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, Kruskall Wallace). In one part of the paper, a Mann Whitney is used to assess group differences. Although I generally do the boxcox 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 boxcox transformation. With that, the p-values became significant and the effect sizes increased.

So, with that background, a couple of questions:

1. Am I to interpret the discrepancy as due to random fluctuations (i.e., the boxcox is committing a Type I error)?

2. Am I to interpret the rank transformation as more conservative? (i.e., the rank transformation is committing a type II error). 

3. (Related to #1 and #2) Does one transformation tend to be more conservative than the other? Or does it depend on the dataset?

Thanks!