However, the bottom line is that you can't have it both ways: If you try to exclude a false negative, you allow a chance of false positives, and vice versa.
Again, this is incorrect. False positives and false negatives are not complementary. Reducing the chance of a false negative
does not necessarily increase the chance of a false positive.
The chance of a false positive is the alpha level, which can be set independently of any other parameter and is simply a matter of choosing a number.
The chance of a false negative is the beta level, and it is
not a single number which is independently chosen, but rather the result of the alpha level, the effect size (which is independent of alpha and of sample size), and the sample size. Increasing the power by changing the effect size or the sample size
has no influence on the chance of a false positive (i.e. the alpha level).
And, of course, the JREF must opt to exclude a false positive, which means that there is some chance of a false negative.
This is the part that I really, really wish would stop getting passed around as though it is true. The JREF can both exclude false positives
and exclude false negatives. The two are independent, not complementary. The JREF can be fair, if it chooses.
- And this is exactly the reason a claimant is asked to predict her performance, and required to stick to that prediction.
Hans
It is my impression that the claimant is asked to predict their performance only so that the JREF can exclude false positives. I don't think I've ever heard mention of the false negative level from the JREF. I'm willing to give them the benefit of the doubt and consider that this is done purely through ignorance. And even though I've mentioned it numerous times now, including within threads that Alison has at times participated in, I wouldn't assume that they've seen it from me. But I have to wonder why the statisticians that they claim they've consulted haven't mentioned it to them. The other option is that they've chosen to be unfair. Which, like I said,
I find disappointing, but I realize others do not.
Linda