# How to report exam pass percentage increases

When the GCSE and A-level results came out back in August, I got to thinking about how increases in percentages should be measured. There was the usual mathematical heathenry, with people talking of percentage increases when they meant percentage point increases. But that’s another story.

Even when percentage points are reported responsibly, they’re open to misinterpretation. Not all five point increases are as easy to achieve. If 25% of grades are an A, then it’s arguably easier to achieve a five point increase than if your current percentage is 90%.

And even percentage increases can be confusing. A 20% increase on the 25% takes you to 25%. But a 20% increase is not possible on the 90%.

Maybe comparisons would be best achieved if increases were reported as the percentage of fails that are now successes, or in other words, penetration into the failures. So an increase from 20% passes to 25% would be reported as 6.25% penetration into the fails, as would an increase from 90% to 90.625%. Arguably, each is equally difficult to achieve.

Or else, maybe it should be reported as the percentage penetration into the failures, divided by the prior pass rate. So 20% to 25% would be reported as a 31.25% weighted penetration (stop it), as would an increase from 90% to 92.8%. This latter coefficient takes into account the difficulty of getting people to pass. At 90%, it’s arguably easier to convert the failures than if the pass rate was at 20%.

Although while mathematically these quotients might be a better representation of the truth, explaining them to the masses might be tricky.

This is what I think about of a Friday night.