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Jan 10, 2012 8:44 AM
(1132 views)

Hi All,

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?

Thanks!

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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.

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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?

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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.

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Were there any center point runs included to see if there was a lack of fit and evidence of a potential polynomial term? Any replicates run?

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Thanks for all the info. I think im slowly getting there! I plan to augment the design now to add center points to see any lack of fit and go from there