Linearity of calibration curves: use and misuse of the correlation coefficient

Abstract

The correlation coefficient is commonly used to evaluate the degree of linear association between two variables. However, it can be shown that a correlation coefficient very close to one might also be obtained for a clear curved relationship. Other statistical tests, like the Lack-of-fit and Mandel's fitting test thus appear more suitable for the validation of the linear calibration model. A number of cadmium calibration curves from atomic absorption spectroscopy were assessed for their linearity. All the investigated calibration curves were characterized by a high correlation coefficient (r >0.997) and low quality coefficient (QC <5%), but the straight-line model was systematically rejected at the 95% confidence level on the basis of the Lack-of-fit and Mandel's fitting test. Furthermore, significantly different results were achieved between a linear regression model (LRM) and a quadratic regression (QRM) model in forecasting values for mid-scale calibration standards. The results obtained with the QRM did not differ significantly from the theoretically expected value, while those obtained with the LRM were systematically biased. It was concluded that a straight-line model with a high correlation coefficient, but with a lack-of-fit, yields significantly less accurate results than its curvilinear alternative.

Quality control of test iodine in urine by spectrophotometry UV–Vis

“…This is due to the measured absorbance is the residual Ce 4+ ion of the reaction with the iodide. This study shows the high correlation because r value in this research is -0.9987 [13].…”

Possibility of the Spectrophotometric Determination of Europium by Means of Arsenazo Iii

“…The VAN LOCO et al, 2002). Results for determination of repeatability of measurement and trueness of measurement are given in Table 1.…”

The Role of and the Place of Method Validation in Drug Analysis Using Electroanalytical Techniques

“…A lack of significance means that there are no detectable general matrix effects either in pharmaceutical dosage forms or in biological samples. If the calibration is not linear, a more complex technique for significance tests [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][48][49][50][51][52]. However, using the electroanalytical methods this kind of interferences are not detected because of the electro-inactive nature of the excipients of pharmaceuticals and most of the endogenous substances of biological media.…”

“…Then, when the correlation coefficient values reach at least 0.999 the linearity can be assumed in the concentration range for which standard solutions had been prepared during the calibration procedure. However, this parameter is mostly used, but correlation coefficient (r) is neither a proof of linearity nor suitable for quantitative measurement [19,25,[48][49][50][51][52]. Correlation coefficient (r) just indicates the extent of the relationship between the dependent and independent variables such as the electroanalytical response and the electroactive compound concentration.…”

“…If the slope is negative, y decreases as x increases. The slope of the calibration curve also refers to the sensitivity of the method [10,14,[48][49][50][51][52][53][54]. Hence, sensitivity is measured at the same time as the linearity tests.…”