John Weaver wrote:
>
> << Firstly, the Z test is inappropriate unless you know the variance of the
> population you are testing a sample
> from, not deducing it from the data. >>
>
> Robert,
> Please refresh my memory. I don't recall the variance of the population
> being a concern when calculating confidence intervals. What is the reason?
> Are you talking about the fact that using the sample variance in place of
> the pop variance is theoretically a crude substitution (although necessary)?
> The pop variance is rarely known, right?
The point is that if you are using an inferred variance/SD your test
statistic has (under Ho) a t distribution not a Z distribution; and
there is no reason, in this day, to deliberately use an approximate
distribution rather than the correct one.
Ninety-nine times out of 100 when people refer to a "Z test" they do
not mean the theoretically-justified-but-very-rare test with known
variance, but a badly-done t test, in which quantiles of Z are used
where those of t should be, that was once taught as "the right thing to
do" when n was greater than 30.
It's a separate issue from the question of hypothesis testing versus
confidence intervals. The only link is that both practices were more
common in the past than they are now - a fime illustration of the danger
of inferring causal connections form correlated time series <grin>
-Robert
PS: I know some math faculty at Manitoba, but did not know Dr Shue.
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
