Loose 10% level on 80 fair coins

Question

An analyst tests 80 coins for bias, using a relaxed 10% significance level ( $\alpha = 0.10$ ). Every coin is in fact perfectly fair.

About how many of these 80 fair coins will be declared "biased" by the test, and what does that number reveal about $\alpha$ ?

Accepted Answer

The calculation. Each coin is fair, so the null (no bias) is true every time. A fair coin is wrongly declared biased with probability equal to the significance level, 0.10. Over 80 coins you expect 80 	imes 0.10 = 8 false verdicts of "biased." What alpha means. At a loose 10% level, one in ten fair coins gets convicted of bias by chance alone. The looser the level, the more noise you let through. Alpha is simply the rate at which truly-null cases are wrongly rejected, chosen in advance as your acceptable false-alarm budget. The nuance. None of these 8 coins is actually biased. They are the p…

Loose 10% level on 80 fair coins

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