There has been a side note to "rules" concerning z --
On 13 Dec 1999 13:58:31 -0800, [EMAIL PROTECTED] (Robert
Dawson) wrote:
> Exactly... An example - we've been using Devore & Peck, which
> unfortunately introduces the Z test for the mean, supposedly for pedagogical
> reasons but without nearly a strong enough indication of this. A lot of
> students infer a rule "if n>30 use z rather than t" despite my repeated
> statements that Z is NEVER a better test for the mean under circumstances
> they are likely to encounter [in psychology]. < snip >
If you *never* wanted z, that might call for a different rule.
But you find z (or its square, chisquare) actually in use in the
large-sample versions of tests on ranks or dichotomies -- the
variance meets that necessary requirement for having z instead of t;
that is, it has a "KNOWN" variance.
For data consisting of dichotomies or ranks, the total variance is
known in advance, though there is a question of what to do with ties.
Indeed, the F-test might work better than another formula for
estimating the "exact" variance when there are a lot of ties, but the
known-variance version of ANOVA can use chisquared instead of F --
If you have a small enough N, the distinction can matter. But the
direction of error if you use F is on the conservative side, so doing
various ANOVAs on ranks, as an alternative to exact testing, is a
handy tool to know about. Even though the exact test might be
available.
Teaching?
I think it is good have EXAMPLES available, to go along with rules.
Perhaps you want examples that just skirt the rules, too. I keep
thinking that I want to internalize the best set of rules and
examples by browsing 3 or 4 books on the particular topic, in addition
to seeing a few examples by Monte Carlo.. But I can't do that myself,
for every topic.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
