----- Original Message -----
From: Jerry Dallal <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, December 16, 1999 10:08 AM
Subject: Re: teaching statistical methods by rules?
>
>
> Robert Dawson wrote:
> >
> > Jerry Dallal wrote:
> >
> > > The problem for
me
> > > with the statement "Z is NEVER a better test for the mean under
> > > circumstances they are likely to encounter [in psychology]" is that it
> > > reads like an indictment
> >
> > It is. The last thing students in Intro Stats need is one more red
> > herring.
> >
>
> If I'm reading you properly ("NEVER"; it is an indictment),
Not an indictment of the approximation, but of the idea that there is
some n at which one *ought* to _stop_using_t_ and start using Z. There is
simply no reason for this extra complication unless Z works *better*, and it
never does.
then
> one of the important rules students are to get from your course is
> that there is a critical distinction between the percentiles of the t
> distribution and the standard normal distribution when talking about
> means of large samples.
Not at all. The approximation is, of course, an excellent one. I tell
the students that, and it is implicit in the use of any sanely-devised t
table (one that does not have rows/columns for 61, 62, ..., 733, ...
degrees of freedom).
The lack of a critical distinction is itself a sufficient condition for "Z
over 30" to be a waste of time, and for the superstition that it is somehow
wrong to use t for large samples to be just that - a superstition.
> I guess we'll have to agree to disagree on this one. I hope
>I'm not misstating your case.
Myself, I hope we *can* agree that there are no circumstances where
Z-with-s is a better test than t; that the rule
"use t for the mean"
is preferable - mainly on the grounds of simplicity and elegance - to
"use t for the mean unless n is over 30 in which case you may use z";
and that it is preferable on the grounds of factual accuracy to
"use t for the mean unless n is over 30 in which case you must use z".
A final point: Getting across - in the face of the psychology texts saying
the opposite that are sometimes quoted to me by students - that the Central
Limit Theorem does not magically start working exactly at n=30 is hard
enough. Assigning *other* magical powers to n=30 just reconfounds the
confusion.
-Robert Dawson
