Combining examination marks

Abstract

In n set of examinations it is often the rase thnt not every c*antlitlnte takes every pnpcr nntl yct a single overall insrk must be itssigned to each of the cnntliclntes. Some methods for tackling the problem of producing such rnnrlts, nntl difficulties they mny lead to, nre cliscussetl. A fitirly general frsmework into which many particular proposals can be fittccl is tlesrribccl.

Scaling and combining examination marks

“…Viewed in this way, the two problems (obtaining overall marks and transforming the marks on papers to make them comparable) are seen to be very closely linked. The reader is referred to Biggins et al (1986) and papers cited therein for more discussion of these issues.…”

“…Slight refinements of Broyden's approach, but still within the context of multiplicative adjustment, are discussed by Colwell & Gillett (1985) and Wilson (1986). All these papers can be considered as taking a loss function approach to the problem, falling within the general framework given in Biggins et al (1986), though the only case considered in detail there was multiplicative adjustment; here the same basic approach is applied to a different class of transformations. We use the commonest loss function, the 'error' sum of squares, so our approach is in the least squares tradition.…”

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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 examination. Their approach is to obtain the transformations and the overall marks by the minimization of a suitably chosen loss function subject to a single constraint.

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