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Topic: normal probability plots
Replies: 1   Last Post: Mar 6, 1997 10:13 AM

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KINGB@WCSUB.CTSTATEU.EDU

Posts: 144
Registered: 12/6/04
normal probability plots
Posted: Mar 1, 1997 3:32 PM
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Almost three weeks ago, in a discussion on normal probability plots, I
commented as follows:

> So why use Y-hat instead of X, if they provide the same information in
> the residual plot? Because in multiple regression there is no e_i vs X
> plot; you have only the e_i vs Y-hat plot available. So it's (at least
> partly) a matter of foreshadowing later developments.
>


Chris Olsen subsequently asked me:

> do you think there is
> any reason to use this plot with kids given that __multiple__
> regression is not in the AP Stat syllabus?


I am not anxious to continue that thread, but I don't want to ignore a
direct question (any longer than I already have!) either. It's easy
for me to say "Yes, I think we should teach normal probability plots to
AP Statistics students." But, of course, that's because I don't have
the privilege of teaching the course, and am not well-attuned to the
problems that arise, or to the tradeoffs that must be considered.

All I can say is that I see many places in elementary statistics where
I want to say to my students: "Look: sensible analyses take advantage
of BOTH visual evidence and numerical evidence." And there are
numerical ways of assessing normality (say, a goodness of fit test).
So I want my students to encounter at the same time what I understand
to be the best available visual device for assessing normality.

To be fair, I should say that I probably was not sure about this (in my
own professinal life, that is) until I encountered David Moore's
section on "Assessing Normality" in IPS, and the interesting examples
one finds there on pp.73-86. That convinced me, utterly.

But, again: the Development Committee certainly had to agonize over
many do-we-include-this/do-we-exclude-that issues. I do not intend my
comments so second-guess their decisions; I might very well have made
the same judgment, had I the benefit of any discussion that led to a
decision to exclude these plots from the AP course.

And, finally (I promise!): I think we should not forget Bob Hayden's
comments during that discussion. Bob asserted that assessing whether
or not a curve is "bell shaped" is not important; that what's important
is "symmetry, lack of outliers, and weight of the tails".

Sorry to be so slow to respond, Chris.

==============================================
Bruce King
Department of Mathematics and Computer Science
Western Connecticut State University
181 White Street
Danbury, CT 06810
(kingb@wcsu.ctstateu.edu)





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