# Is MANOVA the correct way to handle multiple response variables that are additive?

### Context:

I am trying to analyze an experiment on plant community response to two treatments. Here’s a simplified description of the experiment, there are a few extra complications in reality.

Treatments were applied to small patches of ground arranged in blocks with a mix of naturally occurring plant species present in each patch. I have measured biomass of the plants in each patch in years one and two as the response variables. Analyzing total biomass seems simple enough with a repeated measures GLM or linear mixed model and block a random effect.

However I am also interested in breaking down total biomass into four response groups of interest: perennial grasses, perennial forbs, annual grasses and annual forbs (forbs are plants that aren't grasses).

### Question:

• Because these groups sum up to total biomass can I go a head and analyze these responses with four separate repeated measures ANOVAs, or will I be guilty of re-analyzing the same experiment?

It’s been suggested to me that I do a MANOVA followed by “protected ANOVA’s” but this doesn’t make sense to me because I am not interested in the multivariate response, rather I am interested in testing whether these specific variables have been affected by the treatments. I also don’t know how to do a repeated measures MANOVA correctly and it seems unduly complicated. Any general advice would be appreciated—I’ll try and design a more easily analyzable experiment next time.

• You could apply a Bonferonni correction to your $\alpha$ level (e.g., $\alpha=.05 /4=.0125$) so that your family-wise $\alpha$ is kept at an acceptable level.