[R] small sample techniques

[Rolf Turner]

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

######################################################################
Attention:\ This e-mail message is privileged and confidenti...{{dropped}}