Investment manager selection

Vol 6 page 250 we have last paragraph explaining when the both the type 1 and 2 error are low:

  1. when the difference in sample size and distribution mean is small

I am not clear here -what do they mean by this?

My understanding is that the discussed population is the universe of managers, into two categories, skillful versus not (assuming correctly labeled). Sample size difference is small means that there are equally amount of skillful versus unskillful and sample mean difference is small means that the track record (returns under management) is also close.

As the more similar the mean of the two groups, to me, it sounds like hiring a professional/unprofessional has similar returns. Hence, the lower the cost for both types of errors Type I and Type II. On the other hand, if the difference is large, it means that hiring a unprofessional will have a huge relative performance deterioation and at the same time, not hiring your Bobby Axelrod will incur a huge opportunity cost.

I am not quite sure about the dispersion though…