## Testing times

### August 4, 2009

The rather worrying story that a quarter of 11-year-olds in England have failed to reach the expected standard in English and maths has been widely reported (Guardian here, for example) [link opens new window].

But when it comes to reporting the story, it is embarrassing to note that a common maths error has crept in, concerning the difference between a percentage increase and an increase in percentage points. My example is from the Liverpool Echo [new window] but as it’s agency copy, I’ve no doubt the story and its error are pretty widespread (although The Guardian’s report by Jessica Shepherd [new window] avoids the trap).

Let’s look at the offending sentence: “The proportion of 11-year-olds reaching Level 4 in English fell by 1% this year”. The Guardian puts it thus: “In English, 20% of boys and girls did not achieve the required standard. This is a drop of one percentage point on last year.”

The Echo’s agency copy says it is a drop of “1%” while the Guardian correctly describes it as a drop of “one percentage point”. So what’s the difference? Well, let’s take a closer look.

A quick check on the Department for Children, School and Families website gives link to the spreadsheet here [nw]. This tells us that in 2008, 596,000 children were eligible for the English Sats test in 2008, with 577,000 eligible this year (the figure for 2009 is provisional, but no matter).

Now – and here is the key point – the proportion (expressed as a percentage) who passed fell from 81% to 80% – and that is a fall of 1.2% (the difference between 81 and 80, divided by 81 and multiplied by 100), not 1%. But it is a fall of precisely one percentage point (the difference between 81 and 80).

(Note that we can’t reasonably talk about the percentage change in the number of children who passed, which comes to 4.4% (since 81% of eligible pupils passed in 2008, that’s 482,760 who made the grade. This year, only 80% passed, and that’s 461,600 pupils, a difference of 21,160). The reason this isn’t reasonable is that number of children – the base – changes between years, and a big percentage decrease may only reflect the fact that fewer children took the test this year).

OK, so in this instance the effect of confusing percentage change with percentage point change isn’t huge – but it can be highly significant. Here is a different example – let’s say interest rates are 0.5% and climb to 1%. That means interest rates went up by half a percentage point, but by 100 percent (since they doubled).

So a small enough mistake in the Echo story – but still ironic in a story about numeracy.