On Sun, 22 Oct 2000, dennis roberts wrote:
> don ... no wonder students go bananas in statistics ... if we "sink" to
> this level of discussion about a formula ... a formula that really has
> so little utility ... how much time do we spend on the really important
> ones?
I would have thought there were some distinctions to be made among (inter
alia) what may usefully be discussed in an introductory course, what might
usefully discussed in other courses, and technical points that might be
discussed between intructors at various levels.
You raised a technical point; I replied with respect to that
technicality. If you don't want to continue conversations about special
cases of the correlation coefficient, you needn't do so; but it is a tad
illogical to complain about having such a discussion at all, while
continuing to contribute to it.
> i would submit that for most intro courses ... where correlation is
> discussed prior to significance testing and/or effect sizes ... the
> comparison and points you are making here about the pb correlation
> FORMULA ... are totally irrelevant ...
I'm not sure that total irrelevance can in fact be shown: it seems to me
akin to the task of trying to "prove a negative".
> now, maybe at the end of the course ... one could lay out the most popular
> 25 formulas for things ... and then show connections between some of them
> ... that MIGHT be nice
>
> but WHEN correlation is discussed? to link that to a t test and/or
> effect size? or, even to bring to bring the formula into the
> conversation ... what is the rationale for doing so when the basic PPM
> formula handles all of this?
Ah. Now, YOU may be able easily to perceive some of these more arcane
characteristics of correlation coefficients, directly from "the basic PPM
formula" (although "the basic PPM formula" is not a well-defined term),
and even _I_ may be able to see some of them; it does not follow that
your (or my) STUDENTS will perceive all these interesting implications,
without their being explicitly mentioned, at least in passing.
> let's see
>
> i want to talk about the pb formula ... so as to show how IT relates to
> the two sample t test ...
Well, if you want to do that, why not?
> when i haven't even talked about the t test yet ...
Really? Why do you introduce this sequencing distraction into the
conversation? And if it disturbs you even to mention things you haven't
yet talked about, what prevents you from waiting until you have done?
> and i don't need the pb formula in the first place ... to find the
> correlation between two variables, one that happens to be dichotomous
Agreed. So what? Is your only interest (in presenting correlation in
the first place) to give students some new "thing" that can be
calculated, with no information about what such a quantity might mean,
or be equivalent to?
> as for your reference to glass and hopkins ... they say: "when one
> dichotomous variable ... is correlated with one continuous variable,
> the formula for the product-moment correlation coefficient CAN BE
> SIMPLIFIED .... [caps for emphasis ... ] ..."
>
> they don't say it HAS to be simplified nor do they say it should be
> simplified ...
Again, agreed. So? Are you taking the philosophical position that
anything not expressly insisted upon shall be forbidden?
> and, we all know of course that this statement ... has no practical
> meaning anymore
Which statement? That a formula can, under certain conditions, be
simplified (or otherwise re-expressed)? Again, sounds to me as though
you're trying to argue a negative, which puts you on pretty shaky logical
ground.
> and hasn't been so since the introduction of the
> simple hand held calculator ...
Dunno about "simple". If you want to adjust the correlation you have in
hand by adding one (or several) new cases to the data set, the adjustment
ain't easy with a SIMPLE calculator; and even with a less simple one,
more information about the detailed workings of alternative algorithms
may have some utility.
But speaking of calculators, and by extension of statistical software,
your position on this point would seem to imply that there's no utility
to presenting "the basic PPM formula" either. Just read the data into
Minitab (or SPSS or JMP or whatever) and press the button labelled
"correlation". No need to confuse students with formulas at all.
Is there?
> in what way is the formula simplified? it has been changed ... altered
> ... rearranged ... resubstituted for ... but, the normal context of
> using the word "simplified" in THIS specific case has been historically
> given in the form of ... it makes it easier to calculate ...
And so it does. Do you have a problem with making things easier to
calculate? It also makes certain connections easier to notice, a point
with which you seem to have violent disagreement.
> so, what it appears to me is that the rationale for showing the pb
> formula nowadays boils down to linking it to the two sample t test ...
_A_ rationale, surely. Possibly not the only imaginable one.
> which i suggest is a no brainer when, the pb formula does not have to
> be introduced in the first place
Which rather begs the question, What formula does (or, What formulas do)
have to be introduced in the first place? And why?
-- Don.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
