Ensuring both normality and homocedasticity of chromatographic data-ratios for internal-standard least-squares calibration

Because the quotient of two normal variables does not fit a normal distribution and tends to be heterocedastic, the use of internal-standard least-squares regression on data obtained from such ratios gives a calibration function which can result in inaccurate determination of the concentration of analyte in a sample. In this work we have studied simulated situations in which area-ratios are fitted to a normal distribution. It is shown that the least-squares model is inappropriate when the ordinate data-ratios are not normally distributed, and some recommendations are proposed to ensure both normality and homocedasticity of the quotient of analyte/internal-standard signals. Finally, GC-MS separation and quantification of nine fatty acids by use of an internal standard are used for experimental verification of the conclusions reached.