# [R] Comparing two groups

Andrej andrej.g.miller at web.de
Fri Oct 18 08:55:29 CEST 2013

```glsnow wrote
>>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
> 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
> 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