What's the Denominator

When you want to try to fiddle people with statistics, to make yourself look better, one thing you can do is to try to change the denominator in your equation. (The denominator is the underneath number of a fraction, so if we say 3/4, the numerator is 3, the denominator is 4).

There was a story in today's Guardian that gives a nice example of this. The story was about ticket touting, and whether Ebay is used by touts. Here's the quote:

Ebay disputes that large-scale ticket touting takes place on its site, citing research by ICM last year that showed nine out of 10 eBay sellers who had listed tickets in the previous 12 months had listed less than five.

(We'll ignore the fact that they should have said 'fewer than', not less than.)

They are using sellers as the denominator, but that's not the right one. The appropriate denominator is tickets. Let's imagine that we had 10 sellers. 9 of those 10 sellers sold 4 tickets (making 36 tickets). The tenth seller sold 964 tickets. This matches what Ebay said, but it's not relevant. What is relevant is that 96.4% of tickets are sold by people who sell more than 500 per year. That looks like a problem.

It isn't necessarily the case that this is true - but it's not ruled out by what they say. Lies, damn lies and statistics may be true - but the lies aren't very hard to see through.