ANOVA Two Way Calculator

Work out anova two way instantly with clear inputs, formula shown and shareable results.

About ANOVA Two Way Calculator

Two-way ANOVA partitions the variation between cell means into a row effect, a column effect and their interaction, each tested against the within-cell mean square error using an F ratio.

Formulas

Row sum of squares

SS_row = reps × columns × Σ(row mean − grand mean)²

F ratio

F = (SS / df) / MSE

Worked example

With the default values below, ANOVA Two Way Calculator returns F for the column factor of 16.444444. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cell means, row by row: 12, 15, 18, 14, 17, 22
Number of columnsaccepts 2–8: 3
Observations per cellaccepts 2–100: 4
Within-cell variance (MSE)minimum 0: 6

Results

F for the column factor: 16.444444
F for the row factor: 7.111111
F for the interaction: 0.444444
p value for the row factor: 0.01572467

Step by step

1Values used
2Row sum of squares
3F ratio
4F for the column factor= 16.444444
5F for the row factor= 7.111111
6F for the interaction= 0.444444
7p value for the row factor= 0.01572467

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does the interaction test?

Whether the effect of one factor depends on the level of the other. A significant interaction means the main effects cannot be interpreted in isolation.

Why divide by MSE?

MSE estimates the pure random variation, so the F ratio asks whether the factor explains more than chance would.