04/26/2026
A Two-Way ANOVA (Analysis of Variance) is a statistical test used to determine how two different categorical independent variables (factors) simultaneously affect a continuous dependent variable.
While a One-Way ANOVA looks at one factor (e.g., Does brand of fertilizer affect plant growth?), a Two-Way ANOVA looks at two (e.g., Does brand of fertilizer and amount of sunlight affect plant growth?).
The Three Main Questions
A Two-Way ANOVA doesn’t just give you one result; it tests three distinct hypotheses:
Main Effect of Factor A: Does the first independent variable have a significant effect on the outcome?
Main Effect of Factor B: Does the second independent variable have a significant effect on the outcome?
Interaction Effect (A × B): Does the effect of one variable depend on the level of the other? (e.g., Does Fertilizer A only work well when there is high sunlight?)
Key Assumptions
To ensure the results are valid, the data should meet these criteria:
Normality: The residuals (the differences between observed and predicted values) should be approximately normally distributed.
Homogeneity of Variance: The variance among the groups should be roughly equal (often checked using Levene’s Test).
Independence: Observations must be independent of each other.
Type of Data: The independent variables must be categorical (groups), and the dependent variable must be continuous (interval or ratio scale).