st: Comparing correlation from two separately weighted samples

[Andrew Mackinnon <andrew@biostats.com.au>]

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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