Two way ANOVA

Two-way ANOVA is a hypothesis test that examines how two categorical factors, separately and in interaction, affect the mean of a continuous outcome.

이원분산분석(two-way ANOVA)은 두 범주형 요인이 각각 그리고 상호작용을 통해 연속형 결과변수의 평균에 미치는 영향을 검정하는 방법이다.

How do I test the effects of two categorical factors and their interaction on a continuous outcome?

두 범주형 요인과 그 상호작용이 연속형 결과변수에 미치는 효과를 어떻게 검정하나요?

Two-way ANOVA tests the main effect of each of two categorical factors and their interaction on a continuous outcome. It fits factorial designs, such as treatment by gender, where you want to know whether the effect of one factor depends on the level of the other.

When to use Two way ANOVA

• A 2 × 3 or other factorial design with a continuous outcome
• Testing whether a treatment effect differs by a second factor such as sex or site
• Independent groups formed by crossing two categorical variables

When to use something else

• Only one grouping factor: use one-way ANOVA
• The same subjects are measured repeatedly on one factor: use mixed (split-plot) ANOVA

Assumptions and requirements

• Independent observations
• Normally distributed residuals within cells
• Homogeneity of variance across cells
• Continuous outcome

What the analysis reports

• F statistics for each main effect and the interaction
• Partial eta squared
• Cell and marginal means
• Interaction plot
• Simple effects or post hoc comparisons

How to report it

There was a significant interaction between [factor A] and [factor B] on [outcome], F([df1], [df2]) = [value], p = [value], partial η² = [value].

Related methods

• One way ANOVA
• ANCOVA
• Mixed ANOVA

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