ABSTRACT
This chapter begins with a review of non-parametric procedures. It considers robust parametric and non-parametric procedures, and describes their efficiency. The chapter concludes with a review of a number of alternative distribution-free procedures. Today access to computers makes the fitting of simple models, such as the logit or probit, to ‘well-behaved’ data a formality. Nevertheless, modern developments in the areas of robustness and influence have resulted in a re-examination of the relative merits of parametric and non-parametric procedures. An alternative method for fitting the standard logit model to quantal assay data has been provided by Cobb and Church. Based on Spearman–Karber type estimators, the method is shown to possess good small sample properties, subject to the equations for the parameter estimates having a solution. As Glasbey points out, the methods of his paper have application also to estimating relative potency, and also in experimental design. Schmoyer's sigmoidal constraint approach was originally presented as potentially useful for low-dose extrapolation.
