SUMMARY The fact that diagnostic measurements are often subject to error, with the extent of the imprecision varying from case to case, is largely ignored in current methodology of statistical diagnosis. Models taking full account of such imprecision are proposed and the necessary methods developed. In particular, a useful combination of a cumulative-normal diagnostic model with a normal error model is studied. Applications to two specific medical diagnostic problems illustrate the differing extents of the misrepresentation that may be involved in the use of techniques that ignore imprecision.