Converting raw scores to numerical grade equivalents: a data modelling study

Mclachlan, John Charles orcid iconORCID: 0000-0001-5493-2645, Davies, Rhian and Sawdon, Marina (2023) Converting raw scores to numerical grade equivalents: a data modelling study. BMC Medical Education . (Submitted)

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Selected response items in assessments generate score outcomes which are not in themselves scaled to a grade equivalent. The commonly used scaling algorithm results in loss of information to students and may lead to inaccuracies in aggregating multiple assessments. Scaling to a pass mark alone does not take into account the impact on other grade boundaries, such as a “Merit” grade.


Working with score distributions from idealised medical student exams, we explored several methods for scaling raw scores to numerical grade equivalents. We aimed to devise methods which (a) offered the possibility of converting to both a cut score for “Pass” and one for “Merit” or “Distinction”; (b) reduced information loss. For ease of use and accessibility Excel spreadsheets were used for all calculations.


Variants of the commonly employed algorithm were devised which (a) allow for use of a cut score for a “Distinction” or “Merit” grade, and (b) minimise the loss of information between raw and scaled scores, potentially reducing student concerns over the discrepancy between raw and scaled scores and giving them more accurate information on their performance against the exam.


Scaling so as to reduce information loss to students is likely to prove both beneficial and popular. Permitting the use of more than one cut score will improve the accuracy of outcomes, particularly for distinction decisions. Excel spreadsheets for each algorithm are available from the authors.

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