Wow, that sounds good...Wait a minute!

This article talks about framing in statistics.

Here's how it works.

Imagine 1,000 people worried about contracting a smelly disease called Statisticitisis. If they all take a new wonder-pill, their risk is cut by 50%. Sound good?

Meanwhile, one in 1,000 suffer side effects. Trifling, a risk worth taking for such benefit, surely?

Here's the scam. 1 in 1,000 turns out to be the same as 50%. You are as likely to suffer side effects as to be protected from the illness.

How can 1 in 1,000 be the same as 50%? Because only two people out of 1,000 ever have the illness. Cut that by 50% and only one of them has the illness. So one person in 1,000 is protected. But we also know that one person in 1,000 suffers side effects.

One number is a relative risk reduction expressed as a percentage - 50% - and sounds impressive. The other is an absolute number of people - 1 in 1,000 - and sounds like not much to worry about. In fact, they represent the same number of people. That's mixed framing.