SCALING AND COMBINING EXAMINATION MARKS

Biggins, Loynes & Walker (1986) considered the problem of scaling and combining examination marks from several papers to obtain transformed marks and an overall measure of each candidate's performance in the ex amination. Their approach is to obtain the transformations and the ove rall marks by the minimization of a suitably chosen loss function subj ect to a single constraint. In the main, following Broyden (1983), the y consider the case where the allowed transformation is multiplication by a constant (which varies from paper to paper). This paper discusse s the same problem but with a richer class of possible transformations , the main example being regression splines with end-point restriction s. These end-point restrictions will mean that the curve can be forced to preserve the mark range, by passing through (0,0) and (100,100), f or example. If grades rather than marks are returned the problem becom es the well-studied one of scaling categorical attributes. Our formula tion applies in this case also, allowing us to connect the proposals w ith existing scaling literature. The general issue of how to incorpora te the expectation that transformation curves should not be too far fr om the 45-degrees line is also addressed, with the device of using fic titious candidates, introduced by Biggins et al. (1986), being extende d to this context.