Fluctuation Scaling, the Calibration of Dispersion, and the Detection of Differences

2.50
Hdl Handle:
http://hdl.handle.net/2436/620771
Title:
Fluctuation Scaling, the Calibration of Dispersion, and the Detection of Differences
Authors:
Holland, Rianne; Rebmann, Roman; Williams, Craig D.; Hanley, Quentin S.
Abstract:
Fluctuation scaling describes the relationship between the mean and standard deviation of a set of measurements. An example is Horwitz scaling which has been reported from inter-laboratory studies. Horwitz and similar studies have reported simple exponential and segmented scaling laws with exponents (α) typically between 0.85 (Horwitz) and 1 when not operating near a detection limit. When approaching a detection limit the exponents change and approach an apparently Gaussian (α = 0) model. This behavior is generally presented as a property of inter-laboratory studies which makes controlled replication to understand the behavior costly to perform. To assess the contribution of instrumentation to larger scale fluctuation scaling, we measured the behavior of two inductively coupled plasma atomic emission spectrometry (ICP-AES) systems, in two laboratories measuring thulium using 2 emission lines. The standard deviation universally increased with the uncalibrated signal indicating the system was heteroscedastic. The response from all lines and both instruments was consistent with a single exponential dispersion model having parameters α = 1.09 and β = 0.0035. No evidence of Horwitz scaling was found and there was no evidence of Poisson noise limiting behavior. The “Gaussian” component was a consequence of background subtraction for all lines and both instruments. The observation of a simple exponential dispersion model in the data allows for the definition of a difference detection limit (DDL) with universal applicability to systems following known dispersion. The DDL is the minimum separation between two points along a dispersion model required to claim they are different according to a particular statistical test. The DDL scales transparently with the mean and works at any location in a response function.
Citation:
Fluctuation Scaling, the Calibration of Dispersion, and the Detection of Differences 2017 Analytical Chemistry
Publisher:
ACS Publications
Journal:
Analytical Chemistry
Issue Date:
11-Oct-2017
URI:
http://hdl.handle.net/2436/620771
DOI:
10.1021/acs.analchem.7b02909
Additional Links:
http://pubs.acs.org/doi/abs/10.1021/acs.analchem.7b02909
Type:
Article
Language:
en
ISSN:
0003-2700
Appears in Collections:
FSE

Full metadata record

DC FieldValue Language
dc.contributor.authorHolland, Rianneen
dc.contributor.authorRebmann, Romanen
dc.contributor.authorWilliams, Craig D.en
dc.contributor.authorHanley, Quentin S.en
dc.date.accessioned2017-10-16T08:56:54Z-
dc.date.available2017-10-16T08:56:54Z-
dc.date.issued2017-10-11-
dc.identifier.citationFluctuation Scaling, the Calibration of Dispersion, and the Detection of Differences 2017 Analytical Chemistryen
dc.identifier.issn0003-2700en
dc.identifier.doi10.1021/acs.analchem.7b02909-
dc.identifier.urihttp://hdl.handle.net/2436/620771-
dc.description.abstractFluctuation scaling describes the relationship between the mean and standard deviation of a set of measurements. An example is Horwitz scaling which has been reported from inter-laboratory studies. Horwitz and similar studies have reported simple exponential and segmented scaling laws with exponents (α) typically between 0.85 (Horwitz) and 1 when not operating near a detection limit. When approaching a detection limit the exponents change and approach an apparently Gaussian (α = 0) model. This behavior is generally presented as a property of inter-laboratory studies which makes controlled replication to understand the behavior costly to perform. To assess the contribution of instrumentation to larger scale fluctuation scaling, we measured the behavior of two inductively coupled plasma atomic emission spectrometry (ICP-AES) systems, in two laboratories measuring thulium using 2 emission lines. The standard deviation universally increased with the uncalibrated signal indicating the system was heteroscedastic. The response from all lines and both instruments was consistent with a single exponential dispersion model having parameters α = 1.09 and β = 0.0035. No evidence of Horwitz scaling was found and there was no evidence of Poisson noise limiting behavior. The “Gaussian” component was a consequence of background subtraction for all lines and both instruments. The observation of a simple exponential dispersion model in the data allows for the definition of a difference detection limit (DDL) with universal applicability to systems following known dispersion. The DDL is the minimum separation between two points along a dispersion model required to claim they are different according to a particular statistical test. The DDL scales transparently with the mean and works at any location in a response function.en
dc.language.isoenen
dc.publisherACS Publicationsen
dc.relation.urlhttp://pubs.acs.org/doi/abs/10.1021/acs.analchem.7b02909en
dc.rightsArchived with thanks to Analytical Chemistryen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectICP Spectroscopy reproducibilityen
dc.titleFluctuation Scaling, the Calibration of Dispersion, and the Detection of Differencesen
dc.typeArticleen
dc.identifier.journalAnalytical Chemistryen
dc.date.accepted2017-10-
rioxxterms.funderInternalen
rioxxterms.identifier.projectUoW161017CWen
rioxxterms.versionAMen
rioxxterms.licenseref.urihttps://creativecommons.org/CC BY-NC-ND 4.0en
rioxxterms.licenseref.startdate2018-10-11en
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