Re: T-test possible with one observation?



Tim Witort <trw7at@xxxxxxxxxxxxxxxxxx> wrote:
> Am I correct that it is not possible to perform a T-test on
> two groups of observations when one of the groups has only
> one observation? I find that, using the formulas I have, a
> divide-by-zero will always take place unless there are at least
> two observations in each group - the pooled variance becomes
> zero, hence the standard error of the difference becomes zero,
> so the difference of the means cannot be divided by the zero
> pooled variance. Perhaps there is an alternate formula that
> allows for a T-test in such a case? I can post the formula
> I am using if necessary.

> -- TRW

If you think of the goal of this problem as determining a
"prediction interval" for the value of a single future observation, from a
hypothesized IID sequence of normal observations, with mean and
variance estimated in the usual way from your historical set,(rather
than as setting up a confidence interval on the difference of two
parameters) then you get a very simple probability statement involving
the t-distribution and the expression Sqrt(1+1/n), and which is
probably a much more practical tool for evaluating the "novelty"
of the N+1st observation. I think this is probably what the
poster wishes to do -- to make a probability statement about the
size of a single (observable) future value; to do so by employing the logical
framework of confidence intervals on (unobservable) parameters is
not the natural way to frame the problem, and it does lead to
troubles in the arithmetic.
.

Relevant Pages

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