THE CALCULATION OF THE DOSAGE‐MORTALITY CURVE

Abstract

Summary.: The sigmoid dosage‐mortality curve, secured so commonly in toxicity tests upon multicellular organisms, is interpreted as a cumulative normal frequency distribution of the variation among the individuals of a population in their susceptibility to a toxic agent, which susceptibility is inversely proportional to the logarithm of the dose applied. In support of this interpretation is the fact that when dosage is inferred from the observed mortality on the assumption that susceptibility is distributed normally, such inferred dosages, in terms of units called probits, give straight lines when plotted against the logarithm of their corresponding observed dosages. It is shown that this use of the logarithm of the dosage can be interpreted in terms either of the Weber‐Fechner law or of the amount of poison fixed by the tissues of the organism. How this transformation to a straight regression line facilitates the precise estimation of the dosage‐mortality relationship and its accuracy is considered in detail. Statistical methods are described for taking account of tests which result in 0 or 100 per cent, kill, for giving each determination a weight proportional to its reliability, for computing the position and slope of the transformed dosage‐mortality curve, for measuring the goodness of fit of the regression line to the observations by the X 2 test, and for calculating the error in position and in slope and their combined effect at any log. dosage. The terminology and procedures are consistent with those used by R. A. Fisher, who has contributed an appendix on the case of zero survivors. Except for a table of common logarithms, all the tables required to utilise the methods described are given either in the present paper or in Fisher's book. A numerical example selected from Strand's experiments upon Tribolium confusum with carbon disulphide has been worked out in detail.