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Non parametric, unequal variance, equality of mean significance test
7 messages · Reena Bansal, Brian G. Peterson, Moshe Olshansky +1 more
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
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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 ? ? ? ? [[alternative HTML version deleted]] _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first. ________________________________ 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 ________________________________ ??? [[alternative HTML version deleted]] _______________________________________________ R-SIG-Finance at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. -- If you want to post, subscribe first.
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