In statistical computations, intuition can be very misleading

Guess Again

Article from Issue 178/2015
Author(s):

Even hardened scientists can make mistakes when interpreting statistics. Mathematical experiments can give you the right ideas to prevent this from happening, and quick simulations in Perl nicely illustrate and support the learning process.

If you hand somebody a die in a game of Ludo [1], and they throw a one on each of their first three turns, they are likely to become suspicious and check the sides of the die. That's just relying on intuition – but when can you scientifically demonstrate that the dice are loaded (Figure 1)? After five throws that all come up as ones? After ten throws?

Figure 1: These dice, purchased in Las Vegas, always come up with winning combinations.

Each experiment with dice is a game of probabilities. What exactly happens is a product of chance. It is not so much the results of a single throw that are relevant, but the tendency. A player could throw a one, three times in succession from pure bad luck. Although the odds are pretty low, it still happens, and you would be ill advised to jump to conclusions about the dice based on such a small number of attempts.

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