Happy bodmas everyone!

1 04 2015

In our last journal club, we limbered up for our next ‘Cognitive Illusions‘ chapter (which is on Bayesian inference and quite intimidating). We needed something easier to get us going, and Andrea found a great undergraduate essay online. Now ordinarily, anything with sections like this…

Screen Shot 2015-03-31 at 8.32.13 PM… would have me running a mile, but this essay proved the perfect introduction: well-written and interesting. With the help of the whiteboard we managed to follow the derivation of Bayes’ Theorem, which had all the Canadians shouting ‘bedmas! bedmas!‘. Puzzling at first, but of course they meant ‘bodmas‘ (how I learnt the algebraic ‘order of operations’ at school in the UK, and something I’ve not thought about for at least 25 years).


It gradually linked up with understanding the roles of false positives and false negatives, and we started remembering that we already knew a bit about base rate fallacies (something we’d covered from the Fallacy Files that I think I never wrote up).

So. when it came to the example below, although most of us would still have got it wrong, we could totally see why and how the right answer was obtained.

Get this:  A particular disorder has a base rate occurrence of 1/1000 people. A test to detect this disease has a false positive rate of 5%– that is, 5% of the time that it says a person has the disease, it is mistaken. Assume that the false negative rate is 0%– the test correctly diagnoses every person who does have the disease. What is the chance that a randomly selected person with a positive result actually has the disease?

Seems like 95%?  (that’s most most Harvard medical students think, if you thought that too). But no, it’s 2%!!! (To see why, read the essay)