# I don't understand what is going on with my t-test and Mann-Whitney results

I have 2 samples, A and B. I subjected both samples to extraction and got the amount of yield (the dependent variable).

I just want to see if there is a significant difference between the yield for A and B.

Sample A:

0.003,0.0029, 0.003


Sample B:

4.832, 4.828, 4.662


Since it's just 2 samples, I went for a two-sample t-test.

I tested for normality, which indicated the data was not normal.

I did a log transform, but it was still not normal.

Anyway I subject the log yield to the t-test and got equal variance and p value 0.00

And I tried non-parametric test (Mann-Whitney) and got p-value 0.046.

I don't get why is the p-value of Mann-Whitney so close to 0.05. Can it be that the means of sample A and B do not differ significantly when the values seem so far apart?

What am I doing wrong?

• Why did you do a one=-tailed test for the Mann-Whitney? (for that matter, how do you get 0.046 for a p-value? I just computed the entire permutation distribution by hand and I don't get that). May 24, 2014 at 7:44
• The correct test for normality in this case would be complicated, unnecessary, and unduly influenced by the lack of precision in the data for sample A. The distribution of the residuals (on a log scale) should give you comfort that the two-sample t-test (based on logs) is giving useful and reliable information.
– whuber
May 25, 2014 at 21:50