How to use
- Arrange the data in three columns, the level of factor A, the level of factor B and the value, one observation per row, with names in the first row.
- Start with the interaction row. p < 0.05 means the effect of one factor depends on the other.
- If the interaction is significant, interpret it with the cell means and the interaction plot; otherwise report the main effects.
- Copy the APA lines for each effect.
Options explained
- Type III sums of squares
- Each effect is tested after adjusting for the others, so the order doesn't matter even with unequal cell sizes. It is the SPSS Univariate default.
- Partial η²
- Effect SS ÷ (effect SS + error SS), the share of variance explained after removing the other effects. About 0.01, 0.06 and 0.14 are small, medium and large.
- One value per cell
- The interaction can't be estimated, so the calculator fits the main-effects model (two-way ANOVA without replication).
Worked example
The sample has factor A with three levels (a1, a2, a3) and factor B with two (b1, b2), three values per cell.
| Source | SS | df | F | p | Partial η² |
|---|---|---|---|---|---|
| A | 27.0 | 2 | 13.50 | 0.0008 | 0.69 |
| B | 60.5 | 1 | 60.50 | < 0.001 | 0.83 |
| A × B | 13.0 | 2 | 6.50 | 0.012 | 0.52 |
| Error | 12.0 | 12 |
Cell means:
| A \ B | b1 | b2 |
|---|---|---|
| a1 | 5 | 7 |
| a2 | 6 | 9 |
| a3 | 6 | 12 |
The interaction is significant (p = 0.012): b2 is 2 points above b1 at a1 but 6 points above at a3, and the lines on the interaction plot spread apart to the right. So the effect of B has to be described separately for each level of A.
APA style: A × B interaction, F(2, 12) = 6.50, p = .012, ηp² = .52.
Frequently asked questions
My data are a grid in Excel (rows A, columns B). How do I convert it?
Convert to long format first, one value per row with its A and B levels in the first two columns. In Excel, Power Query's "Unpivot" does this.
What does a significant interaction mean?
The effect of one factor changes with the level of the other, for example a new method raises boys' scores by 10 points but girls' by only 2. Describe the effect separately rather than reporting a single main effect.
Does it match SPSS and R?
It matches SPSS (General Linear Model → Univariate), which uses Type III by default. R's aov() uses Type I, which differs with unequal cell sizes; use car::Anova(type = 3) with sum-to-zero contrasts to match.
Can I use it for repeated measures?
No. Observations are assumed independent. Repeated measurements on the same people need a repeated-measures ANOVA.
Privacy
This tool runs entirely in your browser. Your files and text are processed on your device and are never uploaded to our servers.