Wednesday, February 15, 2012

Likelihood methods for comparative biology incorporating uncertainty in the estimation of species means

A recent search string that lead a user to this blog was as follows:

"comparative phylogenetics standard error or standard deviation"

By this, I presume they were trying to figure out whether functions such as fitContinuous in the geiger package; or phylosig and brownie.lite in phytools (in which we are fitting an evolutionary model for the evolution of the phenotypic mean of a continuously valued trait to the data for species means and the tree) accepts measures of uncertainty for species as the standard errors of the species means or the standard deviations of the observations for each species. Obviously, the parametric estimate of the former is just the latter divided by the square-root of the sample size for each species.

The answer is that we use the standard errors of the means for each species in these analyses, not the standard deviations. It is only the former that tells us how uncertain we are about our estimates of the means for species. This is because even for very large standard deviation σ, our uncertainty about any given sample mean goes to zero as n → ∞. Parametric estimates of σ, by contrast, are theoretically unaffected by sample size.

I hope that the previous searcher found what he or she was looking for, and now it should be even easier!

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