Limits of detection in linear regression with errors in the concentration

This paper discusses a method for calculating the limit of detection in analytical methods in which the calibration stage takes into account the errors in both concentrations and instrumental responses. The proposed method considers the heteroscedastic individual errors on both axes, i.e. it uses the bivariate least squares (BLS) regression method. The expressions were applied to X-ray fluorescence (XRF) and capillary electrophoresis (CE) determinations to calculate the limits of detection of nine elements in solid rocks and three anions in water respectively. The limits of detection with these expressions have been compared with those obtained with ordinary least squares (OLS) and weighted least squares (WLS). The results show that the limits of detection when the BLS procedure is used are smaller than when the other techniques are used. Copyright (C) 2003 John Wiley Sons, Ltd.