I previously replicated some simulations from a journal article by Ratcliff (1993) 1. These sims demonstrate that transformations such as taking inverse RTs typically improve power to detect RT differences across conditions. The problem is that the mean alone is a poor estimate of the central tendency of the underlying RT distribution, particularly in the presence of outliers - see the previous post for details.
Reaction times are a very common outcome measure in psychological science. Frequently, people use the mean to summarise reaction time distributions and compares means across conditions using ANOVAs. For example, in a typical experiment, researchers might record reaction times to familiar and unfamiliar faces, and look for differences in mean reaction time across these two types of stimuli. An issue with this is that reaction time distributions are skewed: there are many more short values than long values, so their distribution has a long right tail.