What Is ANOVA Table?
An ANOVA table splits the total variation in a data set into variation between groups and variation within groups. It lists the sums of squares (SS), degrees of freedom (df), mean squares (MS), the F statistic and the p-value.
Enter one line per group as name, n, mean and SD. The calculator computes the grand mean, SS between, SS within, the mean squares, F, the p-value, the critical F at your α and the effect size η², and charts the group means and the two sources of variation.
Below are the formulas, variables, a worked example with three groups and answers to common ANOVA questions.
How to Use the ANOVA Table Calculator
- Enter each group on its own line as Name: n, mean, SD.
- Choose α.
- Read the ANOVA table with SS, df, MS, F and the p-value.
- Check the effect size η² and the group chart.
ANOVA Table Formula
Between-group sum of squares
Within-group sum of squares
F statistic
ANOVA Table Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| SSB | Between-group sum of squares | |
| SSW | Within-group sum of squares | |
| MS | Mean square | SS ÷ df |
| F | F statistic | MSB ÷ MSW |
| η² | Effect size | SSB ÷ SST |
ANOVA Table Worked Example
Three groups of 12 have means 24.5, 28.3 and 31.0 and SDs 4.1, 4.6 and 5.0. The grand mean is 27.93. SSB = 12 × (11.7 + 0.14 + 9.4) ≈ 255 and SSW = 11 × (16.8 + 21.2 + 25) ≈ 693. With df = (2, 33): F ≈ 6.1, p ≈ 0.006.
With the example values loaded in the calculator above, the steps are:
- Grand mean = Σ nᵢx̄ᵢ ÷ N = 27.933333.
- SS between = Σ nᵢ(x̄ᵢ − grand mean)² = 255.92, df = k − 1 = 2.
- SS within = Σ (nᵢ − 1)sᵢ² = 692.67, df = N − k = 33.
- MS between = 127.96; MS within = 20.99; F = 6.09624.
- p = P(F ≥ 6.096) with (2, 33) df = 0.00558328.
Result: F statistic = 6.09624; p-value = 0.00558328; Decision = Reject H₀ at α = 0.05: the group means differ.
How to Read an ANOVA Table
ANOVA compares between-group variation with within-group variation. For three groups of 12 with means 24.5, 28.3 and 31.0, the between-group sum of squares is about 256 and the within-group sum is about 693. With df = (2, 33), the mean squares are 128 and 21.0, so F ≈ 6.10.
The 5% critical value for F(2, 33) is about 3.28, and the p-value is about 0.006, so the group means differ significantly. The effect size η² = SSB ÷ SST is about 0.27, which means group membership accounts for roughly 27% of the variation. A significant F says some means differ, not which ones. A post-hoc test is needed to find them.
Where ANOVA Table Is Used
Summary data
Build the table from each group’s n, mean and SD without the raw data.
Checking software
Compare with the ANOVA table from a statistics package.
Effect size
Read η² alongside the p-value.
Course work
See sums of squares, degrees of freedom, mean squares and F laid out in one table.
Common ANOVA Table Mistakes to Avoid
- One-way ANOVA assumes independent groups, roughly normal data and similar spread across groups.
- A significant result does not say which groups differ. Follow it with a post-hoc test.
- Degrees of freedom are k − 1 between groups and N − k within groups.
- Unequal group sizes are allowed, but a large imbalance makes the test more sensitive to unequal variances.
ANOVA Table Terms and Definitions
- SSB
- Variation of group means around the grand mean.
- SSW
- Variation of observations around their own group mean.
- η²
- The share of total variation explained by group membership.
ANOVA Table FAQs
How do I make an ANOVA table?
Compute the between-group and within-group sums of squares, divide each by its degrees of freedom to get mean squares, then divide MSB by MSW to get F. The calculator lays this out for you.
Can I run ANOVA without the raw data?
Yes. The n, mean and SD of each group are enough to compute the sums of squares and F.
What do the degrees of freedom mean?
Between groups it is k − 1, where k is the number of groups. Within groups it is N − k, where N is the total sample size.
What does a significant ANOVA mean?
It means the data are unlikely if all group means were equal. At least one mean differs, but the test does not show which.