The Guardian’s Corrections and Clarifications column yesterday picked up on a distinction which — much to my shame — I have never made:

In a report headed Tories still in decline, warn modernisers, page 8, July 21, we spoke of a decline in support for the Conservative party among women from 45% in 1992 to 32% in 2005 as a fall of 13%. In fact it fell by 13 percentage points, a fall equivalent to 29%. In relation to support among other groups, we similarly confused percent with percentage points. We often do.

It took me a moment to get that.

To explain further: percent is relative, percentage points are absolute.

13% is approximately one eighth of whatever you’re talking about. That’s about an eighth of whatever you’re talking about. So 13% of 45 oranges is about an eighth of 45 oranges, which is about 6 oranges. So a 13% reduction from 45 oranges is a reduction of about 6 oranges which gives you 39 oranges. Similary a 13% fall from 45% is 39%.

But 13 percentage points are 13 percentage points, whatever you’re talking about. You can’t take 45 oranges and remove 13 percentage points any more than you can take 45 oranges and remove 13 orangutans.

However you can take 45 percentage points (which was the Conservatives’ support among women in 1992) and remove 13 of them. That gives you 32 percentage points, which is the Conservatives’ support among women in 2005.

As a proportion, 13 is 29% of 45. Which is why a 29% drop from 45 percentage points support reduces it by 13 percentage points, giving the 32 percentage points support.

I shall endeavour to use these words more carefully in future.

Tags: words, percent, percentagepoints, maths