R help - Jan 2024 - Use of geometric mean for geochemical concentrations

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


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On Tue, 30 Jan 2024, Leo Mada wrote:
> It depends how the data is generated.
> Although I am not an expert in ecology, I can explain it based on a
> biomedical example.
Leo,

My data are environmental, observational concentrations of water
constituents. It's not only how data are generated, what question
they're
supposed to answer matters, too.

Rich

Dear Rich,

There are geochemical processes and biological processes that generate the
compounds/metabolites/etc: nitrates, heavy metals, and other ions may be
generated differently.

Such processes may differ based on season or some other event: rain, melting of
ice, rare events like a spill from an artificial source.

I am not an expert in geochemistry or agriculture, but I would say that certain
events happen occasionally and do not reflect the "baseline". Melting
of ice in the mountains may increase the concentrations of certain ions.
Application of fertilizers on the crops may increase some organic compounds.
Algal blooms happen during summer.

Furthermore, the increase in concentration may be *non*-linear! This is the
reason why a "robust" alternative (in this case the geometric mean) is
used.

If you want specific details, then you would need to research the possible
sources for each of the specific constituents and assess if those events release
exponential (large) amounts of the compound of interest.

Sincerely,

Leonard



________________________________
From: Leo Mada <leo.mada at syonic.eu>
Sent: Tuesday, January 30, 2024 3:49 PM
To: Rich Shepard <rshepard at appl-ecosys.com>
Cc: r-help at r-project.org <r-help at r-project.org>; Richard O'Keefe
<raoknz at gmail.com>
Subject: Re: [R] Use of geometric mean for geochemical concentrations

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


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