measures total variation in the data
Between-Groups SS (SSB)
SSBetween = Σnj(X̄j - X̄grand)²
Measures variation between group means
Within-Groups SS (SSW)
SSWithin = ΣΣ(Xij - X̄j)²
Measures variation within groups
Degrees of Freedom
dfBetween = k - 1
dfWithin = N - k
dfTotal = N - 1
Mean Squares
MSBetween = SSBetween / dfBetween
MSWithin = SSWithin / dfWithin
F-statistic
F = MSBetween / MSWithin
Test statistic for ANOVA