In a two-way ANOVA, how many independent variables are analyzed and how many means are compared?

In a two-way ANOVA, how many independent variables are analyzed and how many means are compared?

• A. Two independent variables; three or more means
• B. Two independent variables; two means
• C. One independent variable; three means
• D. Three independent variables; four means

Answer: (A)

In a two-way ANOVA you analyze two independent variables (two factors) at once, looking at how each factor affects the outcome and whether their effects depend on each other (the interaction). The means you’re comparing aren’t just a single group mean or two means; you’re comparing the cell means that come from all combinations of the factor levels. Since there are two factors, and each factor has at least two levels in a typical design, you end up with multiple cell means (at least four in the common 2-by-2 case, and more if there are more levels). So the statement that there are two independent variables and three or more means best captures what’s being compared. This isn’t describing a one-factor comparison (one independent variable) or a design with more than two factors (which would be a three-way or higher ANOVA).

In a two-way ANOVA you analyze two independent variables (two factors) at once, looking at how each factor affects the outcome and whether their effects depend on each other (the interaction). The means you’re comparing aren’t just a single group mean or two means; you’re comparing the cell means that come from all combinations of the factor levels. Since there are two factors, and each factor has at least two levels in a typical design, you end up with multiple cell means (at least four in the common 2-by-2 case, and more if there are more levels). So the statement that there are two independent variables and three or more means best captures what’s being compared.

This isn’t describing a one-factor comparison (one independent variable) or a design with more than two factors (which would be a three-way or higher ANOVA).