Probit Analysis

Excerpt

The idea of probit analysis was originally published in Science by Chester Ittner Bliss (1899–1979) in 1934. He was primarily concerned with finding an effective pesticide to control insects that fed on grape leaves. By plotting the response of the insects to various concentrations of pesticides, he could visually see that each pesticide affected the insects at different concentrations, but he did not have a statistical method to compare this difference. The most logical approach would be to fit a regression of the response versus the concentration or dose and compare between the different pesticides. The relationship of response to dose was sigmoid in nature and at that time regression was only used on linear data. Therefore, Bliss developed the idea of transforming the sigmoid dose–response curve to a straight line. When biological responses are plotted against their causal stimuli (or their logarithms) they often form a sigmoid curve. Sigmoid relationships can be linearized by transformations such as logit, probit, and angular. For most systems the probit (normal sigmoid) and logit (logistic sigmoid) give the most closely fitting result. Logistic methods are useful in epidemiology, but in biological assay work, probit analysis is preferred. David Finney, from the University of Edinburgh, took Bliss’ idea and wrote a book entitled Probit Analysis in 1947, and since this year it is still the preferred statistical method in understanding dose–response relationships. …