21 May '04 22:09

A particular type of coin is suspected of being biased towards tails if you toss it. Assume that all coins are equally biased, if they're biased at all.

Experimenter A tests this by tossing one of these coins six times. His results are:

T,T,T,T,T,H

He decides this isn't enough evidence to conclude that the coin is biased.

Experimenter B tests a coin by tossing it until she gets a heads. The coin tosses are:

T,T,T,T,T,H

She concludes that the coin is probably biased.

Both tests were done at the same significance level (ie the strength of evidence needed to show bias), both experimenters tossed the coin the same way, and both of the experimenters' calculations were correct. So why are their conclusions different?

Experimenter A tests this by tossing one of these coins six times. His results are:

T,T,T,T,T,H

He decides this isn't enough evidence to conclude that the coin is biased.

Experimenter B tests a coin by tossing it until she gets a heads. The coin tosses are:

T,T,T,T,T,H

She concludes that the coin is probably biased.

Both tests were done at the same significance level (ie the strength of evidence needed to show bias), both experimenters tossed the coin the same way, and both of the experimenters' calculations were correct. So why are their conclusions different?