What is a two-way ANOVA?

A two-way ANOVA tests the effect of two independent categorical factors on a continuous dependent variable. It partitions the total variance into three sources: the main effect of Factor A, the main effect of Factor B, and the interaction between them (A x B). Each source gets its own F-statistic and p-value.

What does the interaction term mean?

A significant interaction (A x B) means the effect of Factor A depends on the level of Factor B, and vice versa. For example, if a drug works better for women than men, sex and drug interact. When the interaction is significant, main effects alone do not tell the full story.

What does "balanced design" mean?

A balanced design requires an equal number of replicates (observations) in every cell. This tool assumes a balanced design. If your cell sizes differ, the results will be incorrect and you should use statistical software that supports unbalanced ANOVA.

What is the minimum data requirement?

You need at least 2 levels for each factor and at least 2 replicates per cell to estimate the within-cell error (SS_Error). With only 1 replicate per cell there is no error term, so interaction cannot be tested.

How is the p-value computed?

P-values are computed using the F-distribution via a regularized incomplete beta function (the standard numerical method). Results match those from R, Excel, and SPSS for typical data sizes.

Is my data sent to any server?

No. All calculations run entirely in your browser using JavaScript. Your data never leaves your device.

Two-Way ANOVA Calculator

Name: Two-Way ANOVA Calculator
Availability: InStock
Author: Nham Vu

Paste a data grid and instantly compute SS, df, MS, and F-ratios for Factor A, Factor B, their interaction, and error in a balanced two-way ANOVA.

Data Entry

Factor A levels (rows)

Factor B levels (cols)

Factor A name

Factor B name

Each cell: enter replicate values separated by commas or spaces. All cells must have the same number of replicates (balanced design).

Fill in the data grid and click Calculate ANOVA to see results.

ANOVA Summary Table

Source	SS	df	MS	F	p-value

Cell Means

Summary

Paste a data grid and instantly compute SS, df, MS, and F-ratios for Factor A, Factor B, their interaction, and error in a balanced two-way ANOVA.

How it works

Enter the number of levels for Factor A (rows) and Factor B (columns).
Fill in each cell with comma- or space-separated replicate values (all cells must have the same number of replicates for a balanced design).
Click "Calculate ANOVA" to run the analysis.
The tool computes sums of squares for Factor A, Factor B, their interaction (A x B), and the within-cell error.
F-ratios and p-values are computed for Factor A, Factor B, and the interaction term.
Review the ANOVA table and the cell-means grid to interpret the results.

Use cases

Analyze the effect of two teaching methods across multiple age groups simultaneously.
Test how fertilizer type and irrigation level jointly affect crop yield.
Evaluate whether drug dosage and patient gender interact to influence response time.
Assess the combined effects of temperature and humidity on material strength.
Examine how two manufacturing factors affect product defect rates.
Study whether diet type and exercise frequency interact to affect weight loss.
Compare software performance across multiple hardware configurations and OS versions.
Investigate how advertising channel and region jointly influence conversion rates.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu