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.

Each sample had 3 replicates.

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?

  • 1
    $\begingroup$ 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). $\endgroup$
    – Glen_b
    May 24, 2014 at 7:44
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    $\begingroup$ 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. $\endgroup$
    – whuber
    May 25, 2014 at 21:50

2 Answers 2


The Mann-Whitney doesn't care about how far apart they are, only their order. Therefore it would give the same result regardless of the distance between the groups as long as the orders were the same. Conversely, the t-test is strongly influenced by how far apart the means actually are because that difference is the numerator of the t statistic.



You probably aren't doing anything wrong. You only have three observations per sample. Therefore the difference must be very large for a small p-value.

  • $\begingroup$ (1) There are two samples, not three. (2) To which p-value do you refer: the t-test or the MW test? $\endgroup$
    – whuber
    May 25, 2014 at 21:43

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