Question

Why is factorial design with two or more independent variables can be difficult to interpret?

Answer 1

Factorial design experiments include the interaction effect between the variables. So, when you are using 2 independent variables (say X and Y) in your experiment there is only one possible interaction (i.e. interaction between X and Y).

But if there is increase in the number of independent variables, the interaction terms increases too. For example, if you have three independent variables (say X,Y and Z), then there would be 3 possible two-way interactions (i.e. between X and Y, between Y and Z, between Z and X) and one possible three way interaction(i.e. between X,Y and Z).

When you take 4 independent variables there would be 6 two-way interaction effects, 4 three-way interactions and 1 four-way interaction. And so on for more number of variables.

These interaction effects become very difficult to calculate and are time consuming too. That is why its difficult to use factorial design for more than 2 independent variables.