Wednesday, 21 July 2010

The Certainty of Chance

I was struck with an interesting thought I heard on the radio the other day: if you want to be lifted from poverty then it is a good idea to play the lottery.

What might be a morally corrupt statement is mathematically sound because if you don't play the lottery then you have no chance of winning it. For those of you interested in a little bit of further reading (which I'm sure you all are) then take a look at the excellent article here.

I've always been facinated by chance. Here is a true story I use in my teaching... which by chance is very similar to a scenario Derren Brown describes in his book Tricks of the Mind.

When my youngest son was born I was approached by the paediatrician asking if they could take a blood sample because they had performed a test and it seemed he might have Thalassemia. This is a disease that effects 0.1% of the population and the test is approximately 90% accurate. His test had come back positive and they wanted to retest.

The question: should I be worried?

Well... assuming that 0.1% of 60,000,000 people have the condition then that's 6,000,000 people. If they were all tested then 90% of 6,000,000 people would get a positive result. That's 5,400,000 definite positives.

However, 10% of 54,000,000 people would also get a positive result (albeit a false positive) - so that's 5,400,000 people who definitely don't have the condition but are told they have.

So in fact there is a roughly 50/50 chance of my son having the disease.

Odd, isn't it?


There is a postscript (as there tends to be with my teaching). When he was older we finally got access to his medical records when it transpires that my young son was actually being used as a control for a piece of medical equipment that the lab technicians were worried might be giving false positives.

Statistically-speaking, was this a sensible test for the hospital to carry out?

What do you think?

No comments:

Post a Comment