in the pre to post example i gave ... we saw that higher scoring students
on a pretest can GAIN MORE than lower scoring students on a pretest ...
there, we looked at RAW data ... and RAW gains (ie, there was a + r between
pre and gain)
now, both pre and post tests could have been put in a position measure like
ranks ... and you would have seen data like
Row rankpre rankpost
1 1.0 4.0
2 2.5 5.5
3 2.5 13.5
4 5.0 7.0
5 5.0 13.5
6 5.0 5.5
7 7.5 18.5
8 7.5 2.5
9 10.5 1.0
10 10.5 13.5
11 10.5 24.0
12 10.5 2.5
13 13.5 30.0
14 13.5 20.5
15 15.0 9.0
16 16.5 10.5
17 16.5 10.5
18 19.5 8.0
19 19.5 18.5
20 19.5 20.5
21 19.5 22.0
22 23.5 16.0
23 23.5 17.0
24 23.5 13.5
25 23.5 26.5
26 26.0 23.0
27 27.5 28.0
28 27.5 29.0
29 29.0 26.5
30 30.0 25.0
now, if you take the top 6 ... average their pre and post ranks ... you get
3.5 and about 8.2 respectively ... a DROP ON AVERAGE IN RANK
if you take the bottom 6 and do the same thing ... we see 27.25 and 26.3
... or a gain UPward on average of about 1 rank point ...
this is what we normally mean and jump to the conclusion to interpret RTM
as ... highs drop and lows go up ...
but this is in terms of RELATIVE POSITION ... because we clearly saw in the
previous data ... that the highs GAINED MORE and the lows GAINED LESS
again, it is very important to keep in mind that RTM relates to positions
... relative positions ... not raw scores
At 01:30 PM 1/17/01 +0000, you wrote:
>On 17 Jan 2001 01:49:33 GMT, Elliot Cramer <[EMAIL PROTECTED]>
>wrote:
>
> >There seems to be some confusion about what regression to the mean
> >means. Noone is penalized (or advantaged) because of regression to the
> >mean. You ALWAYS have RTM in a population whether everyone improves or
> >gets worse. It is a property of standardized scores only for a
> >population. The simplest explanation is in terms of the regression
> >equation for standardized scores
> >
> >E(z2) = rz1
> >
> >For positive r<1 if you select individuals with a given z1, their average
> >z2 will be smaller than z2 (in absolute value)
> >
> >Thus Galton found that the offspring of his geniuses regressed towards
> >mediocrity. He apparently thought it was a law of nature rather than a
> >law of statistics. If he had studied the feeble-minded we would not have
> >a technique called regression analysis
>
>OTOH, assuming Galton had used a subject set from a different locus on
>the IQ scale: if these so-called mentally challenged subjects
>reproduced themselves, their offspring might indeed tend to move
>toward the mean, i.e., higher on the IQ scale, right? Would this not
>be the same as the offspring of either the very tall or the very short
>among us moving toward an arithmetic average? Is it inconceivable
>that a pair of dullards could produce a Beethoven or a Fermi for
>example? Frankly, I believe old Sir Frances was on to something here.
>:-)
>
>
>
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