theory of t-test
- From: pauldepstein@xxxxxxx
- Date: 5 Sep 2006 06:03:24 -0700
Suppose I know that my data sample comes from a normal distribution,
but I don't know the mean and variance of what that normal distribution
is.
Suppose I want to predict the next data point. I then use a t-test
with n-1 degrees of freedom and variance (s ^ 2 + s^2/n).
Now, we come to the question -- the part that troubles me.
Elementary texts say that the t-test is given by a p.d.f and they give
the equation for the pdf.
However, if you are using a t-test to investigate a normal dist, it
doesn't make much sense (to me) to talk about the p.d.f. of that t-test
without a priori assumptions about the variance and mean of the
underlying normal.
When using a t-test to investigate an underlying normal, what
assumptions (if any) are made about the mean and variance of that
normal? I would guess that there is some type of assumption that all
means are equally likely and all positive variances are equally likely.
However, I would like to know how this is formalized since it
obviously doesn't make sense to have a uniform distribution on an
infinite interval.
Paul Epstein
.
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