Factor analysis of a simulated data matrix involving aqueous complex equilibria

Standard test data (STD) are simulations of analytical instrument responses that help to determine the veracity of computer‐based, data analysis procedures that are typically used with instruments. The STD were developed for determining errors in peak parameters obtained from data analysis algorithms used in x‐ray photoelectron spectroscopy (XPS). The STD were mainly C 1s doublet spectra constructed from spline polynomial models of measured C 1s polymer spectra. Different spectra were created based on a replicated factorial design with three factors: peak separation; relative intensity of the component peaks; and fractional Poisson noise. These doublet spectra simulated XPS measurements made on different two‐component specimens. Single‐peak C 1s spectra for individual polymers were also simulated, to provide the null case for identification of the doublet spectra. Twenty analysts used a variety of data analysis programs and a variety of curve‐fitting approaches to determine peak binding energies. Results indicate that data analysis of doublet spectra may be problematic, because up to 50% of the STD doublets were assigned incorrectly as singlets. For spectra that were correctly identified as doublets, bias and random error in peak binding energies depended on the amount of separation between the component peaks and on their relative intensities. Biases ranged from ‐0.055 eV to 0.34 eV, while random errors ranged from 0.012 eV to 0.13 eV. Use of the Gaussian–Lorentzian function fitted to spectra resulted in smaller biases than the use of a Gaussian function alone. As a guide to evaluating peak energy uncertainties in their own analyses, analysts may find it useful to analyze the STD themselves and then compare their results with those reported here. The spectra may be obtained at http://www.acg.nist.gov/std/main.html. © 1998 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 99%

Standard test data for estimating peak-parameter errors in x-ray photoelectron spectroscopy. I. Peak binding energies

Conny

Powell

Currie

1998

Standard test data for estimating peak parameter errors in x-ray photoelectron spectroscopy: II. Peak intensities

Conny

Powell

2000

Standard test data for x-ray photoelectron spectroscopy (XPS-STD) have been developed for determining bias and random error in peak parameters derived from curve fitting in XPS. The XPS-STD are simulated C 1s spectra from spline polynomial models of measured C 1s polymer spectra. Some have a single peak, but most are doublet spectra. The doublets were created from a factorial design with three factors: peak separation, relative intensity of the component peaks, and fractional Poisson noise. These doublet spectra simulated XPS measurements made on different two-component polymer specimens. This, the second of a three-part study, focuses on bias and random errors in determining peak intensities. We report the errors in results from 20 analysts who used a variety of programs and curve-fitting approaches. Peak intensities were analyzed as a ratio of the intensity of the larger peak in a doublet to the total intensity, or as a ratio of intensities for singlet peaks in separate but related spectra. For spectra that were correctly identified as doublets, bias and random errors in peak intensities depended on the amount of separation between the component peaks and on their relative intensities. Median biases for doublets calculated on a relative, unitless scale from −1 to 1 ranged from −0.33 to 0.17, whereas random errors for doublets calculated on the same scale ranged from 0.016 to 0.18. In most cases the magnitude of the median bias exceeded the median random error. On this scale, errors of −0.33 and 0.18 corresponded to errors of factors of 4 and 2, respectively, in determinations of the relative intensities as a ratio of the larger peak in a doublet to the smaller peak. Analysts may evaluate uncertainties in their own analyses of the XPS-STD by visiting the web site http://www.acg.nist.gov/std/. Copyright © 2000 John Wiley & Sons, Ltd.KEYWORDS: XPS; curve fitting; peak intensity; reference data; bias; accuracy; random error; precision; algorithm testing INTRODUCTIONModern developments in chemical instrumentation have necessarily led to greater complexity in the way response data are acquired, processed and converted to chemical information. As the flow and manipulation of chemical data become more complicated, it becomes more difficult to validate chemical information derived from data evaluation procedures. Standard test data (STD) are simulations of instrument responses that help to determine the veracity of data analysis procedures designed to convert instrument responses into relevant chemical information. The STD are analogous to certified reference materials produced by various organizations (e.g. Standard Reference Materials (SRMs) produced by the National Institute of Standards and Technology) in that both are used to 'calibrate' (i.e. assure the accuracy of) the chemical measurement process. This 'calibration' process can be divided into two domains: the sample preparation/measurement domain and the data evaluation domain.1 Although SRMs are used to calibrate the complete chemical measurement process, STD ...

Standard test data for estimating peak parameter errors in x-ray photoelectron spectroscopy III. Errors with different curve-fitting approaches

Conny¹,

Powell²

2000

We present results in the final part of a three‐part study employing standard test data (STD) to estimate errors in peak parameters derived from data analysis procedures used in x‐ray photoelectron spectroscopy (XPS). The XPS‐STD are simulated doublet and singlet XPS spectra based on spline polynomial models of measured C 1s spectra. The XPS‐STD contained 10 sets of spectra, each of which consisted of 18 doublets and 4 singlets. The doublet spectra in each set were created from a factorial design with three factors: peak separation; relative intensity of the component peaks; and fractional Poisson noise. Each of the XPS‐STD sets contained the same complement of doublet and singlet spectra and Poisson noise at the same levels; however, the noise distributions were unique in each spectral set. Seven curve‐fitting approaches were used by a group of 20 analysts to represent single peaks: a single Gaussian (G), a Gaussian–Lorentzian (G–L), a Voigt function, a G function with an asymmetry term, a G–L function with an asymmetry term and dual G or G–L functions. We statistically analyzed errors in binding energies and intensities by the type of curve‐fitting approach using the Kruskal–Wallis test and the Mann‐Whitney U‐test. Bias was used to measure the accuracy of a curve‐fitting approach, whereas random error was used to measure the precision of the approach. Despite the fact that individual peaks were nearly symmetrical, curve‐fitting approaches that accounted for peak asymmetry proved to be the most accurate for determining both peak intensities and binding energies. For the doublets exhibiting the larger peak at the higher binding energy, the use of dual G–L functions to fit individual peaks, as a way to account for peak asymmetry, produced the highest accuracy in determining peak binding energy. This dual peak‐shape approach for this particular spectral condition is also preferable for determining peak intensities and produces better precision. The XPS‐STD and the statistical analysis methods presented here provide a means to distinguish differences in the accuracy of various curve‐fitting approaches for spectral conditions that resemble those of the XPS‐STD. To obtain the XPS‐STD and to have an online evaluation of curve‐fitting accuracy and precision, consult the following web site: http://www.acg.nist.gov/std. Copyright © 2000 John Wiley & Sons, Ltd.