I'm interested in calculating the required sample size for detecting a future hypothetical 30% increase in a marginal mean from a model based on historical data (accounting for covariates and random effects), but I'm not sure which standard deviation to use in the effect size calculation. I'm assuming I can use cohen's D in the power analysis, where the difference would be a 30% increase of the mean minus the mean, divided by a standard deviation (of something).
Cohen's D = M - u / signma
My response is fish count data from an ecological monitoring project. The goal is to determine our ability to detect changes in metrics like fish abundance, something that restoration efforts may be having a positive effect on.
I'm mostly wondering if effect sizes can be estimated from marginal means and SD of random effects. I would use the pwr package once I calculate the appropriate effect size. Would it make sense to input the SD from VarCorr below to calculate cohen's D? I'm open to alternatives of course.
If marginal mean was 3.57, effect would then:
(3.57*1.3) - 3.57 / sd (of something…)?