Statistical power of KH and SH tests?

[Peter Werner]

I was wondering if anybody could point me to literature that would
explain how to estimate beta (the probability of making a Type II
error) for a given Kishino-Hasegawa or Shimodaira-Hasegawa test. I'm
wondering about cases where one of these tests results in a p-value of
greater than 0.05 resulting in the acceptance of the null hypothesis
that two trees are not significantly different - I want to know the
probability that in that case I may be failing to reject a false null
hypothesis.

BTW, I'm aware of the paper by Goldman, et al (2000) pointing out the
problems of using a KH test to compare a tree derived through maximum
likelihood with an alternate tree. I'm using it in an exploratory way
and would only use an SH test or the more computationally difficult
SOWH test for reporting of any such tree comparisons.

Peter Werner
Graduate Student, Mycology
San Francisco State University