I have a variable, I'll call it Y, which is skewed, and another variable X, which is binary. I wish to perform a t-test.

I have calculated the LOG transformation of Y (using a base e), and ran a t-test on the transformed data, yielding a p-value of 0.046. The CI limits for the mean difference are -0.29 and -0.002.

Now I wish to report it. I know that by using the inverse transformation, I get a geometric mean rather than arithmetic one, and the CI limits are not symmetrical around the mean. Is this OK ?

Is it valid to report the inverse transformed means and SD's (or perhaps the original ones ?), along with the P-Value and CI of the transformed variable ?

And one more thing, I also ran the Mann-Whitney U test, and the P-Value was above 0.05. Is this due to the lack of power of this test compared to the t-test ? Which P-Value is more "reliable" ? Are the results significant or not ? The sample size in both groups is 32 samples.

Thank you !