Sorry to prolong a thread on something that is clearly off topic, but when
Michael Meyer wrote
>by using the geometric mean all asymptotic results no longer apply.
that is flat our wrong. It's true that the geometric mean converges to
something different that E[X], but it does indeed have an
By the Strong Law of Large Numbers applied to log(X) the geometric mean of
X_1,...,X_n > 0 and IID like X converges toexp(E[log(X)]] which, by Jensen's
inequality, is always <= E[X] and is strictly less than E[X] except in trivial
extreme cases.
In short: by using the geometric mean all
I've advised people consulting me that if their data is loaded with
zeros, while they are absolutely certain that something should be where
the zeros are, then they either need a better measuring tool, or to
carefully document the results of limits on detectability and then note
what fraction
Still OT... but here is my own (I think previously mentioned here) rant on
people thrashing about with log transformation and an all-too-common kludge to
deal with zeros mixed among small numbers...
https://gist.github.com/jdnewmil/99301a88de702ad2fcbaef33326b08b4
OP perhaps posting a link
In the spirit of Martin's comments, it is perhaps worthwhile to note one of
John Tukey's (who I actually knew) pertinent quotes:
"The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
Ah LOD's, typically LLOD's ("lower limits of detection").
Disclaimer: I am *NOT* in any sense an expert on such matters. What follows
are just some comments based on my personal experience. Please filter
accordingly. Also, while I kept it on list as Martin suggested it might be
useful to do
Dear Martin,
Helpful general advice, although it's perhaps worth mentioning that the
geometric mean, defined e.g. naively as prod(x)^(1/length(x)), is
necessarily 0 if there are any 0 values in x. That is, the geometric
mean "works" in this case but isn't really informative.
Best,
John
--
On Mon, 22 Jan 2024, Martin Maechler wrote:
I think it is a good question, not really only about geo-chemistry, but
about statistics in applied sciences (and engineering for that matter).
John W Tukey (and several other of the grands of the time) had the log
transform among the "First aid
> Rich Shepard
> on Mon, 22 Jan 2024 07:45:31 -0800 (PST) writes:
> A statistical question, not specific to R. I'm asking for
> a pointer for a source of definitive descriptions of what
> types of data are best summarized by the arithmetic,
> geometric, and harmonic
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