On Fri, 30 May 2008 12:56:41 -0700, Jim Clark wrote:
>I guess I do not understand the concerns about this correction (or 
>the mention of a similar concern about ANCOVA) raised by Mike. 

Consider:
One form of the formula for the Pearson r is following:

r = cova(X,Y)/[SD(X) * SD(Y)]

where
cova(X,Y) is the covaraince of X and Y
SD(X) is the standard deviation of X, and
SD(Y) is the standard deviation of Y

In the classic restriction of range situation both SD(X)
and SD(Y) are underestimates of the the population 
standard deviation.  Using knowledge of the sample SD
and its relationship to the population SD might correct
for the restriction of range of values in the sample.
However, if only SD(X) is restricted (e.g, SAT > 1200)
and SD(Y) is an unrestricted estimate of the population
standard deviation, what happens?  Assume SD(X)=50
in the restricted sample but in the population SD(X)=100.
What would happen to r above if we inserted the population
value for X into the equation?  Counterintuitive, no?

What is really going on if there is restriction of range only for
one variable?

-Mike Palij
New York University
[EMAIL PROTECTED]






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