Ok so I'm trying to compare the means of two sets of data using a 2-sample t-test. Unfortunately, both sets of data are non-normal. It appears box-cox or Johnson transforms will work, but my question is, wouldn't I need to transform both sets of data using the same transform parameters (lambda for BC and the transform function for the Johnson) in order for the comparison to be valid? I would think if I use two different sets of transform parameters than the data would be shifted in differing amounts, potentially spreading out the means (incorrectly??). Hopefully this makes sense! Thanks.