Statistical mean/median test between two datasets

#1
Hi,

I am writing to share a doubt I have.

I have to compare two datasets with 352 entries. One of them has gaussian (normal) distribution and the other an unknown distribution. When I look at both histograms distributions, they are superimposed, and visually there is no statistical significance between the means and medians. However, running a Wilcoxon rank-sum test (matlab), I discovered there is a statistical significance that seems to be counterintuitive. Must I use another test to compare the datasets? I tried t-test too and I got a similar result. Somebody could give me some tips?

Tks in advance
 

Karabiner

TS Contributor
#2
The t-test deals with the question, whether or not we can reject the assumption that
the mean difference between the 2 populations from which the data were drawn
is exactely 0.000000000000 .

Therefore, "visual statistical difference between sample means" does not make too
much sense in several ways.

If there is a tiny mean difference between the 2 samples, but that tiny difference
is very reliable (i.e. there is only a small standard error for the difference found,
which can especially happen if sample size is large), then one can reject the
null hypothesis.

But I don't know whether this is the case here, although n=352 points in that
direction. Maybe you could post the visual display of the two distributions?

With kind regards

Karabiner
 

Karabiner

TS Contributor
#4
One of the distributions is distinctly right skewed, therefore I would not expect its mean and median
to be located about where the center of the other distribution lies. In addition, as said before, even
tiny differences between sample means or medians can lead to rejection of the "no difference in the
population" hypothesis, if sample size is large (and n=704 is already quite large). Did you calculate
the means and medians of both distributions?

With kind regards

Karabiner