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I have a problem with the idea behind this - there's no proof that the coin is biased; even flipping it a hundred times and getting the same result is possible

I have a problem with the idea behind this - there's no proof that the coin is biased; even flipping it a hundred times and getting the same result is possible with an unbiased coin. All that statistics gives you is the probability of having a result at least this extreme with an unbiased coin. If this probability is low enough (often 1 in 20 or 1 in 100, but sometimes as low as 1 in 5), the "hypothesis" of the coin being unbiased is rejected, but this rejection will happen erroneously 1 in 20 or 100 or 5 times. As exemplified by the XKCD cartoon: http://xkcd.com/882/ http://xkcd.com/882/

defen 15y ago
> All that statistics gives you is the probability of having a result at least this extreme with an unbiased coin. If you subscribe to frequentist statistics and use the null hypothesis of "coin is not biased", yes. But if you're a Bayesian you can compute the probability that the coin bias is greater than a given amount.
- thelema314 15y ago
  Granted. But in either case, there's no proof - only a probability that you haven't reached an incorrect conclusion. I associate the concept of proof with logical certainty, and no statistical method will give you that.