Dear Rich, It depends how the data is generated.
Although I am not an expert in ecology, I can explain it based on a biomedical example. Certain variables are generated geometrically (exponentially), e.g. MIC or Titer. MIC = Minimum Inhibitory Concentration for bacterial resistance Titer = dilution which still has an effect, e.g. serially diluting blood samples; Obviously, diluting the samples will generate the following concentrations: 1, 1/2, 1.4, 1/8, 1/16, ... (or the reciprocal: 1, 2, 4, 8, 16, ...) It makes no sense to compute the arithmetic mean. Results are usually reported as some quantile (median or 90%); alternatively, one computes the geometric mean. ### Ecology /Environmental Chemistry I suppose that certain chemicals may be generated/released in the environment through a non-linear process. The LLOD may also play a role, but may NOT be the main reason. If the generating process is exponential, then the arithmetic mean would strongly skew the results (also inconsistently based on season, particular year, etc - the generating processes may differ). ### Harmonic Mean Did not encounter it often: maybe because of the problematic handling of 0. I do have in the meantime a nice workaround for 0 (which also works with the geometric mean), see also (unfortunately not well documented): https://github.com/discoleo/R/blob/master/Stat/Moments.Stat.R v0 = 1; # some initial "skew" 1 /(xharm + v0) = sum( 1 / (x + v0) ) / length(x) xgeom = prod(x + v0)^(1/length(x)) - v0; I apologize for the late reply; I did not have much time to read messages during the past weeks. Sincerely, Leonard [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
