[R-sig-ME] most conservative df for mixed effects anova

[Carrie Perkins]

Hello!

I have data from an experiment and would like to run an anova with fixed
and random effects in R. Here is information on the data:

In the experiment, 3 replicates of 48 plant genotypes were planted into
each of 4 salinity treatments. This resulted in a total of 144 individuals
per treatment, amounting to a grand total of 576 individuals in the whole
experiment. Within each treatment, random sets of 24 plants were grouped
into a total of 6 pools to make it easier to monitor salinity levels. I
would like to model these pools as random Experimental Units.

I would like to make Experimental Unit the random effect and look at the
treatment X genotype interaction as fixed effects.

lmer_model_3 <- aov(Y~Genotype*Treatment + Error(1|Experimental Unit),
data=dataframe)

What would be the most conservative method for calculating degrees of
freedom for the random effects term of an anova? When I've tried
researching this question online, I find a lot of information on
calculating degrees of freedom for basic 1- and 2-way anovas (which I
understand) but I can't find clear guidance on how to calculate the degrees
of freedom for anovas with random effects.

Thank you!

Sincerely,
Carrie Perkins

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