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

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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

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