Chemical Measurement and Fluctuation Scaling

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Hanley, Q.S. ORCID: 0000-0002-8189-9550, 2016. Chemical Measurement and Fluctuation Scaling. Analytical Chemistry. ISSN 0003-2700

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Official URL: http://doi.org/10.1021/acs.analchem.6b02335

Abstract

Main abstract:
Fluctuation scaling reports on all processes producing a data set. Some fluctuation scaling relationships, such as the Horwitz curve, follow exponential dispersion models which have useful properties. The mean-variance method applied to Poisson distributed data is a special case of these properties allowing the gain of a system to be
measured. Here, a general method is described for investigating gain (G), dispersion (β), and process (α) in any system whose fluctuation scaling follows a simple exponential dispersion model, a segmented exponential dispersion model, or complex scaling following such a model locally. When gain and dispersion cannot be obtained directly, relative parameters, GR and βR, may be used.
The method was demonstrated on data sets conforming to simple, segmented, and complex scaling. These included mass, fluorescence intensity, and absorbance measurements and specifications for classes of calibration weights.
Changes in gain, dispersion, and process were observed in the scaling of these data sets in response to instrument parameters, photon fluxes, mathematical processing, and calibration weight class. The process parameter which limits the type of statistical process that can be invoked to explain a data set typically exhibited 0<α<1 with α>4 possible. With two exceptions, calibration weight class definitions only affected β. Adjusting photomultiplier voltage while measuring fluorescence intensity changed all three parameters (0<α<0.8; 0<βR<3; 0<GR<4.1). The method provides a framework for calibrating and interpreting uncertainty in chemical measurement allowing robust compar ison of specific instruments, conditions, and methods.
Supporting information abstract:
On first inspection, fluctuation scaling data may appear to approximate a straight line when log transformed. The data presented in figure 5 of the main text gives a reasonable approximation to a straight line and for many purposes this would be sufficient. The purpose of the study of fluorescence intensity was to determine whether adjusting the voltage of a photomultiplier tube while measuring a fluorescent sample changes the process (α), the dispersion (β) and/or the gain (G). In this regard, the linear model established that PMT setting affects more than the gain. However, a detailed analysis beginning with testing for model mis-specification provides additional information. Specifically, Poisson behavior is only seen over a limited wavelength range in the 600 V and 700 V data sets.

Item Type:

Journal article

Description:

Includes Supporting Information

Publication Title:

Analytical Chemistry

Creators:

Hanley, Q.S.

Publisher:

American Chemical Society

Date:

2016