Here's another installment of rationality quotes. The usual rules apply:
- Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
- No more than 5 quotes per person per monthly thread, please.
My intended correct answer is that, on this data, you technically can adjust your belief very slightly; but because the prior for a biased coin is so tiny, the update is not worth doing. The calculation cost way exceeds any benefit you can get from gruel this thin. I would say "Null hypothesis [ie unbiased coin] not disconfirmed; move along, nothing to see here". And if you had a political reason for wishing the coin to be biased towards heads, then you should definitely not make any such update; because you certainly wouldn't have done so, if tails had come up six times. In that case it would immediately have been "P-level is in the double digits" and "no statistical significance means exactly that" and "with those errors we're still consistent with a heads bias".
I would think that our prior for "health care improves health" should be quite a bit larger than the prior for a coin to be biased.