[R] Code Verification

[Christoph Buser]

Dear Andy

Since the power of the t-test decreases when there are
discrepancies in the data to the normal distribution and there
is only a small loss of power if the data is normal distributed,
the only reason to use the t.test is his simplicity and the
easier interpretation.
Generally I'd prefer the wilcoxon test even if the data is
normal distributed.
But I agree that for a gamma distribution there is no huge loss
of power.

## example simulation:

n <- 1000
z1 <- numeric(n)
z2 <- numeric(n)

## gamma distribution
for (i in 1:n)
{
x<-rgamma(40, 2.5, 0.1)  
y<-rgamma(40, 3.5, 0.1)  
z1[i]<-t.test(x, y)$p.value
z2[i]<-wilcox.test(x, y)$p.value
}
## Power
1 - sum(z1>0.05)/1000  ## 0.71
1 - sum(z2>0.05)/1000  ## 0.76

##################################

## t distribution
for (i in 1:n)
{
x<-rt(40, df = 3)      
y<-1 + rt(40, df = 3)  
z1[i]<-t.test(x, y)$p.value
z2[i]<-wilcox.test(x, y)$p.value
}
## Power
1 - sum(z1>0.05)/1000  ## 0.76
1 - sum(z2>0.05)/1000  ## 0.91

##################################

## normal distribution
for (i in 1:n)
{
x<-rnorm(40, 0, 3)      
y<-1 + rnorm(40, 1, 3)  
z1[i]<-t.test(x, y)$p.value
z2[i]<-wilcox.test(x, y)$p.value
}
## Power
1 - sum(z1>0.05)/1000  ## 0.83
1 - sum(z2>0.05)/1000  ## 0.81

Regards,

Christoph Buser

--------------------------------------------------------------
Christoph Buser <buser at stat.math.ethz.ch>
Seminar fuer Statistik, LEO C13
ETH (Federal Inst. Technology)	8092 Zurich	 SWITZERLAND
phone: x-41-44-632-4673		fax: 632-1228
http://stat.ethz.ch/~buser/
--------------------------------------------------------------

Liaw, Andy writes:
 > > From: Christoph Buser
 > > 
 > > Hi
 > > 
 > > "t.test" assumes that your data within each group has a normal
 > > distribution. This is not the case in your example.
 > 
 > Eh?  What happen to the CLT?
 > 
 > Andy
 > 
 > 
 > > I would recommend you a non parametric test like "wilcox.test" if
 > > you want to compare the mean of two samples that are not normal
 > > distributed. 
 > > see ?wilcox.test
 > > 
 > > Be careful. Your example produces two gamma distributed samples
 > > with rate = 10, not scale = 10. 
 > > rate = 1/scale.
 > > If you want to use scale, you need to specify this argument 
 > > x<-rgamma(40, 2.5, scale = 10)
 > > see ?rgamma
 > > 
 > > I do not see the interpretation of your result. Since you do
 > > know the distribution and the parameters of your sample, you
 > > know the true means and that they are different. It is only a
 > > question of the sample size and the power of your test, if this
 > > difference is detected.
 > > Is that something you are investigating? Maybe a power
 > > calculation or something similar.
 > > 
 > > Regards,
 > > 
 > > Christoph Buser
 > > 
 > > --------------------------------------------------------------
 > > Christoph Buser <buser at stat.math.ethz.ch>
 > > Seminar fuer Statistik, LEO C13
 > > ETH (Federal Inst. Technology)	8092 Zurich	 SWITZERLAND
 > > phone: x-41-44-632-4673		fax: 632-1228
 > > http://stat.ethz.ch/~buser/
 > > --------------------------------------------------------------
 > > 
 > > pantd at unlv.nevada.edu writes:
 > >  > Hi R Users
 > >  > I have a code which I am running for my thesis work. Just 
 > > want to make sure that
 > >  > its ok. Its a t test I am conducting between two gamma 
 > > distributions with
 > >  > different shape parameters.
 > >  > 
 > >  > the code looks like:
 > >  > 
 > >  > sink("a1.txt");
 > >  > 
 > >  > for (i in 1:1000)
 > >  > {
 > >  > x<-rgamma(40, 2.5, 10)  # n = 40, shape = 2.5, Scale = 10
 > >  > y<-rgamma(40, 2.8, 10)  # n = 40, shape = 2.8, Scale = 10
 > >  > z<-t.test(x, y)
 > >  > print(z)
 > >  > }
 > >  > 
 > >  > 
 > >  > I will appreciate it if someone could tell me if its alrite or not.
 > >  > 
 > >  > thanks
 > >  > 
 > >  > -dev
 > >  > 
 > >  > ______________________________________________
 > >  > R-help at stat.math.ethz.ch mailing list
 > >  > https://stat.ethz.ch/mailman/listinfo/r-help
 > >  > PLEASE do read the posting guide! 
 > > http://www.R-project.org/posting-guide.html
 > > 
 > > 
 > > ______________________________________________
 > > R-help at stat.math.ethz.ch mailing list
 > > https://stat.ethz.ch/mailman/listinfo/r-help
 > > PLEASE do read the posting guide! 
 > > http://www.R-project.org/posting-guide.html
 > > 
 > > 
 > > 
 > 
 > 
 > 
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