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Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean

Jacques De Beer, Thomas De Beer UGent and Leo Goeyens (2007) Analytica Chimica Acta. 584(1). p.57-65
abstract
In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined. The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation. The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s(x0) calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature. It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
INVERSE REGRESSION METHODS, ATOMIC-ABSORPTION SPECTROMETRY
journal title
Analytica Chimica Acta
Anal. Chim. Acta
volume
584
issue
1
pages
57 - 65
publisher
Elsevier Science BV
place of publication
PO Box 211, 1000 AE Amsterdam, Netherlands
Web of Science type
Article
Web of Science id
000244020700009
JCR category
CHEMISTRY, ANALYTICAL
JCR impact factor
3.186 (2007)
JCR rank
10/69 (2007)
JCR quartile
1 (2007)
ISSN
0003-2670
DOI
10.1016/j.aca.2006.11.032
language
English
UGent publication?
yes
classification
A1
copyright statement
I don't know the status of the copyright for this publication
id
677958
handle
http://hdl.handle.net/1854/LU-677958
date created
2009-06-04 13:56:03
date last changed
2017-01-02 09:55:44
@article{677958,
  abstract     = {In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined.
The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation.

The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s(x0) calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature.

It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.},
  author       = {De Beer, Jacques and De Beer, Thomas and Goeyens, Leo},
  issn         = {0003-2670},
  journal      = {Analytica Chimica Acta},
  keyword      = {INVERSE REGRESSION METHODS,ATOMIC-ABSORPTION SPECTROMETRY},
  language     = {eng},
  number       = {1},
  pages        = {57--65},
  publisher    = {Elsevier Science BV},
  title        = {Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean},
  url          = {http://dx.doi.org/10.1016/j.aca.2006.11.032},
  volume       = {584},
  year         = {2007},
}

Chicago
De Beer, Jacques, Thomas De Beer, and Leo Goeyens. 2007. “Assessment of Quality Performance Parameters for Straight Line Calibration Curves Related to the Spread of the Abscissa Values Around Their Mean.” Analytica Chimica Acta 584 (1): 57–65.
APA
De Beer, Jacques, De Beer, T., & Goeyens, L. (2007). Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean. Analytica Chimica Acta, 584(1), 57–65.
Vancouver
1.
De Beer J, De Beer T, Goeyens L. Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean. Analytica Chimica Acta. PO Box 211, 1000 AE Amsterdam, Netherlands: Elsevier Science BV; 2007;584(1):57–65.
MLA
De Beer, Jacques, Thomas De Beer, and Leo Goeyens. “Assessment of Quality Performance Parameters for Straight Line Calibration Curves Related to the Spread of the Abscissa Values Around Their Mean.” Analytica Chimica Acta 584.1 (2007): 57–65. Print.