I'm in materials science. I have a fractional factorial experiment. I am investigating the main effect of various treatments on a measured response. The exact details are probably not needed to understand my question so I will simplify things in order to frame my question a more straight forward way (I have 7 factors, but lets just consider 2).
The problem I have is that my replicates are not true replicates, for each set of measurements (with factors set at defined levels) I am only able to make a single batch of material. I then produce individual specimens from that particular batch for testing (say 10 individuals from a batch).
I am aware that the variation within a particular batch is lower than the variation between batches when the treatment factors are kept constant. Nevertheless, economic reasons prevent me from making multiple batches of materials for all cases.
If I ignore this fact and run an ANOVA in R my p-values suggest that the treatment factors have significance than I suspect they really have. I'm using R for the analysis and at the moment I am using something like:
anova = aov(Response ~ TreatmentA * TreatmentB, data=dataframe)
As a separate experiment I have done some complete replications, e.g. 3 different batches with 10 specimens tested from each batch and not changed the treatment factors. This gives me an indication of batch-to-batch variability.
Is there a way I can plug results of this second experiment as some sort of additional error factor into my first experiment?
As I said, I'm sure the answer to the question is out there but I might be struggling to find the right search term.