Abstract
A calibration curve is used to express the relationship between the response of the measuring technique and the standard concentration of the target analyst. The calibration equation verifies the response of a chemical instrument to the known properties of materials and is established using regression analysis. An adequate calibration equation ensures the performance of these instruments. Most studies use linear and polynomial equations. This study uses data sets from previous studies. Four types of calibration equations are proposed: linear, higher-order polynomial, exponential rise to maximum and power equations. A constant variance test was performed to assess the suitability of calibration equations for this dataset. Suspected outliers in the data sets are verified. The standard error of the estimate errors, s, was used as criteria to determine the fitting performance. The Prediction Sum of Squares (PRESS) statistic is used to compare the prediction ability. Residual plots are used as quantitative criteria. Suspected outliers in the data sets are checked. The results of this study show that linear and higher order polynomial equations do not allow accurate calibration equations for many data sets. Nonlinear equations are suited to most of the data sets. Different forms of calibration equations are proposed. The logarithmic transformation of the response is used to stabilize non-constant variance in the response data. When outliers are removed, this calibration equation’s fit and prediction ability is significantly increased. The adequate calibration equations with the data sets obtained with the same equipment and laboratory indicated that the adequate calibration equations differed. No universe calibration equation could be found for these data sets. The method for this study can be used for other chemical instruments to establish an adequate calibration equation and ensure the best performance.
Highlights
The performance characteristics include accuracy, precision and sensibility of the sensors or instrument is so important, especially in chemical analysis [1,2,3]
After evaluating the adequacy of equations for that are listed in Table 1, the results of the regression analysis involve four types of calibration equations: a
This study uses seventeen data sets from previous studies to evaluate the adequacy of calibration equations
Summary
The performance characteristics include accuracy, precision and sensibility of the sensors or instrument is so important, especially in chemical analysis [1,2,3]. Most quantitative analytical techniques for chemical analysis, such as spectrometry, Inductively Coupled. Plasma Mass Spectrometry (ICP-MP) or electrophoresis, require a calibration curve to express the relationship between the response of the measuring technique and the standard concentration of the target analyst [4,5]. According to the definition of Dux, the calibration equation is used to verify the response of an instrument to the known properties of a material [6]. A calibration curve is established to express the relationship between the response and the standard concentration for physical, chemical, and biological sensors [7,8,9]. The calibration curve is fitted using regression analysis to fit different models to experimental data [10,11]
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