All of this standard deviation talk suggests it is a good time to ask a
question which has been bothering me for the last couple of years.....
Back in the "good old days" all (or at least most) of the undergraduate
statistics texts taught the standard deviation using ther "N-1" formula.
The "N" formula was perhaps mentioned in a footnote, but often not
mentioned at all...
Now, virtually all of the texts teach the "N" formula in the beginning
under descriptive stats, then introduce N-1 later under inferential.
I hate the new way of doing it, partly because I have to remember new
formulas but more because it seems to confuse the students.
Why the change? What was wrong with the old method?
My guess is that using the "N" formula allows one to use the z-score
formula for Pearson r (the z-score formula for r does not work if you use
N-1, a fact I unfortunately discovered in the middle of a lecture
demonstration...).
But - why use the z-score formula for r? The old covariance formula is far
more intuitive than the z-score formula. Yes - you can easily show how the
product of z-scores works the same way as covariance, but students really
don't grasp z-scores very well to begin with and it is hard for them to get
the translation back from z to covariance.
My guess is that texts want to use the z-score formulation for r because
it makes a smoother transation into multiple regression. But (sigh) I
don't think multiple regression really belongs in a 200-level intro stat
course....
Lots of room for answers and commentaries here....shoot away....
-- Jim
