Test for effect of treatment for subjects of different origin?

Question

I have a collection of subjects differing in location (origin) and treatment. I am looking for differences due to treatment but I have been warned that location might be significant.

• n locations, m(i) replicates (identical subjects) from location i.
• all subjects from one location submitted to the same treatment t(i).
• p different treatments and q(j) locations subjected to treatment j.
• in general m(i) /= m(j) and q(i) /= q(j)

Again, I expect most variation to originate from the treatment but there might be some due to location (although I expect this to be negligible).

Ideally I'd have liked to pool the subjects according to treatment, but apparently that is not the right way to do things so I would be very thankful for guidance.

(1) How to test for the effect of different treatments and account for location? Can I test first for effect of location and finding none pool subjects by treatment? Or would a two-way ANOVA (factors location and treatment) or a repeated-measures ANOVA (since the data is nested) be appropriate? Or, should location be treated as a "random effect"? I am new to random effects, so if the latter, a little guidance on how to handle this would be helpful (I've only looked into multiway and RM-ANOVA before).

(2) The response variable of interest is continuous. However I've also been considering analysing a binomial response variable by performing survivorship tests using GLM/logit binomial regression and am not sure how to proceed given the structure of the dataset. Any guidance there would be welcome.

Answer 1

Well overall, it's a bit of a study design issue. You can never be confident whether differences between locations are the result of your treatment, or a different, unmeasured variable that changes between your locations. This is known as Pseudoreplication.

However, reality sometime doesn't allow better design. If you are comfortable proceeding, for your first question, yes use random intercepts for location. This essentially says that the mean value for each location is drawn from a normal distribution, centered at the expected mean for the treatment it receives. This can help absorb some of the error and reveal treatment effects.