Hi Dennis et al.
The best reference concerning regression to the mean(rtm) is Dave Kenny!
Bookmark his homepage:
http://nw3.nai.net/~dakenny/kenny.htm
(Its an exciting one for still others reason than rtm )
Dave had finalized a book about rtm which he had started to write which the
late Don Campbell,
rtm is Don's favorite brainchild, despite its origins with Sir Francis
Galton.
See the regression artifact primer at Dave's homepage:
http://nw3.nai.net/~dakenny/rrtm.htm
>From the book's front page you'll see when rtm is relevant:
rtm= perfection-correlation.
So whenever the pre/post correlation is less than one rtm exists,
is what Don and Dave say.
But you have also to consider the reliability of the pre- and posttest.
Whenever the double correction for pre- and posttest reliability (correction
for
attenuation) leads to a correlation of one, rtm vanishes.
Dennis might be right that the pre/post means are relatively reliable.
We would need parallel test for the means to estimate how reliable actually
they are and need also the pre/post correlation for the means of classes or
schools, districts etc. (we have to be clear about the unit of analysis).
Guess that the attenuation corrected pre/post correlation with the *.means
will still be lower
than one, so rtm is seriously to consider.
Another point is fan-spread. This happens when the variance of the posttest
is greater than that of
the pretest, the correlation coefficient does not map that effect, it maps
only rank order changes.
(fan shrinkage is also possible..i.e. lower variance at post than at
pre-test).
Fan spread would map the Matthew effect.
Such an effect is only to be detected with a split-plot design.
And finally the true answer what happened there can only be given, when
you've assessed the causes for
the change(whatever is was,i.e. mean change, variance change,skew,and still
higher moment changes).
So these guys should map the causes, say as a variable z.
If x is pre and y post and you're able to demonstrate that
Ry(true).x(true),z(true)=1 ,
(this means that the multiple correlation of predicting the posttest true
score with a combination
of the pretest and the causes true scores equals one)
than rtm has completely disappeared.
A complicating factor to consider are ceiling and floor effects of pre- and
posttests, but not very
reasonable with most standardized tests used.(they would lead to nonlinear
change effects)
Nonlinear growth effects are also well-known from economics as the law of
diminishing returns.
Werner
Werner W. Wittmann;University of Mannheim; Germany;
e-mail: [EMAIL PROTECTED]
-----Ursprungliche Nachricht-----
Von: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]Im Auftrag von dennis roberts
Gesendet: Freitag, 12. Januar 2001 15:54
An: Gene Gallagher; [EMAIL PROTECTED]
Betreff: Re: MA MCAS statistical fallacy
At 01:12 PM 1/12/01 +0000, Gene Gallagher wrote:
>I do believe that regression to the mean is involved here.
i just reiterate that regression in this case ... involves a correlation
between two columns of MEANS ... means for schools OR means for districts
... and means do NOT change that much .... from year to year ... and
certainly ... schools with low or high means one year just CANNOT change
their position much
(this is certainly not true of individual students but ... none of this
discussion has anything directly to do with individual students ... only
means of schools or districts)
does anyone have any information from mass. directly in their reports ...
as to what the correlation is/was between the (for example) 4th grade means
for the schools 1 year and 4th grade means for the same schools the next
year??? or the same r value based on district means?
unless we know either of these two correlations ... we cannot talk
meaningfully about whether regression is important in this discussion ...
or not
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