Suppose I apply a Box-Cox transformation to my data and now it looks rather like a normal distribution. I then add another dataset, transform it by Box-Cox with the same lambda and run a t-test to compare the means. Would this approach make sense if my data is non-normal by its nature? In other words, is the fact that a Box-Cox transform produces a Gaussian-like distribution sufficient to then use standard methods for normally distributed data such as t-test and ANOVA?
Update - to formulate this question a bit more specifically: I want to test whether there are significant differences between the means of two samples. I can see that the distributions in each sample are very much non-normal. My question is: if I force them to look normal by using a transformation, will this be enough to essentially forget about their "original" non-normal nature for testing this hypothesis?
Update 2 - I suppose my question is similar in spirit to this one, which asked the same thing about log-transformation.