Reena,

>> So far the literature I have seen mentions that the data itself has to be normally populated.

I am almost positive that this is not true. The CLT is explained in every introductory statistics and probability theory book.

maybe an example will be instructive:

#---------------------------------------------------------------------
# lets say the data is uniformly distributed and you only have 20 obs.
library(lattice)
means <- numeric(5000)

for (i in 1:5000) {
mydata <- runif(20,-2,2) # data itself is uniformly distributed
means[i] <- mean(mydata)
}

densityplot(~means) # looks normally distributed
shapiro.test(means) # standard normality test confirms this
#---------------------------------------------------------------------


in the case of the uniform distribution, 20 observations are enough. If your data is very asymmetric (e.g. lrnorm(20,6,1.5) then 20 observations will not be sufficient to get an approximate normal distribution.


Zeno
 


-----Original Message-----
From: Reena Bansal [mailto:Reena.Bansal@moorecap.com]
Sent: Wed 12/23/2009 5:48 PM
To: Adams, Zeno; r-sig-finance@stat.math.ethz.ch
Subject: RE: [R-SIG-Finance] Non parametric, unequal variance,equality of mean significance test
 
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@ebs.edu] 
Sent: Wednesday, December 23, 2009 11:36 AM
To: Reena Bansal; r-sig-finance@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@stat.math.ethz.ch on behalf of Reena Bansal
Sent: Wed 12/23/2009 4:33 PM
To: r-sig-finance@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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EBS European Business School gemeinnuetzige GmbH - Sitz der Gesellschaft: Wiesbaden, Amtsgericht Wiesbaden HRB 19951 - Umsatzsteuer-ID DE 113891213 Geschaeftsfuehrer: Prof. Dr. Christopher Jahns,  Praesident; Prof. Dr. Rolf Tilmes, Dekan; Sabine Fuchs, CMO; Aufsichtsrat: Dr. Hellmut K. Albrecht, Vorsitzender
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