Therefore, assuming two separate groups of managers (e.g., strong and weak), the greater the differences in sample size and mean, the greater the costs of Type I and II errors.

So if dispersion go up, the cost goes up. Same direction.

The wider the dispersion of returns between strong and weak managers, the easier it is to distinguish between their relative skills. Therefore, it makes it less likely to have a Type I or II error which results in a lower expected cost of a Type I or II error.

Here, if dispersion go up (wider), the expected cost goes down?? Opposite direction. this contradicts the previous sentence?

`In an efficient market, the dispersion of return distributions between the two groups is probably smaller due to greater difficulty in achieving alpha through active management, which would lessen the costs of hiring or retaining weak managers (Type I error)`

If dispersion goes down, cost goes down, same direction.

Really confused about the correlation between dispersion of return and cost of errors in hiring managers.