Taking into account both preparation and injection in high-performance liquid chromatography linearity studies

As mentioned in International Conference on Harmonisation publications, linearity is a principal parameter in method validation. The most popular statistical tool used is linear least-squares regression. Contrary to what is still very often practiced, the correlation coefficient can in no way be considered as an indicator of the fit quality. There is in fact a test called the "lack-of-fit test" that enables one to answer the question, "Is the linear model adapted to the calibration curve?". However, this test can give erroneous conclusions when, at each level, several sources of variation for the response are influent. It often occurs in high-performance liquid chromatography, as shown in a following example, where the calibration curve is obtained from repeated injections of repeated dilutions of a parent solution. The lack-of-fit test rejected linearity, although it was at least questionable. In fact, the reason for a discrepancy of this kind lies in the presence of a double source of variation: injection and dilution. It is possible to overcome the problem by mixing a nested ANOVA with the standard least-square linear regression. As shown in an example, implementing this methodology for data processing allows one not only to carry out an unbiased lack-of-fit test but also give estimates of the dispersion introduced respectively by the preparation and the injection.