Actually, it’s quite interesting what happens if you run trials until you reach significance. Turns out that if you want a fraction p of all trials you do to end up positive, but each trial only ends up positive with probability q<p, then with some positive probability (a function of p and q) you will have to keep going forever.
(This is a well-known result if p=1/2. Then you can think of the trials as a biased random walk on the number line, in which you go left with probability q<1/2 and right otherwise, and you want to return to the place you started. The probability that you’ll ever return to the origin is 2q, which is less than 1.)
Ah, but that’s not what it means to run until significance—in my interpretation in any case. A significant result would mean that you run until you have either p < 0.005 that your hypothesis is correct, or p < 0.005 that it’s incorrect. Doing the experiment in this way would actually validate it for “proof” in conventional Science.
Since he mentions “running until you’re bored”, his interpretation may be closer to yours though.
Actually, it’s quite interesting what happens if you run trials until you reach significance. Turns out that if you want a fraction p of all trials you do to end up positive, but each trial only ends up positive with probability q<p, then with some positive probability (a function of p and q) you will have to keep going forever.
(This is a well-known result if p=1/2. Then you can think of the trials as a biased random walk on the number line, in which you go left with probability q<1/2 and right otherwise, and you want to return to the place you started. The probability that you’ll ever return to the origin is 2q, which is less than 1.)
Ah, but that’s not what it means to run until significance—in my interpretation in any case. A significant result would mean that you run until you have either p < 0.005 that your hypothesis is correct, or p < 0.005 that it’s incorrect. Doing the experiment in this way would actually validate it for “proof” in conventional Science.
Since he mentions “running until you’re bored”, his interpretation may be closer to yours though.