[R] t test problem?

kan Liu kan_liu1 at yahoo.com
Wed Sep 22 11:21:55 CEST 2004

Hi, Many thanks for your helpful comments and suggestions. The attached are the data in both log10 scale and original scale. It would be very grateful if you could suggest which version of test should be used. 
By the way, how to check whether the variation is additive (natural scale) or multiplicative (log scale) in R? How to check whether the distribution of the data is normal? 
PS, Can I confirm that do your suggestions mean that in order to check whether there is a difference between x and y in terms of mean I need check the distribution of x and that of y in both natual and log scales and to see which present normal distribution? and then perform a t test using the data scale which presents normal distribution? If both scales present normal distribution, then the t tests with both scales should give the similar results?
Thanks again.

Andrew Robinson <andrewr at uidaho.edu> wrote:
Hi Dimitris,

you are describing a more stringent requirement than the t-test
actually requires. It's the sampling distribution of the mean that
should be normal, and this condition is addressed by the Central
Limit Theorem.

Whether or not the CLT can be invoked depends on numerous factors,
including the distribution of the sample, and the size of the sample,
neither of which we have any information about. 

Liu, the problem you describe is associated with the application of
the test rather than the test itself. The difference between log- and
natural- scaled data can often profitably be thought about by asking
whether you would naturally assume that the variation is additive
(natural scale) or multiplicative (log scale). Given the information
that you've presented there's no way we can tell which version of the
test is more reliable. 

I hope that this helps.


On Wed, Sep 22, 2004 at 10:00:16AM +0200, Dimitris Rizopoulos wrote:
> Hi Liu,
> before applying a t-test (or any test) you should first check if the 
> assumptions of the test are supported by your data, i.e., in a t-test 
> x and y must be normally distributed.
> I hope it helps.
> Best,
> Dimitris
> ----
> Dimitris Rizopoulos
> Ph.D. Student
> Biostatistical Centre
> School of Public Health
> Catholic University of Leuven
> Address: Kapucijnenvoer 35, Leuven, Belgium
> Tel: +32/16/396887
> Fax: +32/16/337015
> Web: http://www.med.kuleuven.ac.be/biostat/
> http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm
> ----- Original Message ----- 
> From: "kan Liu" 
> To: 
> Sent: Wednesday, September 22, 2004 9:52 AM
> Subject: [R] t test problem?
> >Hello,
> >
> >I got two sets of data
> >x=(124738, 128233, 85901, 33806, ...)
> >y=(25292, 21877, 45498, 63973, ....)
> >When I did a t test, I got two tail p-value = 0.117, which is not 
> >significantly different.
> >
> >If I changed x, y to log scale, and re-do the t test, I got two tail 
> >p-value = 0.042, which is significantly different.
> >
> >Now I got confused which one is correct. Any help would be very 
> >appreciated.
> >
> >Thanks,
> >Liu
> >
> >__________________________________________________
> >
> >
> >
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