Advantages of a two-factor design

Efficiency: Two one-factor experiments requires two independent controlsInteractions: Two one-factor experiments cannot test for an interactionMain effect: Effect on response that can be attributed to the levels of either factor alone (two separate ANOVA's would tell us this)

A two-factor design is advantageous because it allows for the efficient testing of two independent variables simultaneously. This design requires only two independent controls, which is more efficient than conducting two separate one-factor experiments. Additionally, a two-factor design can test for interactions between the two factors, which is not possible with two one-factor experiments. Furthermore, it can identify the main effect, which is the effect on the response attributable to the levels of either factor alone. This can be determined through separate ANOVA analyses for each factor.