Calibration and the Straight Line: Current Statistical Practices

Abstract

A recent article used data involving high pressure liquid chromatographic (HPLC) analyses of known concentrations of FD&C Red No. 2 (and other colors) and statistical methods to determine prediction intervals and an estimate of the limit of detection. Using data from this article, the present paper expands on these uses of statistics. Described are the various confidence interval estimates associated with a fitted straight line that use Student′s t statistic, the construction and use of a confidence region for the slope and intercept of the line using Snedecor′s F, the construction of the Working-Hotelling-Scheffé bounds for the true line, and limits appropriate to the repeated use of the fitted line. The inverse use of the fitted line (the calibration problem) is next discussed, and an interval estimate is constructed for the true amount of Red No. 2, given future HPLC readings. The statistical methods described are of general applicability and should be in wider use.