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st: Comparing correlation from two separately weighted samples


From   Andrew Mackinnon <andrew@biostats.com.au>
To   statalist@hsphsun2.harvard.edu
Subject   st: Comparing correlation from two separately weighted samples
Date   Thu, 28 Feb 2013 12:15:33 +1100

Dear Stata users,

I want to test whether correlation coefficients from two independent, separately weighted samples are significantly different. I assumed that using sampling weights with correlations would be straightforward but I now understand that this is not so (thanks to www.stata.com/support/faqs/statistics/estimate-correlations-with-survey-data/).

I have come up with two ways this might be done. The first would use Fisher's z transformation and use the design df rather than N in the formula for the se of the Fisher's z. The second idea is analogous to that recommended for estimating the significance of a weighted r, i.e., use svy: regress y x and svy: regress x y in each sample, and for each sample take the larger se of the two and use these to estimate the significance of the difference of the standardized regression coefficients.

Both of these approaches are essentially 'made up' - I haven't been able to find any formal recommendations for doing this. I'd be grateful for any comments about my proposed approaches, particularly the first which would be easy to implement. Equally, I'd be grateful for alternative, defensible solutions.

Andrew Mackinnon

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