Hi Kan Lui, 

I've had a quick look at the data. The logged data seems reasonably nicely
distributed (roughly symmetrical + equal variance). Indeed the y variable
passed the (very strict) shapiro.test for normality. 

However the main problem is that I do not get the same results as you for
the significance of the t.test. 

The only significant test I see is the paired t.test on the logged data. Is
your data paired data? To see what I mean check out:
http://www.texasoft.com/winkpair.html

The non-parametric tests show no significance (paired data or not) (logged
and natural data). Although in general they do tend to be less strict than
parametric tests. 

Unless the data is paired then the means of these samples most certainly do
not significantly differ from one another.



Here are my workings: 

Temp.Dat<-read.table("data_natural.txt",header=T)


hist(log(Temp.Dat$x,10))
hist(log(Temp.Dat$y,10))

shapiro.test(log(Temp.Dat$x,10))
shapiro.test(log(Temp.Dat$y,10))

t.test(log(Temp.Dat$x,10), log(Temp.Dat$y,10))


       Welch Two Sample t-test

data:  log(Temp.Dat$x, 10) and log(Temp.Dat$y, 10) 
t = 0.9126, df = 195.806, p-value = 0.3626
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -0.0599837  0.1633168 
sample estimates:
mean of x mean of y 
 4.891313  4.839647


> t.test(log(Temp.Dat$x,10), log(Temp.Dat$y,10),paired=T)

        Paired t-test

data:  log(Temp.Dat$x, 10) and log(Temp.Dat$y, 10) 
t = 2.3535, df = 98, p-value = 0.02060
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 0.008101002 0.095232132 
sample estimates:
mean of the differences 
             0.05166657 

> wilcox.test(log(Temp.Dat$x,10), log(Temp.Dat$y,10),paired=T)

        Wilcoxon signed rank test with continuity correction

data:  log(Temp.Dat$x, 10) and log(Temp.Dat$y, 10) 
V = 2972.5, p-value = 0.0828
alternative hypothesis: true mu is not equal to 0 

> wilcox.test(log(Temp.Dat$x,10), log(Temp.Dat$y,10),paired=F)

        Wilcoxon rank sum test with continuity correction

data:  log(Temp.Dat$x, 10) and log(Temp.Dat$y, 10) 
W = 5206, p-value = 0.4491
alternative hypothesis: true mu is not equal to 0



> wilcox.test(Temp.Dat$x, Temp.Dat$y,paired=F)

        Wilcoxon rank sum test with continuity correction

data:  Temp.Dat$x and Temp.Dat$y 
W = 5206, p-value = 0.4491
alternative hypothesis: true mu is not equal to 0 

> wilcox.test(Temp.Dat$x, Temp.Dat$y,paired=T)

        Wilcoxon signed rank test with continuity correction

data:  Temp.Dat$x and Temp.Dat$y 
V = 2896.5, p-value = 0.1417
alternative hypothesis: true mu is not equal to 0 

> t.test(Temp.Dat$x, Temp.Dat$y,paired=T)

        Paired t-test

data:  Temp.Dat$x and Temp.Dat$y 
t = 1.6731, df = 98, p-value = 0.0975
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -2351.81 27623.53 
sample estimates:
mean of the differences 
               12635.86 

> t.test(Temp.Dat$x, Temp.Dat$y,paired=F)

        Welch Two Sample t-test

data:  Temp.Dat$x and Temp.Dat$y 
t = 0.6432, df = 191.177, p-value = 0.5209
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -26116.18  51387.89 
sample estimates:
mean of x mean of y 
 120544.9  107909.0 

>

-----Original Message-----
From: kan Liu [mailto:kan_liu1@yahoo.com] 
Sent: 22 September 2004 10:22
To: Andrew Robinson; Dimitris Rizopoulos
Cc: r-help@stat.math.ethz.ch
Subject: Re: [R] t test problem?

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.
 
Liu

Andrew Robinson <andrewr@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.

Andrew

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
> >
> >__________________________________________________
> >
> >
> >
> >[[alternative HTML version deleted]]
> >
> >______________________________________________
> >R-help@stat.math.ethz.ch mailing list
> >https://stat.ethz.ch/mailman/listinfo/r-help
> >PLEASE do read the posting guide! 
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> >
> 
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-- 
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Department of Forest Resources Fa: 208 885 6226
University of Idaho E : andrewr@uidaho.edu
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Moscow ID 83843 Or: http://www.biometrics.uidaho.edu
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