# Reporting Log Transformed T-Test Results

#### Yankel

##### Member
Dear all,

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 !

#### GretaGarbo

##### Human
Yes, the mean in the normal distribution will be an estimate of the expected value. But it will also be an estimate of the median in the normal distribution, since the population mean and the population median is the same.

But what is the median in the normal distribution, the mu, will also, after transformation, taking the exp(mu), be an estimate of the median in the lognormal distribution.

So, the exp(mu_hat) is an estimate of the median in the original lognormal distribution, (but it is not an estimate of the mean in the lognormal distribution) and it is completely OK.