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.
Where ANOVA Table Is Used
Published results
Reconstructing an ANOVA from reported means and SDs.
Comparing treatments
Testing whether several group means differ.
Coursework
Filling in an ANOVA table from summary data.
Meta-analysis checks
Verifying F values reported in papers.
Common ANOVA Table Mistakes to Avoid
- Use the sample SD (n − 1) for each group.
- A significant F does not tell you which means differ.
- Check that the group SDs are of similar size.
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 SS between and within, divide by their df to get mean squares, then divide MSB by MSW for F.
Can I run ANOVA without the raw data?
Yes. Group sizes, means and standard deviations are enough for one-way ANOVA.
What do the degrees of freedom mean?
Between = k − 1 for k groups; within = N − k.
What does a significant ANOVA mean?
At least one group mean differs; use post-hoc tests to find which.