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] --- To make changes to your subscription contact: Bill Southerly ([EMAIL PROTECTED])
