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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