I am planning to conduct a study with three hypotheses in a 2x2 between subjects design.
Both independent variables are categorical and the dependent variable is metric. Let's say the levels of my first independent variable is A1 and A2 and for my second independent variable B1 and B2.
I have three hypotheses stating that (1) A2 > A1, (2) B2 > B1 and the interaction (3) (A2-A1) > (B2-B1).
How would you recommend testing it? Would you test (1) and (2) in separate one-way ANOVAs and then the (3) in a two-way ANOVA? Or would you rather recommend to test it all at once with one two-way ANOVA? Is there any disadvantage with splitting it into three tests?
EDIT: to be more clear: The experiment is is related to task performance. One variable is a goal level (high goal vs. low goal) and the second variable is the dimension of the goal (speed vs. accuracy). so it is predicted that both goal dimensions will lead to higher task performance (1) & (2) , however the effect of the speed goal will be higher than the accuracy goal (3). There are 40 participants per cell, which means a total sample size of n=160. Each participant experiences each condition only once!