# An Introduction to Survivor Bias: Statistics in the Real World

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Here is an interesting fact: did you know that most castles built during the middle ages were made from wood? It's a true fact! But you're probably thinking: wait, if most castles were made of wood, how come when you google the word "castle," all you see are stone edifices?

The answer is: survivor bias! Think about it: you build a wood castle, and over the years, what's the thing that threatens it most? FIRE! So all those wood castles burnt to the ground over the last thousand years, while the stone ones stuck around, and were renovated and now allow bazillions of visitors to walk their halls, as well as be the backdrops for lots of movies about witches and wizards. This is an excellent example of something called "survivor bias."

This is an activity that explains the statistical concept of "survivor bias," where a piece of seemingly obvious data leads to the incorrect conclusion. In this case, the story is about a principal who is investigating what snack the students at her school prefer more, apples or oranges? She asks the kitchen to tell her how many apples and oranges are sent back uneaten. From looking at the data, it seems clear that students prefer apples to oranges, and she decides to serve apples more often.

But the custodian at the school notices something different. When he goes through the compost bin each day, he notices that lots of apples are left uneaten, with less than half the apple actually eaten. So while the students are taking more apples, they are only eating part of them. In contrast, there are very few uneaten orange parts left over.

This is an example of what statisticians call "survivor bias," and it has to do with the fact that when we look at data, we are sometimes missing important pieces to help us fill in the entire picture. The reality is that the principle is only counting the fruit that came back to the kitchen uneaten. What she really should have been looking back was the fruit that was only partially eaten and made a decision from that (like serving smaller apples, or having them cut up in the kitchen.)

I've included a detailed description of "survivor bias" and how it applies to standardized testing, improving combat planes, scientific research and why you should not use "hot tips" to bet on the outcome of a football game.

This one of a series of activities inspired by ideas developed in Jordan Ellenberg's book "How Not To Be Wrong: The Power of Mathematical Thinking."

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