What is the difference between one-way and two-way ANOVA?

• A. One-way has one independent variable; two-way includes two factors and can test interaction.
• B. One-way has two independent variables; two-way has one.
• C. One-way tests for interaction; two-way tests main effects.
• D. One-way is nonparametric; two-way is parametric.

Answer: (A)

The main idea is how many independent variables (factors) you have and what that allows you to test. One-way ANOVA uses a single independent variable with multiple groups and tests whether the group means differ. It cannot examine interactions because there’s only one factor. Two-way ANOVA uses two independent variables (two factors) and can test not only the main effects of each factor but also whether the effect of one factor changes across levels of the other—this is the interaction. So the correct statement is that one-way has one independent variable, while two-way has two factors and can test interaction. The other options misstate the number of factors or what is tested, and they aren’t accurate descriptions of the difference between one-way and two-way ANOVA.