ANOVA Calculator
Calculate anova instantly with our math tool. Shows detailed work, formulas used, and multiple solution methods. Free to use with no signup required.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
ANOVA Calculator
Calculator
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Formula: F = MSB / MSW = (SSB/dfB) / (SSW/dfW)
Worked example — F = 50.00 (significant)
Formula
F = MSB / MSW = (SSB/dfB) / (SSW/dfW)
ANOVA tests whether means of 3+ groups differ significantly. F = between-group variance / within-group variance. High F → significant differences.
Worked Examples
Example 1: Treatment comparison
Problem:G1:[23,25,27], G2:[30,32,28], G3:[35,37,33]
Solution:Means: 25, 30, 35. F = 50.00 → highly significant
Result:F = 50.00 (significant)
Frequently Asked Questions
When do I use ANOVA vs t-test?
Use a t-test for comparing 2 groups and ANOVA for 3+ groups. ANOVA controls for inflated Type I error that occurs when running multiple t-tests.
What does the F-statistic mean in ANOVA?
The F-statistic is the ratio of between-group variance (MSB) to within-group variance (MSW). A large F value indicates that group means vary more than would be expected by chance. When F exceeds the critical value for your chosen significance level (typically alpha = 0.05) and degrees of freedom, you reject the null hypothesis that all group means are equal. The F distribution is always positive and right-skewed.
What are the assumptions of one-way ANOVA?
One-way ANOVA requires four key assumptions: (1) Independence: observations within and between groups must be independent of each other. (2) Normality: the data within each group should be approximately normally distributed, though ANOVA is fairly robust to mild violations with large samples. (3) Homogeneity of variances: group variances should be roughly equal (use Levene's test to check). (4) Continuous dependent variable: the outcome being measured must be on an interval or ratio scale.
What do I do after a significant ANOVA result?
A significant one-way ANOVA only tells you that at least two group means differ — it does not tell you which groups differ. You need post-hoc tests to identify specific pairwise differences while controlling for multiple comparisons. Common post-hoc methods include Tukey's HSD (most common for equal group sizes), Bonferroni correction (conservative but simple), Scheffe's test (most conservative, good for complex comparisons), and Games-Howell (when variances are unequal).
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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