I have done an experiment in which I looked at the prey preference of an aquatic invertebrate. I used 10 containers all with one predator but with different densities of prey. I used two different prey species of which the densities were similar for every container. For example container 1 contained 5 individuals of prey A and 5 of prey B. Container 2 contained 10 individuals of prey A and 10 of prey B and so on. Now I want to see which prey is prefered by the predator. My data looks as followed:
prey.a <- c(5,5,10,10,9,12,13,8,15,17) ## number of captured prey (A)
prey.b <- c(5,5,4,2,8,8,4,9,4,6) ## number of captured prey (B)
prey.density <- c(10,10,20,20,20,30,30,30,40,40) ## total number of prey available (A and B)
My initial thought was to use a paired t-test. The data violate the assumption of independent samples because they are kind of paired that is why I thought a paired t-test. However, my data violate the assumption of normality so perhaps a Wilcoxon test for paired measurements would be suitable.
The thing is that both these test are designed for a before and after treatment which I don't have. Thus, I'm not really sure if I can actually use these tests. The problem is tha it's a paired rank test of the differences and my low density treatments will always be ranked lower than my high density treatments.
My question is; What would be a suitable test to analyse these data?
I also had this wild thought about a GLMM in which I use the container as a random effect and add prey species as a fixed effect, nevertheless, normality.
btw I used different prey densities because I also looked at the effect of prey density on the total number of captured prey, which has nothing to do with my question.