Power Calculation on Mixture Design - Why is the power so low?A customer presented this to me and I don't know how to explain it. Using the factors from the attached table and the default 21 trial experiment, the power calculation is shown below. Is there a good explanation for why the power is so low?
Re: Power Calculation on Mixture Design - Why is the power so low?No, just the main effects (i.e., the mixture component can't be removed from the model).
Re: Power Calculation on Mixture Design - Why is the power so low?Don, does your statement about "non significant factors can't be removed from the model" pertain to the higher order effects, too (non main effects/linear blending terms)?
Re: Power Calculation on Mixture Design - Why is the power so low?And to add one more thing for future reference... Mixtures are often constrained by limited proportions of individual components and limited combinations of proportions. These constraints dramatically increase the correlations of the estimates, which further exacerbates the low power. It can look really scary! But as @DonMcCormack and @Dan_Obermiller have explained, we really don't care about power anyway.
Re: Power Calculation on Mixture Design - Why is the power so low?To add just a little bit to Don's excellent answer, power really does not matter in a mixture experiment because you are not testing to see if the main effect coefficient is 0. You actually would test to see if the main effect coefficients are different from the overall average of the data. That is why you would not set a coefficient to 0. It would actually be stating that the coefficient has an effect.
I actually wish that JMP would not even report the power on the main effects of a mixture design. It causes unnecessary concern because you cannot "fix" the problem, and it makes no sense to consider it.
Re: Power Calculation on Mixture Design - Why is the power so low?Mixture designs have low power because the effects are highly correlated. More correlation == lower power. Ultimately, your interest with a mixture design is response estimation and not factor significance. Non significant factors can't be removed from the model, otherwise you don't have a mixture design (i.e., it breaks the math). What would likely happen to a factor that has no effect on the response is that it gets set to 0. While this may appear to be the same thing from a practical standpoint, it isn't mathematically. You can use a similar argument for retaining non-significant when fitting non-mixture data with LASSO (or Elastic net or Ridge). The focus is on response estimation and throwing out non-significant factors may actually make estimation worse (i.e., inflate the prediction variance).
