Ive carried out a screening expriement looking into the effect of 6 factors on our response. I choose ro look at all two factor interactions when choosing my design. My problem is that there are a couple of significant two-factor interactions, but neither, or just one of the factors are significant as a main effect. Any ideas on what may be going on? Could the interactions be an alias for anything else?
It's difficult to say without understanding the number of runs that you have run. I am asumming from your post that it was a Fractional Factorial (N=16)? Resolution IV screening design? If this was the case then the main effects are aliased with 3-way interactions and the two-way interactions are aliased with other two-way interactions. Have you tried a stepwise regression when you fit your model? This might tease out some of the main effects to be significant when the less important two-way interactions are dropped.
Thanks for this. It was a resolution IV design. Is it true in all resolution IV designs that main effects are aliased with 3-way interactions and two way are aliased with other two way interactions? I have tried a stepwise regression and get similar results. The problem is that the magnitude of one of the factors is very big and accounts for around 80% of the Rsquare value. two other main effects account for another 10% and the two two factor interactions around 3%. Do you think the magnitude of the main factor makes it difficult to analyse?
It is very possible to have significant two-factor interactions but insignificant main effects. Assuming you have a 2^k design, a main effect is the average of all values where factor i is equal to 1 minus the average of all values where factor i is equal to -1 (more or less). If the effect of factor A depends of the level of factor B so that an interaction plot looks like an X then the main effect would be 0 but the interaction would be very strong.
However, given the aliasing structure of a resolution IV design the two factor interactions that appear significant may not be the actual interaction responsible for the cause effect. I would take into account the aliasing structure and what factors appear to be significant to design a follow-up experiement that is resolution V+ to identify the most important effects.