A Simple Definition of Detection Limit

The detection limit of an analytical method tells how low a concentration can be said to be measured. Users, laboratories, and equipment manufacturers prefer low ones. Industries under environmental regulation insist on honest ones. However, the detection limits of environmental regulations generally refer to relatively complex detection experiments (assays) or surveys that differ from the simple measurement operation that gave rise to the detection limit concept in analytical chemistry. The first contribution of this article is to clarify the limited scope of the simple definition and then define the population quantity that is being estimated. Such specificity allows alternative estimates to be evaluated more on statistical grounds of bias and variance rather than on whether they push the resulting value up or down. The fundamental statistical problem is to fit a variance function so that the derived relative standard deviation (RSD) function of concentration is smooth and monotone decreasing and thus can be inverted. The solution is to accept the best-fitting analytical version of the RSD function (log-log and hybrid models are described), fit it, invert it to get the point estimate, and provide a jackknife standard error.