Hello to every one,

it is clear to me that sometimes it is worth trying a data transformation to meet the assumptions of Homoscedasticity and Normality before performing a parametric test. These transformations can be of different types (Log10, SQRT, Box-Cox etc.)

From what I understand, when I want to compare two or more groups, I have to be sure that both group "A" and group "B" or "C" (etc.) meet these two assumptions. If even one of the groups I compare is not normal or worse not Homoscedasticity I could try to apply one of the transformations listed above.

My question at this point is: do I have to apply the same transformation to all data without dividing it into groups?

Let me explain better: let's admit that group "A" becomes normal with only a Log10-transformation and group "B" becomes normal only with an SQRT-transformation, is it legit to apply a different transformation between groups? I don't think so because at that point I would compare two averages with an altered ratio with respect to the initial one.

Put simply: I have to check normality and homoskedasticity for each group analyzed, but then I must necessarily apply the same type of transformation to all the data hoping that it will solve my problems. Is that correct in your opinion?

Thank you