Direct comparison
One-Way vs Two-Way ANOVA: Differences and Uses
One-way vs two-way ANOVA side by side: number of factors, the three tests in a two-way model, interactions, assumptions, and when to choose each.
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How do One-way ANOVA and Two-way ANOVA compare side by side?
The table below compares One-way ANOVA and Two-way ANOVA across 11 dimensions, from number of factors to pick it when.
Side-by-side comparison
| Dimension | One-way ANOVA | Two-way ANOVA |
|---|---|---|
| Number of factors | One categorical factor with three or more levels (groups). | Two categorical factors, each with two or more levels. |
| Outcome variable | One continuous dependent variable. | One continuous dependent variable. |
| Question answered | Do the group means differ? | Does each factor affect the mean, and does the effect of one factor depend on the level of the other? |
| Hypothesis tests run | One F-test. H0: all group means are equal; Ha: not all are equal. | Three F-tests: main effect of factor A, main effect of factor B, and the A × B interaction. |
| Interaction | Cannot be estimated, because there is only one factor. Running two separate one-way ANOVAs on two factors also cannot detect an interaction. | Estimated directly. An interaction means the effect of one factor varies across levels of the other. |
| Design cells and df (balanced design) | k groups; df between = k − 1, df within = N − k. | a × b cells with n per cell; df: A = a − 1, B = b − 1, A × B = (a − 1)(b − 1), error = ab(n − 1). |
| Worked example (illustrative) | Compare mean blood pressure across three drug doses. | Compare mean blood pressure across drug (treated vs control) and smoking status (smoker vs non-smoker); an interaction would show that the drug lowers pressure more in non-smokers than in smokers. |
| Assumptions | Dependent variable approximately normal within each group; similar variability across groups. | Independent observations (randomisation), approximately normal residuals (matters most in small cells), equal variances across cells (checked with Levene's test). |
| Reading a significant result | Says at least one mean differs, not which one; a post hoc test identifies the pairs. | Interpret the interaction first. If it is significant, do not interpret the main effects alone; examine each factor's effect within levels of the other using cell means. |
| If the same subjects are measured repeatedly | Use a repeated-measures design instead of the between-groups version. | If the same subjects appear under all factor combinations, use repeated-measures ANOVA. |
| Pick it when | You have one grouping factor and want to compare three or more group means. | You have two factors and care whether they work together, not just whether each matters alone. |
Sources
- JMP Statistics Knowledge Portal, One-Way ANOVA (read 2026-11-07)
- MedCalc manual, Two-way ANOVA (read 2026-11-07)
- df partition is standard textbook ANOVA algebra
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Common questions
Common questions about One-way ANOVA vs Two-way ANOVA
What is the main difference between one-way and two-way ANOVA?
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One-way ANOVA has one factor and runs one F-test on the group means. Two-way ANOVA has two factors and runs three F-tests: the main effect of each factor and the interaction between them.
Can I run two one-way ANOVAs instead of one two-way ANOVA?
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You can, but each one-way analysis ignores the other factor and neither can estimate the interaction. If the effect of one factor depends on the level of the other, only the two-way model shows it.
What is an interaction in two-way ANOVA?
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An interaction means the effect of one factor varies across levels of the other. In the MedCalc example, a drug lowers blood pressure more in non-smokers than in smokers.
What do I do if the interaction is significant?
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Interpret the interaction first and do not read the main effects alone. Examine the effect of each factor within each level of the other, using the cell means (simple effects).
What are the assumptions of each test?
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One-way ANOVA assumes the outcome is approximately normal within each group with similar variability across groups. Two-way ANOVA assumes independent observations, approximately normal residuals and equal variances across cells.
How are the degrees of freedom split up?
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In a balanced one-way design, between-groups df is k − 1 and within-groups df is N − k. In a balanced two-way design, the df are a − 1 for A, b − 1 for B, (a − 1)(b − 1) for A × B and ab(n − 1) for error.
What if the same participants are measured under every condition?
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Use repeated-measures ANOVA rather than the between-groups one-way or two-way version.
