Hello everyone !
I have a very unbalanced design and wondering how to make my two-way ANOVA.
To give you the context, I am looking at the changes in communities along a salinity gradient in estuaries. I took species density measurements in 8 to 10 quadrats at three levels of stress (Low, Medium, High) in five estuaries, and then took the same measurements in 4 marine control sites (Null stress).
Therefore I have two factors : the Stress (fixed, 4 levels : null, low, medium, high) and the Site ("9"levels : Estuaries E1, E2, E3, E4, E5 and marines sites M1, M2, M3, M4).
As I am more interested by the effect of the stress rather than the site, I was going to consider the site as random :
lmer_biomass <- lmer(biomass ~ Stress + (1|Site), data = data_2019, contrasts = list(Stress = contr.sum))
anova(lmer_biomass, type = 3, singular.ok = TRUE)
Tukey_lmer_biomass <- emmeans(lmer_biomass, tukey ~ Stress)
However, my codirector would like me to use the Site as a fixed factor.
I would use this if the design was "normal" :
biomass.fixe<- aov(biomass ~ Stress*Site, data=data_2019)
However then I don't know (1) how to use a Type III for the unbalanced design, and (2) how to compare the the different stress levels with one another.
I think I should use a function ith contrasts, to do something like null vs. the other stress, but I am at lost here. Any advice would be welcome.