On Mon, 22 Jan 2024, Rich Shepard wrote:
As an aquatic ecologist I see regulators apply the geometric mean to geochemical concentrations rather than using the arithmetic mean. I want to know whether the geometric mean of a set of chemical concentrations (e.g., in mg/L) is an appropriate representation of the expected value. If not, I want to explain this to non-technical decision-makers; if so, I want to understand why my assumption is wrong.
Many of you provided excellent comments, and so did a couple of folks on StackExchange. Rather than responding to individual posts I've waited until the thread petered out to provide an overall response. I've two points to make: one on mean calculations and the second on the context I didn't sufficiently provide when I posted my question. Responses confirmed that the appropriate model for calculating means depends on the data set and the question(s) the data are to answer. So the summary answer to my question (as stated) is: it depends. :-) Thank you. What prompted my thread-starting message is that I work in the realm of environmental regulation compliance, including the Clean Water Act and the Endangered Species Act. There is one state environmental regulator that provides state-wide point source storm water discharges under a General permit for smaller industrial activities. The permit monitoring requirements are 4 samples per year, one each quarter for a small set of water chemical and physical constituents (really!) and the reporting requirements are to use the geometric mean to summarize the four data points. I have my clients calculate an arithmetic mean in addition. (For the record, if you have an Agriculture Department General Storm Water Discharge Permit for a point source such as a livestock feed lot you need only a single sample (after the rains start) to comply with the permit. Feh! Germane to Bert's comments about all the wrong ways to treat non-detected/censored water chemical analyses, I discovered Dennis Helsel by his 2005 article in Environmental Science & Technology (Oct. 16th). Bought his book when it was published in 2012 and have used survival analyses on censored data ever since. (Also presented a Continuing Legal Education talk in 2016 with a nice thank-you email from a state district judge who attended.) I greatly appreciate all your comments and apologize for not better explaining the context of my question when I posted my first message. Regards, Rich ______________________________________________ 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.
