Brandi,
This topic is covered in Appendix C of this book:
Wolter, K.M. (2007). Introduction to Variance Estimation, 2nd edition. Springer-Verlag.
Compute Fisher's z in the standard way:
z = (1/2) ln[ (1 + \hat{r}) / (1 - \hat{r}) ]
where \hat{r} is the estimate of the correlation that uses the survey weights.
Then, put a confidence interval on z and back-transform the endpoints to the correlation scale.
If the confidence level is 0.95 and the first-stage sample is large, the normal approximation interval based on z would be
z +/- 1.96 sqrt{ v(z) }
where v(z) is a variance estimate for z that accounts for the complex sample design. The easiest way to estimate v(z) is probably some kind of replication, like the jackknife or bootstrap. Using a multiplier from a t-distribution (instead of 1.96) would give a more conservative (wider) interval.
The back-transform, which you apply to the endpoints, is
r = [ (exp(2z) - 1 ] / [ (exp(2z) + 1 ]
rv
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Richard Valliant
University of Michigan
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Original Message:
Sent: 11-05-2018 14:24
From: Brandy Sinco
Subject: Fishers r to z transform for complex survey data
Robert,
Thanks for the article link. I'm trying to find an article that adapts Fisher's formula for a complex sample design with weighting, stratification, and clustering.
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Brandy Sinco, BS, MA, MS
Statistician and Programmer/Analyst
Original Message:
Sent: 11-03-2018 11:32
From: Robert Lucas
Subject: Fishers r to z transform for complex survey data
Brandi, I think this may be what you are looking for.
-
Fisher, R. A. (1921), "On the 'Probable Error' of a Coefficient of Correlation Deduced from a Small Sample," Metron, 1, 3–32.
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Robert Lucas
Principal
Robert M. Lucas Consulting
Original Message:
Sent: 11-01-2018 09:15
From: Brandy Sinco
Subject: Fishers r to z transform for complex survey data
Dear ASA Colleagues:
Does anyone have suggestions for references on computing Fishers r to z transformation for data from a complex survey sample with weights, strata, and clusters?
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Brandy Sinco, BS, MA, MS
Statistician and Programmer/Analyst
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