In experiment 2, you allowed subjects to drink 1 or 2 drinks. Suppose that there were an equal number of light and heavy drinkers in experiment 1, and that half of the subjects in experiment 2 drank 1 drink and the other half drank 2 drinks. In the table at right you can see how the outcome of both simple two group experiments might have been the same, even though there were clearly differences between the conditions. The Figure below at right plots the means. So both factors made a difference, but they canceled each other out.
Factorial designs allow both independent variables and the interaction to be tested simultaneously.
For this situation, You get three F statistics - one for each factor, and a separate F that tells you whether you have an interaction. Any one, or all, or none, may be statistically significant. A difference between the overall means of the levels of an IV is called a main effect . So, each IV could be a main effect. Factorial experiments can be expanded to more than 2 levels of each variable, so you can add a 0-drink condition.