This paper is concerned with the analysis of bioassays in which the characteristic reaction of the organism is essentially continuous, although owing to the difficulties of observation it can only be measured in terms of a quantal or semiquantal response. The effect of errors of measurement of both dosage and reaction on the observed quantal dosage-response relationship is examined and the corresponding "true" and "observed" relationships are compared. The estimation of the parameters of the underlying dosage-response relationship from the data of a semi-quantal response is then considered and the application of the proposed methods is illustrated by an example from the field of research into the causes of pneumoconiosis amongst coal miners.