On Mon, 9 Apr 2001, Rich Ulrich wrote:
> On Mon, 09 Apr 2001 10:44:40 -0400, Paige Miller
> <[EMAIL PROTECTED]> wrote:
>
> > "Andrew L." wrote:
>
AL> I am trying to learn what a t-test will actually tell me, in
> simple terms. < snip >, but i still dont quite
> understand the significance.
>
PM> A t-test compares a mean to a specific value...or two means to each
> other...
> [ ... ]
>
RU> I remember my estimation classes, where the comparison was
RU> always to ZERO for means.
Yes, that's what Paige said: here the mean (mean difference, to be
precise) is being compared to the specific value zero.
OR "two means to each other", since the allegation "X1 = X2" is
equivalent to the allegation "(X1-X2) = 0"
That the hypothethical expectation is often zero (that is, null) is the
reason why that hypothesis is colloquially called "the null hypothesis";
Lumsden argued that it were better called "the model-distributional
hypothesis", but that apparently is too much of a mouthful for most
folks. There is, however, no formal or logical REQUIREMENT that the
value expected under the model-distributional hypothesis be zero.
RU> To ONE, I guess, for ratios.
RU> Technically speaking, or writing.
Someone else pointed out that if the ratio were of interest, one should
probably be taking logarithms; in which case the comparison of interest
would be to log(1) = 0.
(Unless the ratio of interest were a ratio of variances; but in that
case the relevant distribution would not be a t distribution.)
RU> For instance, if the difference in averages X1, X2 is expected to
RU> be zero, then "{(X1-X2) -0 }" ... is distributed as t .
This is, I believe, technically inaccurate. "{(X1-X2) - 0}" is
distributed normally, or approximately so under a central limit theorem;
in which case "{(X1-X2) - 0}" divided by its estimated standard error is
distributed as t . Again technically, as the standard central t .
("Standard", implying that the mean and standard deviation of the
sampling distribution are 0 and 1 respectively; "central", implying that
the non-centrality parameter is zero.)
RU> It might look like a lot of equations with the 'minus zero'
RU> seemingly tacked on, but I consider this to be good form.
No argument with that. Nor with this:
RU> It formalizes as <term> minus <Expectation of term>
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
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