If your experiment tells you that [x > 45] with 99% confidence, you may in certain cases be able to confidently transform that to [x > 60] with 95% confidence.
For example, if your experiment tells you that the mass of the Q particle is 1.5034(42) with 99% confidence, maybe you can say instead that it’s 1.50344(2) with 95% confidence.
If your experiment happens to tell you that [particle Q exists] is true with 99% confidence, what kind of transformation can you apply to get 95% confidence instead? Discard some of your evidence? Add noise into your sensor readings?
How does this work for a binary quantity?
If your experiment tells you that [x > 45] with 99% confidence, you may in certain cases be able to confidently transform that to [x > 60] with 95% confidence.
For example, if your experiment tells you that the mass of the Q particle is 1.5034(42) with 99% confidence, maybe you can say instead that it’s 1.50344(2) with 95% confidence.
If your experiment happens to tell you that [particle Q exists] is true with 99% confidence, what kind of transformation can you apply to get 95% confidence instead? Discard some of your evidence? Add noise into your sensor readings?
Roll dice before reporting the answer?
We’re not talking about a binary quantity.