ANOVA Calculator
Paste your raw group data and get a full analysis of variance: the ANOVA table (sums of squares, F and p), effect sizes, a group-means plot and an assumption check, all recomputed as you type. Run a one-way ANOVA to compare several group means, or a two-way ANOVA to test two factors and their interaction at once. Already ran aov() in R and only want the printed table decoded? Use the ANOVA output interpreter instead.
I want to compare several group means (one-way)▾
The group means differ
How it is computed
aov(), car::leveneTest() and effectsize
✓ Free
How the ANOVA table works
Every row of an ANOVA table splits the total variation in your outcome into a piece a factor explains and a piece left over as noise, then compares them with an F ratio.
| Column | What it is | Formula |
|---|---|---|
| Sum Sq (SS) | Variation attributed to the source | sum of squared deviations |
| Df | Degrees of freedom for the source | k - 1 between, N - k within |
| Mean Sq (MS) | Variance estimate for the source | SS / Df |
| F value | Signal-to-noise ratio | MS_factor / MS_residual |
| Pr(>F) | p-value, upper tail of the F distribution | pf(F, df1, df2, lower.tail = FALSE) |
| Eta squared | Share of variance a factor explains | SS_factor / SS_total |
| Omega squared | Less biased effect size | (SS - df*MS_res) / (SS_total + MS_res) |
Two-way designs add an interaction row that asks whether the effect of one factor changes across the levels of the other. This calculator reports the sequential (Type I) sums of squares that R's aov() prints, which coincide with Type II and Type III for a balanced design.
Frequently asked questions
What is the difference between one-way and two-way ANOVA?
One-way ANOVA compares the means of a single outcome across the levels of one grouping factor, for example test scores across three teaching methods. Two-way ANOVA studies two factors at once, for example tooth length by supplement and by dose, and also tests whether the two factors interact, meaning the effect of one factor changes across the levels of the other. Use one-way when you have one grouping column, two-way when you have two.
What does the ANOVA p-value tell me?
The F test compares the variation between group means to the variation within the groups. The p-value is the probability of seeing an F this large if every group truly had the same mean. A small p-value (typically below 0.05) is evidence that at least one group mean differs from the others. ANOVA does not say which pairs differ; follow a significant result with a post-hoc test such as Tukey HSD to locate the differences.
What is eta squared in ANOVA?
Eta squared is the share of the total variation in the outcome explained by a factor, from 0 to 1. It is the effect size for ANOVA, the counterpart of R squared in regression. Common rules of thumb are 0.01 small, 0.06 medium and 0.14 large. Omega squared is a less biased version that subtracts the variance expected by chance, so it is a little smaller and can even be negative when a factor explains nothing. Cohen's f is another form used in power analysis.
Do the groups need equal sizes and equal variances?
ANOVA does not require equal group sizes; this calculator handles unbalanced designs, and the two-way table uses the sequential (Type I) sums of squares that R's aov() reports. ANOVA does assume the groups share a common variance. The calculator runs Levene's test (median-centered, the Brown-Forsythe version) so you can check that assumption. If variances differ a lot, prefer Welch's ANOVA for a one-way design or transform the outcome.
How is this different from the ANOVA output interpreter?
This calculator computes the ANOVA from your raw numbers: paste the group data and it fits the model. The ANOVA output interpreter goes the other way: paste a table you already printed with summary(aov()) or car::Anova() and it recomputes the exact p-values and effect sizes from the sums of squares. Use this calculator when you have data, and the interpreter when you already have R's table and want it decoded.
Does this ANOVA calculator match R?
Yes. The sums of squares, degrees of freedom, mean squares, F statistics and p-values reproduce R's aov() for both balanced and unbalanced designs, the effect sizes match the effectsize package's eta_squared() and omega_squared(), and the homogeneity check matches car::leveneTest() with median centering, verified across PlantGrowth, ToothGrowth and unbalanced test cases to at least six significant figures.
Keep going
Related tools and tutorials for comparing groups and modeling variance.