Looks like an issue of "restriction of range." .4 is not that different from .3. When you deal with the low group, there is probably little variability in there. The variability in the high group is exaggerated and it probably balanced out at .3 for the Total.

You basically probably took a heterogeneous group and made two homogenous subsets. Depending on your question of interest, homogenous subsets USUALLY yield poor rs. It's the same argument used to define why test scores are predictive of college grades. You might get a low association test-statistic between the two, but you have a restriction of range going on- only looking at the folks that went onto college. Would be more association if you had somehow measured everyone.

Zachary zfeinstein@harrisinteractive.com (952) 541-7161

-----Original Message----- From: Jude Cosgrove [mailto:Jude.cosgrove@erc.ie] Sent: Wednesday, December 03, 2003 3:27 AM To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: self-moderated correlation?

Hi,

Yes, it looks like it's non-linear. Have you tried plotting x and y, and trying OLS regression with Y and Y^2 as the explanatory variables? Are there other variables that might be mediating this relationship? E.g., could there be an interaction with a third variable that is moderating r?

Regards Jude

Jude Cosgrove Research Associate Educational Research Centre Drumcondra Dublin 9

jude.cosgrove@erc.ie

Ph +353 1 837 3789 Fax +353 1 837 8997

-----Original Message----- From: Antoon Smulders [mailto:a.smulders@beke.nl] Sent: 03 December 2003 09:21 To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: self-moderated correlation?

Hi, It seems to me that this is a non linear relationship. Are you sure the correlation "starts" exactly midway (at the median)? Antoon Smulders

----- Original Message ----- From: "Wim Beyers" <wim.beyers@psy.kuleuven.ac.be> Newsgroups: bit.listserv.spssx-l To: <SPSSX-L@LISTSERV.UGA.EDU> Sent: Wednesday, December 03, 2003 9:48 AM Subject: self-moderated correlation?

Dear all,

Suppose two observed variables X and Y, show a correlation of .30 in a sample of N = 500 (p < .0001). Now, for good theoretical and conceptual reasons, I split my sample in two equal (n = 250) parts, let's say using a median split of X. And again I calculate the correlation between X and Y, but now within both subsamples, low-x and high-x. Result: within low-x, r = 0 (ns); within high-x r = .40 (p < .0001). So, it looks like the correlation observed in the total sample is driven merely by half of this sample, namely those subjects with relatively high-x. And note, it's not that those with high-x are outliers in the total sample, they constitute half of the sample... I think this is an interesting finding. However, does it have a name (self-moderated correlation might be a suggestion) and did statisticians ever wrote about this phenonemon? Or is it an ignorable thing?

Thanks for all help and suggestions, Dr. Wim Beyers Belgium