students have enough problems with all the stuff in stat as it is ... but,
when we start some discussion about sampling error of means ... for use in
building a confidence interval and/or testing some hypothesis ... the first
thing observant students will ask when you say to them ...
assume SRS of n=50 and THAT WE KNOW THAT THE POPULATION SD = 4 ... is: if
we are trying to do some inferencing about the population mean ... how come
we know the population sd but NOT the mean too? most find this notion
highly illogical ... but we and books trudge on ...
and they are correct of course in the NON logic of this scenario
thus, it makes a ton more sense to me to introduce at this point a t
distribution ... this is NOT hard to do ... then get right on with the
reality case ....
asking something about the population mean when everything we have is an
estimate ... makes sense ... and is the way to go
in the moore and mccabe book ... the way they go is to use z first ...
assume population is normal and we know sd ... spend alot of time on that
... CI and logic of hypothesis testing ... THEN get into applications of t
in the next chapter ...
i think that the benefit of using z first ... then switching to reality ...
is a misguided order
finally, if one picks up a SRS random journal and looks at some SRS random
article, the chance of finding a z interval or z test being done is close
to 0 ... rather, in these situations, t intervals or t tests are almost
always reported ...
if that is the case ... why do we waste our time on z?
At 08:52 PM 4/18/01 -0300, Robert J. MacG. Dawson wrote:
>David J Firth wrote:
> >
> > : You're running into a historical artifact: in pre-computer days,
> using the
> > : normal distribution rather than the t distribution reduced the size
> of the
> > : tables you had to work with. Nowadays, a computer can compute a t
> > : probability just as easily as a z probability, so unless you're in the
> > : rare situation Karl mentioned, there's no reason not to use a t test.
> >
> > Yet the old ways are still actively taught, even when classroom
> > instruction assumes the use of computers.
>
> The z test and interval do have some value as a pedagogical
>scaffold with the better students who are intended to actually
>_understand_ the t test at a mathematical level by the end of the
>course.
>
> For the rest, we - like construction crews - have to be careful
>about leaving scaffolding unattended where youngsters might play on it
>in a dangerous fashion.
>
> One can also justify teaching advanced students about the Z test so
>that they can read papers that are 50 years out of date. The fact that
>some of those papers may have been written last year - or next- is,
>however, unfortunate; and we should make it plain to *our* students that
>this is a "deprecated feature included for reverse compatibility only".
>
> -Robert Dawson
>
>
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_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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