Factorial designs are great in several ways:
By using a 2 x 2 design, we are able to conduct research on an increased number of groups. With this increase, we have the potential to generalize the results in a larger way than with a simple one way analysis of variance. Also, we are able to find out if the independent variables in question yield different or similar results on various populations. For example:
With the 2 way interaction-by adding the male group, this applies our study to a greater majority of the population than just females.
With factorial designs, we are able to discover any interactions between the variables. More specifically, if we were taking a look at the above study, we could determine if eating chocolate is independent of gender, or if there is an interaction between the two.
Interaction: A situation where the effects of one independent variable depend on the level of another independent variable.
More for less! A factorial design will give us a 2 for 1 special.
Why would we get "2 for 1" (or in this case, 3 eggs for the price of 2)? Factorial designs have an advantage because they offer the same degree of power to a study and while requiring fewer participants. For example: