A Likelihood Approach to Scaling Examination Marks

Abstract

Summary One of the common approaches to the problem of scaling and combining examination marks has its roots in the least squares tradition. In this framework, examiners' preconceptions about the transformations must be dealt with in an ad hoc way. This paper investigates another, likelihood‐based, approach which allows preconceptions to be handled by standard Bayesian techniques. The likelihood and least squares approaches are not directly parallel (essentially because a Jacobian must be included in the likelihood). Nonetheless, the device of introducing fictitious candidates to deal with prior beliefs in the least squares set‐up can be understood in a Bayesian sense.