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

[Moshe Olshansky]

Hi Reena,

There is Cramer's theorem stating that the sum of two independent variables has normal distribution if and only if each of them is normally distributed. So to strictly satisfy conditions for t-test you data must be normally distributed.
However, because of the Central Limit Theorem, if the sample is large enough (and has finite second moment/variance) you can use t-test (with unequal variances). I believe that 30 and 20 may be large enough.
As to Mann Whitney test, it checks for equal distributions - equal means are not enough.

Best regards,
Moshe.

--- On Thu, 24/12/09, Reena Bansal <Reena.Bansal at moorecap.com> wrote:

> From: Reena Bansal <Reena.Bansal at moorecap.com>
> Subject: Re: [R-SIG-Finance] Non parametric, unequal variance, equality of mean significance test
> To: "Adams, Zeno" <Zeno.Adams at ebs.edu>, r-sig-finance at stat.math.ethz.ch
> Received: Thursday, 24 December, 2009, 3:48 AM
> Hi Zeno,
>  
> No I am not aware of this assumption. So far the literature
> I have seen
> mentions that the data itself has to be normally populated.
> Do you have
> any references on this assumption?
>  
> Thanks.
> 
> ________________________________
> 
> From: Adams, Zeno [mailto:Zeno.Adams at ebs.edu]
> 
> Sent: Wednesday, December 23, 2009 11:36 AM
> To: Reena Bansal; r-sig-finance at stat.math.ethz.ch
> Subject: RE: [R-SIG-Finance] Non parametric, unequal
> variance,equality
> of mean significance test
> 
> 
> 
> I assume you are aware of the fact that the Student's t
> test assumes the
> means of the data to be normally distributed but does not
> require any
> normality assumptions concerning the data itself? If your
> data fulfills
> the requirements for the central limit theorem to hold
> (i.e. your
> observations are independently distributed) then I don't
> see any reason
> why you cannot use the simple t-test.
> 
> Zeno
> 
> 
> -----Original Message-----
> From: r-sig-finance-bounces at stat.math.ethz.ch
> on behalf of Reena Bansal
> Sent: Wed 12/23/2009 4:33 PM
> To: r-sig-finance at stat.math.ethz.ch
> Subject: [R-SIG-Finance] Non parametric, unequal
> variance,equality of
> mean significance test
> 
> 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.
> 
> Any suggestions.
> 
> Thanks,
> Reena
> 
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