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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.

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I can see the merits in running four separate repeated measures ANOVAs. If your theoretical question concerns the four individual variables, then running the ANOVAs separately is more aligned with your theoretical question.

I guess the main issue is the parsimony of your approach and controlling your Type I error rate. Here are a few possibilities that you could explore:

  • 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.
  • You could distinguish analyses into confirmatory and more exploratory analyses. For example, you could frame the effect of time on overall biomass as confirmatory and interpret the effect of time on individual aspects of biomass as exploratory analyses.
  • You might even include type of biomass as another independent variable in your ANOVA. Then you could see whether there was a time by "type of biomass" interaction. This might be a more parsimonious approach because it, in some senses, starts with the assumption that any effect of time on type of biomass is constant across types of biomass.
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  • $\begingroup$ Thanks for the answer Jeromy, I think you sum up the issue well. If I were to reorganize the data with biomass type as an independent variable would that inflate my degrees of freedom? I have 70 experimental patches, can each plant group be though of as an independent group within those patches (n = 280)? I imagine I would need to nest plant group within patch? $\endgroup$ – Andy Apr 26 '11 at 14:25

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