>From your question it is not clear what your question/concerns really are,
and from what we can see it could very well be that you do not understand
the statistics that you are computing (not just the R implementation).  We
ask for a reproducible example because that helps us to help you, just a
couple of boxplots let us make some guesses, but we do not know the data
values or even the means and standard deviations, even the actual sample
sizes could help.

>From the graph it is not surprising that the wilcox test say that the 2
groups are different and that the t test says that they are not (but
knowing data values would help even more).  The 2 tests are testing very
different hypotheses.  The wilcox test is testing that the 2 distributions
are identical and the more specific way it tests that is by looking at all
possible pairs between the 2 groups and seeing what proportion of them have
each group higher, if the null were true then half the time the data point
from mixed would be higher than the data point from monoculture and half
the time the other way.  From the boxplot we can see that the median of
monoculture is below the 1st quartile of mixed, so it is not surprising at
all that the wilcox test rejects the null hypothesis.

The t-test (which version you used you do not say) is testing if the means
are equal, since monculture is clearly skewed to the right with potential
outliers, it would not be surprising if the sample means were close enough
to each other that the t-test does not see a significant difference.  The 2
tests give different answers because they are answering very different
questions.

You state that "I am not allowed to perform it" referring to the t-test.
 This indicates that you don't have a full understanding or appreciation of
the Central Limit Theorem (an important enough theorem that I have a
cross-stitch based on it hanging on my wall (along with 2 other
cross-stitches of Bayes theorem and the mean value theorem of
integration)).  The plot shows 18 outliers in the monoculture group which
implies a sample size of at least 72, which means the other group has a
sample size of at least 14 if I interpret "five times as big" correctly.
 This is a large enough sample size for the CLT to tell us the t-test will
give a reasonable approximation (provided the other assumptions hold
reasonably well and you are interested in the question being answered).

So, I believe that the advice to read a textbook, or otherwise get some
help in basic understanding of the statistical tools is reasonable.  Once
you have that, then if you still need help then give us a reproducible
example and make it clear what your question really is and you will be much
more likely to receive an answer.


On Tue, Oct 15, 2013 at 6:01 AM, Andrej <andrej.g.miller@web.de> wrote:

> >So why not start with some statistical textbook? There are plenty of them
> available in CRAN.
>
> I wasn't implying, that I haven't read any textbook, or didn't do any
> research. I read some textbooks/Papers/etc. during the research about what
> to do and came across the wilcox test. I meant to imply that I could have
> problems understanding some of the answers, and that maybe additional
> explaining would be necessary.
>
> My doubts stem from the fact, that the wilcox test is a - as far as I know
> -
> ranking test, that states if two groups are different. My assumption is,
> due
> to the fact that the second group has a much higher sample size, it is
> clear
> that it differs from the first group. I performed a t-test (just to see; I
> am aware that I am not allowed to perform it, because my samples aren't
> normally distributed) and it gave me a p-value of 0.3.
> Actually I am not even entirely sure, if wilcox is the right test. I just
> want to know if the means of the two groups are significantly different.
>
>
>
> --
> View this message in context:
> http://r.789695.n4.nabble.com/Comparing-two-groups-tp4678190p4678277.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>



-- 
Gregory (Greg) L. Snow Ph.D.
538280@gmail.com

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