regression to the mean has NOTHING to do with raw numbers ... it ONLY has
to do with relative location withIN a distribution
example: i give a course final exam the first day ... and get scores (on
100 item test) from 10 to 40 ... and an alternate form of the final on the
last day ... and get scores 50 to 95 ... now, the LOWest score on the final
final is higher than the highest score on the first final ... ie, everyone
does at least better than the BEST first go round. the regression to the
mean issue is ... where are the ones who got close to 40 on the first test
... withIN the posttest distribution??? generally, we see some relative
dropping of POSITION ... overall ... on average ... but not in every single
case .. for example the one who got 40 on the first final could have
obtained THE 95 on the post final
the issue that has to be raised with respect to the baseball example is ...
are the two halves PARALLEL HALVES? ... like, parallel tests given at
essentially the same time? well, no, they are not. for parallel tests ...
if i give form A now and ... and hour later ... form B ... then there is no
reason to expect the distributions of A and B to be much different ... nor,
the individual examinees to earn much different scores on form A and form B
this is NOT the case in baseball ... or any sport where there is some
arbitrary division of 1/2 of the season versus the other half of the season ...
these are NOT like parallel tests given to the same examinees ... because
of many factors ...
1. weather is different in second 1/2 than first 1/2
2. players get injured differentially across the halves ... may not be in
first half but is in the second half (or vice versa)
3. the TEAMS you play may not balance out during the second half the same
way they did in the first half (better competition or worse competition)
4. etc. etc.
too many people forget that regression to the mean is in terms of position
.... NOT actual score values ... and only in the case where the 2
distributions are the same ... AND there is less than perfect r between the
two sets ... will there generally be not only a drop in relative position
(if you were at the top on first measurement) but, there will be a downward
change in score too ... and the reverse at the bottom ... BUT, unless both
conditions have been met ... then downward shifting in position could just
as likely be connected with an INCREASE in score ...
and in any case ... regression to the mean is just (as was said) a
description of what happens ... and not some explanation for a root cause ...
At 08:26 AM 7/16/01 -0400, Paige Miller wrote:
>EugeneGall wrote:
> >
> > Jordan Ellenberg, in today's Slate, PROVES that Bonds won't break the
> > HR record because of regression to the mean. The argument is a
> > little sloppy, but there is definitely some RTM involved:
> > "If our discussion above is correct, then hitters who
> > lead the major leagues in home runs at the All-Star break should
> > tend to decline in the second half of the season. ...
> > Of the 74 hitters involved (there are more hitters than years
> because of
> > ties) only 12 equaled their pre-break production in the second
> > half...
> > I'd be curious if reduction in the 1st half leaders was comparable to the
> > improvement in the 2nd half leaders.
> > The link:
> > http://slate.msn.com/math/01-07-12/math.asp
>
>This hardly "PROVES" anything. It is more a statement about what has
>happened in the past. Most people, including myself and probably the
>author you quote, believe it is likely to happen in the future for the
>exact same reasons as it did in the past.
>
>So Bonds will "tend to decline" in the 2nd half...and lets see, the
>record is 70, so if Bonds declines from 38 in the first half to 33 in
>the second half, well...there's a new record. I didn't read the article
>at SLATE, but based upon the quote you provide, you have gone way beyond
>what the author intended with that quote.
>
>--
>Paige Miller
>Eastman Kodak Company
>[EMAIL PROTECTED]
>
>"It's nothing until I call it!" -- Bill Klem, NL Umpire
>"When you get the choice to sit it out or dance,
> I hope you dance" -- Lee Ann Womack
>
>
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_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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