Chemical Measurement and Fluctuation Scaling

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, G_R and β_R, 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 < β_R < 3; 0 < G_R < 4.1). The method provides a framework for calibrating and interpreting uncertainty in chemical measurement allowing robust comparison of specific instruments, conditions, and methods.