[R] small sample techniques

[Moshe Olshansky]

Well, this an explanation of what is done in the
paired t-test (and why the number of df is as it is).
I was too lazy to write all this.
It is nice that some list members are less lazy!

--- Rolf Turner <r.turner at auckland.ac.nz> wrote:

> 
> On 9/08/2007, at 2:57 PM, Moshe Olshansky wrote:
> 
> > As Thomas Lumley noted, there exist several
> versions
> > of t-test.
> 
> 	<snip>
> 
> > 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).
> 
> 	This is seriously misleading.  The assumption is
> not that the sample  
> sizes
> 	are equal, but rather that there is ***just one
> sample***, namely  
> the sample of differences.
> 
> 	More explicitly the assumptions are that
> 
> 		x_i - y_i
> 
> 	are i.i.d. Gaussian with mean mu and variance
> sigma^2.
> 
> 	One is trying to conduct inference about mu, of
> course.
> 
> 	It should also be noted that it is a crucial
> assumption for the  
> ``non-paired''
> 	t-test that the two samples be ***independent*** of
> each other, as  
> well as
> 	being Gaussian.
> 
> 	None of this is however germane to Nair's original
> question; it is  
> clear
> 	that he is interested in a two-independent-sample
> t-test.
> 
> 				cheers,
> 
> 					Rolf Turner
> 
>
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