A note on combining marks from several examination papers

Charlton, Patricia

doi:10.1080/0020739790100202

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…The idea outlined above, that the transformation of the paper marks can be based on the assumption that candidates tend to perform similarly in all papers attempted, has been used quite frequently. Murgatroyd (1975Murgatroyd ( , 1979 and Charlton (1979) considered additive adjustments, in the sense that each examination mark is increased (or decreased) by a certain fixed amount depending on the paper, whilst Broyden (1983) proposed multiplicative adjustment. Slight refinements of Broyden's approach, but still within the context of multiplicative adjustment, are discussed by Colwell & Gillett (1985) and Wilson (1986).…”

Section: 2 Relevant Literaturementioning

confidence: 99%

Scaling and combining examination marks

Biggins

Yue

1993

Brit J Math & Statis

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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. In the main, following Broyden (1983), they consider the case where the allowed transformation is multiplication by a constant (which varies from paper to paper). This paper discusses the same problem but with a richer class of possible transformations, the main example being regression splines with end‐point restrictions. 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), for example. If grades rather than marks are returned the problem becomes the well‐studied one of scaling categorical attributes. Our formulation applies in this case also, allowing us to connect the proposals with existing scaling literature. The general issue of how to incorporate the expectation that transformation curves should not be too far from the 45° line is also addressed, with the device of using fictitious candidates, introduced by Biggins et al. (1986), being extended to this context.

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Section: 2 Relevant Literaturementioning

confidence: 99%

Scaling and combining examination marks

Biggins

Yue

1993

Brit J Math & Statis

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“…I n focusing on multiplicative adjustment factors we differ from Murgatroyd (1975) who mainly considers additive adjustments. Murgatroyd's proposal can also be considered in terms of minimizing an overall loss as has been pointed out by Murgatroyd himself (1979) and Charlton (1979). In a n unpublished 1084 paper, Laurence (personal communication) takes Murgatroyd's proposal somewhat further by allowing some account to be taken of candidate-paper interaction.…”

Section: Introductionmentioning

confidence: 99%