Two-Way ANOVA Calculator
Build a balanced replicated two-factor ANOVA table with main effects, interaction, residual sums of squares and F upper-tail probabilities.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Partition balanced replicated observations into main-factor, interaction and within-cell residual variability, then form the corresponding mean-square F ratios.
SS total=SS A+SS B+SS A×B+SS error; F effect=MS effect/MS error
Worked example
The entered additive 2×2 example with two replicates per cell gives SS A=32, SS B=8, interaction SS=0 and within-cell SS=8. Residual df=4 and MSE=2.
Assumptions and input details
2–8 levels per factor, equal 2–50 replicates in every combination, at most 1000 observations. Independent observations, normal residuals and common within-cell variance are assumed. Unbalanced cells, missing values, repeated-measures designs and covariance adjustments are unsupported. A zero residual mean square leaves inferential F and p values undefined.
References: NIST: replicated two-way factorial ANOVA
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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