Different ANOVAs per species for same variable; how to proceed if only some species hold non-normal data

Question

I am conducting two-way ANOVAs to determine if plant height (mm) is affected by treatment (3 water regimes) in different growth medium types (2). I am also interested in the interactions that may occur between the water treatments and soil so my model is contracted as such.

I have multiple species of plant included in this study. As such, I have decided that the best course of action to statistically analyse the data is to do seperate two-way ANOVAs per species (I am not all that interested in the fact that some plants will be taller than others; its a given). However, after partitioning the data per species, it has become evident that ONLY SOME of the species' heigh values are normal (shapiro.test).

Can I transform the data of ONLY the species that aren't normal? Or should all (even the already normal ones) be transformed?

Answer 1

How many plants per species do you have?

First it’s worth to explore the normality via something different than Levene’s test (this refers to homoscedasticity assumption) so Shapiro-Wilk test or visual exploration of a QQ plot.

There’s no need to transform all species, because those which follow normal distribution will lose it after an additional transformation. After transformation check how the distributions look like. Then for results presentation it will be worth to think about the way to do that effectively as transformed variables are not self-descriptive (i.e., if you use a log transformation than maybe a geometrical mean +/- its SD).

Why I asked about the N of plants per species? If it’s rather small, than maybe instead of a two-way ANOVA it’s more worth to run a mixed model with water regimen and medium as fixed effects and species as a random effect.