When Statistics Go Bad

I watched this TED video which is basically a justification for the job of 'Statistician'. Peter Donnelly, also known as the British Hank Azaria, talks about how almost everyone improperly interprets statistics.

The example he uses to illustrate this failing is fascinating if your geek cred is over 600. For those of you still with me, follow closely.

A large number of people are given coins to toss. They are asked to find how many tosses it takes to see the pattern heads, tails, heads, or HTH. They dutifully toss the coins and the pattern occurs after the 11th toss. They do it again and they get it after the 4th toss etc. They do this a million times and then average the number of tosses necessary.

This same group of people, who obviously have a lot of time on their hands, perform the same experiment, but this time they look for the pattern heads, tails, tails, or HTT.

The question to you, dear reader, is which one of these statements is true:

A) The average number of tosses until HTH is larger than the average number of tosses until HTT.

B) The average number of tosses until HTH is the same as the average number of tosses until HTT.

C) The average number of tosses until HTH is smaller than the average number to tosses until HTT.

Think about it. Got your answer?



The vast majority of people, including myself, would say B is true. The actual answer is A. If you did get it right though, don't say anything because the rest of us don't like you.

The reason people get it wrong is because we assume the patterns are basically the same, which they are not. When trying to get the pattern HTH, the researchers get excited when they get an H, then more excited when they get an HT, and finally they either celebrate the HTH or despair at the HTT.

When researching the patter HTT, the experience is different. They get mildly excited at the H, then more excited with the HT, and finally they celebrate the HTT or they are mildly excited again with the H.

You see they either get the pattern they are after, or they are a third of the way into their next attempt. They only start from scratch at the first toss instead of every time the TT pattern emerges. It takes an average of 8 tosses to get HTT where it takes an average of 10 tosses to achieve HTH.

It's a fun exercise that you might dismiss. However Dr. Donnelly then goes on to give examples of how bad statistics presented in court have lead to innocent people being imprisoned. So be very careful when dealing with statistics because you don't know what kinds of assumptions are present.