ANOVA Calculator
Perform Analysis of Variance to compare means across multiple groups with F-statistic and p-value
One-Way ANOVA Analysis
Choose the significance level for hypothesis testing
Group Data
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Example: Diet Effectiveness Study
Weight Loss Study Data
Research Question: Do three different diets result in different weight loss?
Diet A: 8, 12, 10, 9, 11 pounds lost (Mean = 10.0)
Diet B: 6, 7, 5, 4, 6 pounds lost (Mean = 5.6)
Diet C: 10, 15, 12, 11, 13 pounds lost (Mean = 12.2)
ANOVA Results
F-statistic = 22.587
p-value < 0.001
Conclusion: There is a significant difference between the diets (p < 0.05)
Diet C appears most effective, Diet B least effective for weight loss.
ANOVA Assumptions
Independence
Observations must be independent
Normality
Data should be normally distributed
Equal Variances
Groups should have similar variances
Interval Data
Data should be measured at interval level
Hypothesis Testing
Null Hypothesis (H₀)
μ₁ = μ₂ = μ₃ = ... = μₖ
All group means are equal
Alternative Hypothesis (H₁)
At least one μᵢ ≠ μⱼ
At least one group mean differs
ANOVA Tips
Use at least 15 observations per group for reliable results
Check assumptions before interpreting results
Significant ANOVA requires post-hoc testing
Consider effect size along with significance
Understanding ANOVA (Analysis of Variance)
What is ANOVA?
ANOVA (Analysis of Variance) is a statistical technique used to compare means among three or more groups. It determines whether observed differences between group means are statistically significant or could be due to random chance.
When to Use ANOVA
- •Comparing means of 3+ independent groups
- •Testing effectiveness of different treatments
- •Analyzing experimental data with categorical factors
- •Quality control and process improvement
Key ANOVA Concepts
F-statistic: Ratio of between-group to within-group variance
Sum of Squares (SS): Measures total variation in the data
Degrees of Freedom: Number of independent observations
Mean Squares (MS): SS divided by degrees of freedom
ANOVA Formula
F = MS_between / MS_within
where MS = SS / df