[R-SIG-Finance] Non parametric, unequal variance, equality of mean significance test

[Brian G. Peterson]

Reena Bansal wrote:
> Hello everyone,
>
> I have two samples of data of different sizes. Sample 1 is 30 points and
> sample 2 is 20 points. I have no reason to believe that the two sample
> are normally distributed or have the same variance. I am looking for
> significance test for the null that the two samples have same mean (or
> the two samples come from same population). 
>
> I found the unpaired Student's t test for unequal variance. However this
> test assumes normality.
> The non parametric test I found is the Mann Whitney U test. But this
> test requires equal variance.
>   
I seriously doubt your series are long enough for any standard 
statistical test to have high enough confidence.  Your error bands will 
be quite wide.

I would probably check the fit to non-normal and fat-tailed 
distributions such as the Cornish Fisher, the skewed Student-t and the 
general Pareto.  If your data seems to fit those well, you may be able 
to compare the fitted distributions.

There are a number of distribution fitting functions in 
PerformanceAnalytics, and most have been wrapped into chart.Histogram 
and chart.QQPlot.  Of course, R has a wealth of this kind of 
functionality, and I'm only referring to the code I am most familiar with.

Regards,

     - Brian

-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock