[R] Use of geometric mean for geochemical concentrations [RESOLVED]

[Rich Shepard]

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