I have read through the other responses on this form regarding the "best" non-parametric test to run when you were planning to run a 2-way anova and you determine that your dataset (residuals) are not normal even after attempts at transformation (shapiro test = 0.001032, prior to attempts at transformation). The p value is not far off from being significant assuming significance at p 0.05. I thought transforming the data would solve the problem, but it made it "less" normal (i.e. much smaller p value).
My goal is to determine if there are significant differences in mean monthly chloride data over a period of 31 years. I have single monthly measurements of chloride and was going to use "years" as my replicates/blocks.
To solve the issue I thought I could run a GLM or run a a regression analysis across months to generate a predictive curvilinear model. I have also been told that since my p value is relatively close to "normal" its okay to run a two way anova. I don't know how to choose the best test and am looking for some general feedback.
I can post my data, but I don't know that it is necessary. Thank you.