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 means. 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. TIA, Rich
Use of geometric mean for geochemical concentrations
2 messages · Rich Shepard, Cade, Brian
2 days later
Think I miss sent this just to Phillip Dixon so reposting. Rich: Just to expand on Phillip Dixon's reply a bit. You can always estimate the median in the log transformed scale, with for example quantile regression, and then back-transform to the original concentration scale without bias or loss of information as the median like all quantiles is equivariant to nonlinear monotonic transformations like the logarithmic. And as Phillip indicated the mean estimated in log transformed scale back-transformed is the geometric mean estimate of median in original scale. If you really require an estimate of the expected value (mean in original concentration scale), Duan's (1983) smearing estimate is a general nonparametric retransformation method that can estimate the mean from an estimated median. It is fairly simple to apply. If you need an estimate of median handling below detection limit data, quantile regression (quantreg package) has a censored data estimator option that can be used. Brian Brian S. Cade, PhD U. S. Geological Survey (emeritus) Fort Collins Science Center 2150 Centre Ave., Bldg. C Fort Collins, CO 80526-8818 email: cadeb at usgs.gov<mailto:brian_cade at usgs.gov> tel: 970 404-0447
From: R-sig-ecology <r-sig-ecology-bounces at r-project.org> on behalf of Rich Shepard <rshepard at appl-ecosys.com>
Sent: Monday, January 22, 2024 9:25 AM
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Subject: [EXTERNAL] [R-sig-eco] Use of geometric mean for geochemical concentrations
Sent: Monday, January 22, 2024 9:25 AM
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Subject: [EXTERNAL] [R-sig-eco] Use of geometric mean for geochemical concentrations
This email has been received from outside of DOI - Use caution before clicking on links, opening attachments, or responding. 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 means. 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. TIA, Rich _______________________________________________ R-sig-ecology mailing list R-sig-ecology at r-project.org https://gcc02.safelinks.protection.outlook.com/?url=https%3A%2F%2Fstat.ethz.ch%2Fmailman%2Flistinfo%2Fr-sig-ecology&data=05%7C02%7Ccadeb%40usgs.gov%7Cf051a9748023448e278c08dc1b66e4dd%7C0693b5ba4b184d7b9341f32f400a5494%7C0%7C0%7C638415375936186803%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=ya7lJk8tATR55nvzpsng8vTgiPHPM78i61VOmK3%2Bhro%3D&reserved=0<https://stat.ethz.ch/mailman/listinfo/r-sig-ecology>