GRAPHICAL ESTIMATION OF RELATIVE POTENCY FROM QUANTAL RESPONSES

¹ Design and Analysis of Scientific Experiment, University of Oxford, England

Litchfield and Wilcoxon have proposed a rapid graphical method for estimating relative potency, and assessing fiducial limits for the estimate, in biological assays based upon quantal responses. The method depends upon subjective judgement in the drawing of regression lines by eye. This paper reports an empirical investigation of its accuracy, as shown by analysis of 21 independent drawings of regression lines, by different persons, for one set of data. The results suggest that the method, though admirable for giving a rough indication of the fiducial limits of error in the assessment of relative potency from a graph, is often too inexact in its approximation to maximum likelihood (probit or other) methods to be trusted for refined scientific work. Individual variations in the placing of the lines were responsible for the wide variation in the estimate and the assessments of its limits; inaccuray in the reading of the nomographs appeared to be of relatively little importance. The 21 subjects lacked experience of bioassay and the data chosen for this study were not easy to fit by eye, so that the flaws in the graphical method may be somewhat exaggerated. Nevertheless the results clearly demonstrate the need for caution in adopting a method of analysis whose simplicity is an asset tending to distract attention from its shortcomings.