Statistical dojo

This seems apt – and the book it comes from is available free (or “pay what you want”) at


Imagine reaching into an urn that contains seventy white balls and thirty red ones, and plucking out ten mystery balls. Perhaps three of the ten balls will be red, and you’ll correctly guess how many red balls total were in the urn. Or perhaps you’ll happen to grab four red balls, or some other number. Then you’ll probably get the total number wrong.

This random error is the cost of incomplete knowledge, and as errors go, it’s not so bad. Your estimates won’t be incorrect on average, and the more you learn, the smaller your error will tend to be.

On the other hand, suppose that the white balls are heavier, and sink to the bottom of the urn. Then your sample may be unrepresentative in a consistent direction.

That sort of error is called “statistical bias.” When your method of learning about the world is biased, learning more may not help. Acquiring more data can even consistently worsen a biased prediction.

If you’re used to holding knowledge and inquiry in high esteem, this is a scary prospect. If we want to be sure that learning more will help us, rather than making us worse off than we were before, we need to discover and correct for biases in our data.

The idea of cognitive bias in psychology works in an analogous way. A cognitive bias is a systematic error in how we think, as opposed to a random error or one that’s merely caused by our ignorance. Whereas statistical bias skews a sample so that it less closely resembles a larger population, cognitive biases skew our beliefs so that they less accurately represent the facts, and they skew our decision-making so that it less reliably achieves our goals.

Maybe you have an optimism bias, and you find out that the red balls can be used to treat a rare tropical disease besetting your brother. You may then overestimate how many red balls the urn contains because you wish the balls were mostly red. Here, your sample isn’t what’s biased. You’re what’s biased.

Rob BensingerBiases: An Introduction to Eliezer Yudkowsky‘s Rationality: from AI to Zombies

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