As long as the reputation doctor had committed to publishing the results regardless of what he found, then, yes, the data has equal evidential weight.
However, the story seems to imply he would have continued testing indefinitely until he got it right, and if he didn’t, he would have faded into obscurity.
The issue here is that we must SEE the data in the possible world where he has a 58% cure rate with N=1000 (kept trying, kept trying, kept trying, eventually published), if we are to accept his 70⁄100 results in this world.
If, on the other hand, we would only see the 70⁄100, but wouldn’t have seen the 580/1000, then the 70⁄100 does not carry the same weight as the other doctor’s 70⁄100.
Imagine a world where the true success rate is 58%. We have 1000 biased researchers all doing the experiment and not publishing when they get 580/1000. The few who get lucky and get a 70⁄100 publish, leading to the 70%+ success rate results being very over-represented in the data we see.
As long as the reputation doctor had committed to publishing the results regardless of what he found, then, yes, the data has equal evidential weight.
However, the story seems to imply he would have continued testing indefinitely until he got it right, and if he didn’t, he would have faded into obscurity.
The issue here is that we must SEE the data in the possible world where he has a 58% cure rate with N=1000 (kept trying, kept trying, kept trying, eventually published), if we are to accept his 70⁄100 results in this world.
If, on the other hand, we would only see the 70⁄100, but wouldn’t have seen the 580/1000, then the 70⁄100 does not carry the same weight as the other doctor’s 70⁄100.
Imagine a world where the true success rate is 58%. We have 1000 biased researchers all doing the experiment and not publishing when they get 580/1000. The few who get lucky and get a 70⁄100 publish, leading to the 70%+ success rate results being very over-represented in the data we see.