Maths, Stats and Think Traps – Bayesian Traps

Hi again! Today, I am writing about Bayesian traps which I have recently re-discovered in a video by Veritasium. This is part 2 of a 3 part post about mathematic and statistical oddities. If you haven’t seen the previous post about confirmation bias check it out here! OK, so let’s get into it. The example I remember about goes more or less like this:

You hear about this terrible disease going around that affects around 1:10000 people. This disease is lethal and asymptomatic so there is no easy way for you to know if you have it.

You decide to go to the doctor and she tells you there is a simple blood test you can take and the test is 99% accurate.

You decide to take the test and a week later the results come in. The test came out positive!

The question now is, should you start writing your will?

The short answer is No you have nothing to worry about (although some would argue that it is probably a good idea to write a will in any situation). The clue lies in the fact that as humans we have a hard time dealing with large numbers. Here is what 10.000 boxes (imagine they are people) look like: One of those people will be marked in Red. That is the person that actually has the disease. If you were to test all these people using the 99% accurate test then 1% of all those tests would have come out as False Positives (blue boxes): Which means that the probability of you having the disease knowing that you tested positive is the same as the probability of you being that red box on the space of all the blue and red boxes put together: In a nutshell, you have about 1% chance of having the disease!

I hope you liked this example, next time I will write about the Simpson’s Paradox which is probably the scariest of them all. See you there!

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