Scaling and combining examination marks
#
Scaling and combining examination marks

by J.D.Biggins and K.K. Yue

*Brit. J. Math. Statist. Psych*.
(1993) **46**, 153-179.

## Abstract

Biggins, Loynes and 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 minimisation
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^\circ $ line is also addressed, with the device of
using fictitious candidates, introduced by Biggins {\it et al.}\
(1986),
being extended to this context.

## Availability

postscript file
dvi file

See also the closely related paper

Other publications by J.D. Biggins
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