Two Way Analysis of Variance (ANOVA) Calculator
A more advanced ANOVA that looks at how two different factors affect a result — for example how Diet AND Exercise affect weight loss.
It reveals whether there is an interaction between your two variables.
Significance level (α)
| B1 | B2 | B3 | |
|---|---|---|---|
| A1 | |||
| A2 | |||
| A3 |
F (rows / factor A)
91.17
p = < 0.0001 · df (2, 9)
| Source | SS | df | MS | F | p | Sig? |
|---|---|---|---|---|---|---|
| Rows (factor A) | 243.11 | 2 | 121.56 | 91.17 | < 0.0001 | Yes |
| Columns (factor B) | 524.78 | 2 | 262.39 | 196.79 | < 0.0001 | Yes |
| Interaction (A×B) | 21.89 | 4 | 5.47 | 4.10 | 0.0365 | Yes |
| Error | 12.00 | 9 | 1.33 | — | — | — |
| Total | 801.78 | 17 | — | — | — | — |
Factor A (rows) has astatistically significant effect at α = 0.05.
Factor B (columns) has astatistically significant effect at α = 0.05.
Interaction ISsignificant at α = 0.05. The factors work together — interpret combinations, not main effects alone.
Row & column means
| Level | Mean | vs grand mean |
|---|---|---|
| A1 (row) | 13.33 | -4.56 |
| A2 (row) | 18.00 | 0.11 |
| A3 (row) | 22.33 | 4.44 |
| B1 (column) | 11.67 | -6.22 |
| B2 (column) | 17.17 | -0.72 |
| B3 (column) | 24.83 | 6.94 |
| Grand mean | 17.89 |
About this calculator
When two factors might both matter — Diet AND Exercise, Machine AND Shift — and you want each factor's effect plus whether they interact.
With one value per cell you get the unreplicated model (like Excel's Two-Factor Without Replication); with the same 2+ values per cell you also get the interaction term.
Formula
F = MS(factor) ÷ MS(error), computed for rows, columns and interaction
How to use it
- 1
Set the grid size with the row and column steppers (2–6 each).
- 2
Fill every cell — a single value per cell for the unreplicated model, or the same 2+ values per cell to test interaction.
- 3
Read the ANOVA table: rows test factor A, columns test factor B, and interaction (when replicated) tests whether the factors combine non-additively.
Example: 3×3 grid
The default grid gives SS-rows 56, SS-cols 56, SS-error 16 with F = 7 and p ≈ 0.0494 for both factors — significant at the 5% level.
In Excel: In Excel: Data → Data Analysis → Anova: Two-Factor with or without Replication.