Statistics Calculator

ANOVA Calculator

Perform one-way Analysis of Variance to compare means across multiple groups.

Groups:3

Group 1

Group 2

Group 3

Learning Guide

What is ANOVA?

ANOVA (Analysis of Variance) compares means across three or more groups to determine if at least one group mean is significantly different from the others.

Hypotheses

H₀: All group means are equal (μ₁ = μ₂ = μ₃ = ...)
H₁: At least one group mean is different

Key Calculations

SSB (Between): Σnᵢ(x̄ᵢ - x̄)² - variation between groups
SSW (Within): ΣΣ(xᵢⱼ - x̄ᵢ)² - variation within groups
MSB: SSB / (k - 1)
MSW: SSW / (N - k)
F: MSB / MSW

F-Statistic Interpretation

Large F: More variation between groups than within
F ≈ 1: Similar variation between and within groups
Compare F to critical value from F-distribution table

Assumptions

Independence: Observations are independent
Normality: Data in each group is normally distributed
Homogeneity: Equal variances across groups

Post-Hoc Tests

If ANOVA is significant, post-hoc tests (Tukey, Bonferroni) identify which specific groups differ.

Applications

Comparing treatment effects in clinical trials
Testing teaching methods across classrooms
Evaluating product quality across factories
Analyzing crop yields across fertilizers