The inseparable triad: analytical sensitivity, measurement uncertainty, and quantitative resolution

The formal definition of sensitivity associates the term with the change in the response of a system for a small change of the stimulus causing the response, i.e., the ratio of the response of a system to the stimulus causing it. One interpretation of sensitivity associates the rate of change of the response for a small change of the stimulus as the slope of a calibration plot of response vs stimulus. An alternative interpretation associates sensitivity with the smallest value of the stimulus that can be resolved with a given degree of confidence, i.e., the detection limit. Applications of the first usage to analytical chemistry date at least to the beginning of this century; applications of the second interpretation are of more recent origin. The accompanying paper argues in favor of the second interpretation on the basis that, among other things, the "slope" interpretation conflicts with the formal definition of sensitivity and is meaningless as a descriptor of the performance of a measuring system. In this paper I offer arguments to support my belief that the slope definition of sensitivity is consistent with both formal definitions and accepted usage in analytical chemistry and, more importantly, that it is an invaluable descriptor of one of the most important characteristics of any analytical method. I include information to support my belief that proper use of the slope definition yields much more information than is available in the "detection limit" interpretation.