Here's the thing: I have the concentration of a certain compound measured in each individual. Individuals were sampled on a monthly basis, with varied lucky, some months I caught more than ten, sometimes I caught only two.
Here is a plot showing the data I am dealing with.
What I want to know is if and which months have average levels of the compound that are significantly higher or lower (peaks mostly). Also I want to know if changes in variance among samples are different from the expected given the different sample sizes.
My first thought was simple one-way ANOVA and then a post-hoc, but my data do not support the assumptions of normality nor homoskedasticity.
After various readings including non parametric tests, permutation test and temporal series, I realized that here are many possible analysis and assumptions to consider so at the end I get a bit lost. What would be the best way to analyze my data to answer my questions above?
I have already tried a one way permANOVA and wrote some code in R to perform permutational T-tests contrasting the mean for each sampling date with that of the pooled data, but I am not sure if that is a proper test.
Any advice is welcomed.