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 (email@example.com)