I get lost in the argument with these simple coin flipping examples. The way it's presented is so confusing for the weird second case of how many trials it takes to get a tail.
In the first case, the probability of getting "five tails or more" from a fair coin is 11%, while in the second case, the probability of a fair coin requiring "at least five tails before seeing one heads" is 3%.
I didn't check the numbers here, but this seems perfectly reasonable to me in terms of hypothesis testing. He's playing on the fact that for cases like THXXXX you would get a result of 2 in the second experiment. You are taking the same results, but applying a different metric to them (position of first head versus count of tails). Of course p will be different.
I understand that the value chosen for significance of p is subjective, but the experiment itself makes perfect sense to me.
The problem is that the conditional probability of the coin being biased given the observation of TTTTTH absolutely does not and cannot depend one whether you intended to flip until you saw a heads, or were going to flip 6 times. Therefore you've got a subjective factor influencing your conclusion that probability theory says should not be a factor if you are reasoning consistently.
In the first case, the probability of getting "five tails or more" from a fair coin is 11%, while in the second case, the probability of a fair coin requiring "at least five tails before seeing one heads" is 3%.
I didn't check the numbers here, but this seems perfectly reasonable to me in terms of hypothesis testing. He's playing on the fact that for cases like THXXXX you would get a result of 2 in the second experiment. You are taking the same results, but applying a different metric to them (position of first head versus count of tails). Of course p will be different.
I understand that the value chosen for significance of p is subjective, but the experiment itself makes perfect sense to me.