Saturday, August 4, 2012

An abundance of silver

Statistics can be a really useful way to get a feel for when a "strange event" may just be coincidence, and when it is likely to be something more.

For example, sports fans may have noticed that our gold medal tally is less than stellar so far. Another thing that becomes clear when looking at our medal tally (as of 4th August, 9pm) is that though we have a dearth of gold, we have managed to get quite a lot of silver medals! As it stands, we have 16 medals: 1 gold, 10 silver, and 5 bronze. A curious person might wonder whether there's a reason for that - is it just random chance that it happened that way, or is it something else - maybe our Olympians are psyching themselves up too much and falling at the last hurdle to winning gold?

As it happens, there is a way to get an idea of this using statistics! According to legend, in the 1920s a statistician called Fisher wanted to test his friend's boast that she could always tell whether the milk or tea was added to first to the cup. He tested her boast by giving her 8 cups of tea - four with the milk added first, and four with tea. She got every one of these right and Fisher - using a test known to this day as Fisher's exact test - calculated that if she had guessed, she would have had a less than 1 in 70 chance of getting all 8 correct.

We can use Fisher's exact test to work out the probability of getting 10 or more silver medals if there's an equal chance of getting gold, silver, or bronze and we get 16 medals overall. It turns out there are 153 different combinations, and 28 of those involve 10 or more silver medals. Most of these are incredibly unlikely to occur by chance, with the most likely being 3 gold, 10 silver and 3 bronze - this has an 0.4% chance of happening at random!

All together, the chance of getting at least 10 silver medals at random is 1.6%, or about 1 in 60 - almost as unlikely as the lady having a lucky break with her tea drinking! Most scientific literature counts a value of less than 5% as "statistically significant" - meaning that the result is unlikely to have occurred by chance. Of course, this kind of analysis doesn't tell us why it's happening this way, and unfortunately it sheds even less light on how to fix it...


  1. He he, you could also talk about regression to the mean. With a record of golds like ours, this lack of golds was bound to happen eventually and is nothing significant really?

  2. Conversely, you could argue that it's even more significant because our expected performance (the null hypothesis) is actually better than random (i.e. more gold) in terms of medals! We could generate a more suitable null by looking at historical medal tallies...but that sounds like work :-P