[robotresearcher]

Thanks for these refs. I read [1] carefully and I take your point that it’s ok to strictly report whatever the data says.

On the value itself, we are quibbling about the meaning of ‘arbitrary’: Fisher certainly could have chosen another value, but not all values would be considered useful. Some expertise about the nature of real world data and the minds of statisticians is encoded in the chosen value.

If I propose that we change the convention to use 1e-12 instead and you think ‘that’s too small, I prefer it the way it is’, then it’s not arbitrary in the sense I mean.

[kqr]

The thing you seem to be missing is that there's no one number that's a meaningful limit for all purposes.

What probability you accept as significant should depend entirely on how you plan to use the results. Something with a p value of a staggering 70 % (i.e. it's more likely not true than true) is significant if the payoff is good when it's true, and the cost is small when it's not true.

And 70 % is very far from 5 %!

Then again, if the payoff is tiny compared to the cost, you might ask for a p-value of less than 0.01 %, in order for it to make sense to take the chance on it.

Think like a poker player: a hand that has 1/4 chance of winning needs better than a 3-to-1 payout when it wins to be playable. Conversely, when the pot offers you a 3-to-1 payout, you better make sure your hand has more than a 1/4 chance of winning.

[robotresearcher]

I understand and agree with that. Pascal’s Wager is the extreme example: unlimited upside makes the likelihood irrelevant.