2x2 design - one way anova or two way anova

Question

So i did an experiment with 4 groups, each getting different advertisement communications tasty or healthy benefits:

group 1: control group, no health or taste benefits group 2: only health benefits group 3: only taste benefits group 4: health & taste benefits

I have 4 different dependant variables: purchase intention, attitude, credibility and benefits all measured on 7 point likert scale

So I thought i had to do a 2 way anova because health and taste are the IV. But how do i test these? Because the interaction of them is already tested in group 4?

I work with SPSS

Answer 1

The two methods are statistically equivalent, but a two-way ANOVA will make it easier to test the specific effects of interest (i.e., an interaction between health benefits and taste and main effects of each). The model F-test in a two-way ANOVA will be equivalent to the F-test in the one-way ANOVA.

You can use a one-way ANOVA to test main and interaction effects. To test the main effect of health, you can test whether $\frac{\bar{x}_1+\bar{x}_3}{2}=\frac{\bar{x}_2+\bar{x}_4}{2}$. The t-test for this comparison will be equivalent to the F-test on the main effect of health benefits in a two-way ANOVA. For the interaction, you can test whether $\bar{x}_2-\bar{x}_1=\bar{x}_4-\bar{x}_3$. The t-test on that will be equivalent to the interaction F-test in a two-way ANOVA. A one-way ANOVA makes it easier to compare individual groups and other contrasts (e.g., is there a difference between group 1 and all other groups combined?) while a two-way ANOVA makes it easier to test interactions, main effects, and simple main effects.

Answer 2

You have 1 independent variable with four levels (Group: Control vs. Health Only vs. Taste Only vs. Health + Taste). If your research question relates to finding any difference among these groups in response to a dependent variable, you have a 1-way ANOVA. If you want to do the same for all four dependent variables you describe above, you have four separate 1-way ANOVAs.