Re: Correlation between pre scores and gain scores, regression to the mean

Oliver wrote:
r (pre, gain) > 0 if r(pre,post) * SD(post) - SD(pre) > 0.

For instance, if r (pre, post) = 0.75, SD(post) = 1.5 and SD(pre)=1,
then r(pre, gain) = 0.125.

That's COV(pre, gain), isn't it? Or did I slip up? I get r(pre, gain)
= 0.083.

in the formula above I only presented the nominator of r(pre, gain),
i.e. Cov(pre, gain), for simplicity, because if Cov(pre, gain) is
positive, r(pre, gain) is positive, too. In my example Cov(pre, gain)
is 0.125, indeed. To get r(pre, gain) I divide Cov(pre, gain) by
SD(pre) and SD(gain). Since - in the example - SD(pre) is equal to 1
and -

SD(gain) = SQRT(V(pre)+V(post)-2*r(pre,post)*SD(pre)*SD(post)) -

SD(gain) also is equal to 1, I get r(pre, gain) = 0.125.

Anyway, the correlation is positive.

Kind regards,

Oliver


Right you are. When computing r(pre, gain), I had SD(post) in the denominator where I should have had SD(gain).

--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

Relevant Pages