We all expect GCSE, AS- and A-level exams to be marked correctly, and for the number of marking errors to be low.

The number of grades with underlying marking errors, expressed as a percentage of the total number of grades awarded, is therefore an important metric of the quality of marking.

What is this percentage? Unfortunately, Ofqual’s statistics don’t tell us.

What they do tell us, however, is that, for the summer 2025 exams, the number of exam components for which a review of marking discovered a marking error was 198,880 - 38.8 per cent of the 513,045 components reviewed.

Can we trust the quality of exam marking?

Importantly, these numbers refer not to grades but to components, such as an individual paper in a two-paper exam.

Any one grade is determined by the sum of the marks given to each of multiple components, any or all of which can be reviewed.

Since any or all of the reviewed components may or may not contain marking errors, it is by no means obvious how to infer the number of challenged grades that had marking errors from the corresponding number of components.

That said, it must be the case that no more than 198,880 challenged grades had marking errors - that’s 65.9 per cent of the 301,980 grades challenged - for it is impossible for there to be more erroneous grades than erroneous components.

Furthermore, the number of challenged grades with underlying marking errors cannot be fewer than the number of grades changed, which was 72,875 (58,725 GCSE grades and 14,150 AS and A grades), which is 24.1 per cent of grades challenged, as rules for challenges mean that a grade can be changed only if a marking error is discovered and corrected.

For this minimum number of challenged grades with marking errors to be the reality, though, all of the 198,880 erroneous components would need to be within the 72,875 grades changed, at an average of 2.73 erroneous components per grade, which is, in principle, possible - albeit, to my mind, unlikely.

The percentage of challenged grades that contain marking errors is, therefore, not less than 24.1 per cent, nor more than 65.9 per cent.

Statistically significant insights

Those percentages, however, refer only to the 4.6 per cent of grades that were challenged. What about the 95.4 per cent that weren’t?

One way to get the full picture would be to review all 6,526,780 awarded grades, and the corresponding 17,523,265 components. Which would be a lot of work.

A more sensible way is to study a statistically representative sample, and then extrapolate to the whole population.

And we have a sample. The 4.6 per cent sample of challenged grades.

Is this statistically representative as regards measurements of marking errors?

At first sight, perhaps not, for we know that the sample of challenges is biased in three respects:

• Challengers must be willing to forfeit the fee.
• Challenges are clustered just below grade boundaries, in the hope of an upgrade.
• Challengers have access to marked scripts, so perhaps this pre-selects challenges of components more likely to have marking errors.

Since no examiner knows the identity, let alone the wealth, of the student whose script is being marked, whether or not there is a marking error cannot correlate with the willingness, or otherwise, of a challenger to pay the fee.

Willingness to pay the fee certainly raises the issue of bias with regard to access to challenges, but it can have no bearing on the number of marking errors discovered.

Furthermore, all marking is done - and marking errors happen - before the grade boundaries are set, and no examiner has any knowledge of where any grade boundaries might be.

There is, therefore, no reason why marking errors should be more, or less, numerous just below grade boundaries.

As regards the third point, Ofqual’s statistics show that 61.2 per cent of reviewed components are proven to be error-free, so any pre-selection, if present, has only a marginal effect.

It seems to me that, as regards measuring the incidence of marking errors, perhaps the sample of challenged grades might be more statistically representative than might have been thought.

What’s the truth?

In which case, the inference that between 24 per cent and 66 per cent of awarded grades might have underlying marking errors is alarming indeed.

My analysis, however, might be wrong. If it is, I invite those who know the answer to tell us.

Dennis Sherwood is the author of Missing the Mark: why so many school exam grades are wrong, and how to get results we can trust

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