# [R] small sample techniques

Moshe Olshansky m_olshansky at yahoo.com
Thu Aug 9 04:57:45 CEST 2007

```As Thomas Lumley noted, there exist several versions
of t-test.
If you use t1 <- t.test(x,y) then no assumption is
made of x and y having equal variance and of the two
sample sizes being equal and then an approximate
t-test is used with an approximate number of degrees
of freedom (and this is what you got).
If you use t2 <- t.test(x,y,var.equal=TRUE) then equal
variance is assumed and you get 8 degrees of freedom.
If you use t3 <- t.test(x,y,paired=TRUE) then equal
sample sizes are assumed and the number of degrees of
freedom is 4 (5-1).

--- "Nair, Murlidharan T" <mnair at iusb.edu> wrote:

> Indeed, I understand what you say. The df of freedom
> for the dummy example is n1+n2-2 = 8. But when I run
> the t.test I get it as 5.08, am I missing something?
>
>
> -----Original Message-----
> From: Moshe Olshansky [mailto:m_olshansky at yahoo.com]
>
> Sent: Tuesday, August 07, 2007 9:05 PM
> To: Nair, Murlidharan T; r-help at stat.math.ethz.ch
> Subject: Re: [R] small sample techniques
>
> Hi Nair,
>
> If the two populations are normal the t-test gives
> you
> the exact result for whatever the sample size is
> (the
> sample size will affect the number of degrees of
> freedom).
> When the populations are not normal and the sample
> size is large it is still OK to use t-test (because
> of
> the Central Limit Theorem) but this is not
> necessarily
> true for the small sample size.
> You could use simulation to find the relevant
> probabilities.
>
> --- "Nair, Murlidharan T" <mnair at iusb.edu> wrote:
>
> > If my sample size is small is there a particular
> > switch option that I need to use with t.test so
> that
> > it calculates the t ratio correctly?
> >
> > Here is a dummy example?
> >
> > á =0.05
> >
> > Mean pain reduction for A =27; B =31 and SD are
> > SDA=9 SDB=12
> >
> > drgA.p<-rnorm(5,27,9);
> >
> > drgB.p<-rnorm(5,31,12)
> >
> > t.test(drgA.p,drgB.p) # what do I need to give as
> >
> >
> >
> > I can do it manually but was looking for a switch
> > option that I need to specify for  t.test.
> >
> >
> >
> > Thanks ../Murli
> >
> >
> >
> >
> > 	[[alternative HTML version deleted]]
> >
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