ANOVA Calculator
Perform one-way analysis of variance to compare group means.
One-Way ANOVA: compare means of 2–3 groups
What Is the ANOVA Calculator?
The One-Way ANOVA Calculator tests whether the means of two or more groups are equal. ANOVA (Analysis of Variance) partitions total variability into between-group variability (due to the factor) and within-group variability (random error), then uses their ratio as the F-statistic to test significance.
Formula
How to Use
Enter data for each group (Group 1 and Group 2 are required; Group 3 is optional) as comma-separated values. Click Calculate to get the ANOVA table with SSB, SSW, MSB, MSW, F-statistic, and degrees of freedom. Compare F to the critical value at your desired significance level.
Example Calculation
Group 1 (diet A): 68, 72, 65, 70 Group 2 (diet B): 75, 80, 78, 72 Group 3 (diet C): 60, 63, 58, 65 Grand mean = (68+72+65+70+75+80+78+72+60+63+58+65)/12 ≈ 68.83 SSB = 4(71.25−68.83)² + 4(76.25−68.83)² + 4(61.5−68.83)² ≈ 461.2 SSW ≈ 73.5 F = (461.2/2)/(73.5/9) = 230.6/8.17 ≈ 28.2 Significant at p < 0.05 (F_critical ≈ 4.26)
Understanding ANOVA
ANOVA was developed by Ronald Fisher in the 1920s as a way to analyze agricultural experiments with multiple treatment conditions. It remains one of the most widely used statistical tests in science.
The key insight of ANOVA is that total variance can be decomposed into meaningful components. If the between-group variance is much larger than the within-group variance, it suggests the groups differ systematically — not just by random chance.
ANOVA generalizes easily: Two-Way ANOVA handles two factors (e.g., drug and dose level); Repeated Measures ANOVA handles within-subject designs; MANOVA handles multiple dependent variables simultaneously.
Frequently Asked Questions
Why use ANOVA instead of multiple t-tests?
Running multiple t-tests inflates the Type I error rate. If you run 3 t-tests at α=0.05, the probability of at least one false positive is about 14%, not 5%. ANOVA controls the overall error rate.
What is the F-statistic?
The F-statistic is the ratio of between-group variance to within-group variance (MSB/MSW). A large F means group means differ more than expected by chance. Under H₀ (all means equal), F follows the F-distribution.
What are the assumptions of ANOVA?
Independence of observations, normality of each group (or large enough n by CLT), and equality of variances across groups (homoscedasticity). Violations can be addressed with Welch's ANOVA or Kruskal-Wallis test.
What does ANOVA tell me if it is significant?
ANOVA only tells you that at least two group means differ. It doesn't tell you which groups differ. Follow up with post-hoc tests (Tukey HSD, Bonferroni) to identify specific differences.
What is the null hypothesis for ANOVA?
H₀: μ₁ = μ₂ = μ₃ = ... (all group means are equal). H₁: at least one group mean differs from the others.