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I got a negative correlation value between two variables. Results of running Multiple hierarchical linear regression on the same variables indicated a positive beta coefficient between them. Explain with logic and literature reference how this is possible

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  • $\begingroup$ Say you have two clusters separated in such a manner that within these clusters the correlation between the two variables (examined separately in the clusters) is positive, but the centers of the clusters are situation such that the line between the centers is negative slope. That would lead to the observation you are seeing. Don't need any literature but if you want to search, use: "Simpson's Paradox" as your term. stats.stackexchange.com/search?q=Simpsons+paradox $\endgroup$ – DWin Mar 31 at 16:38
  • $\begingroup$ Actually I am about to write my discussion section for research and my supervisor was surprised at the reversal of signs. This sent me in to a panic that the results may be wrong. But I have since learnt that multiple hierarchical regression controls variables and correlation does not. I would be grateful for a link to a relevant article or research on this $\endgroup$ – Avid Researcher Mar 31 at 16:43
  • $\begingroup$ As I said searching on Simpsons Paradox is the right way to proceed. I'm sure you can find Simpsons original article is you really need a citation to the statistical literature, $\endgroup$ – DWin Mar 31 at 16:44
  • $\begingroup$ Also, I have read that Simpson's Paradox applies when the relationship was initially positive and then becomes negative. In my case, a positive Pearson correlation was obtained first that turned negative in multiple hierarchical linear regression $\endgroup$ – Avid Researcher Mar 31 at 16:50
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