I'm attempting to assess the relationship between two quantitative variables, but the DV is highly skewed (and so are the residuals). I work among biologists who tend to favor non-parametric techniques (e.g., Mann Whitney, Kruskal Wallis). In one part of the paper, a Mann Whitney is used to assess group differences. Although I generally do the Box-Cox when doing simple (or multiple) regression, for continuity I decided to rank transform the DV. Alas, it was all noise (i.e., small effect sizes and non-significant p-values). Out of curiosity, I decided to use a Box-Cox transformation. With that, the p-values became significant and the effect sizes increased.
So, with that background, a couple of questions:
Am I to interpret the discrepancy as due to random fluctuations (i.e., the Box-Cox is committing a Type I error)?
Am I to interpret the rank transformation as more conservative? (i.e., the rank transformation is committing a type II error).
(Related to #1 and #2) Does one transformation tend to be more conservative than the other? Or does it depend on the dataset?