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Hello I have 2 bivariate normal populations with correlation coefficients p1 and p2 respectively. I could easily obtain samples from both. I am interested in testing whether the difference in these correlations is a equal to c. In other words the null hypothesis is H0: p1 - p2 = c . I know you could test H0: p1 - p2 = 0 using fisher transformation but don't this this is possible for this case.

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  • $\begingroup$ Perhaps establish a confidence interval for the difference and see if it includes $c$? $\endgroup$ – mdewey Jan 1 at 16:53
  • $\begingroup$ How would you go about obtaining a confidence interval when you don't know the distribution of the estimator p1_hat - p2_hat? $\endgroup$ – bgsimeon Jan 1 at 22:43
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One approach might be to use confidence intervals. Suppose we have two coefficients $r_1$ and $r_2$ based on independent samples of $n_1$ and $n_2$ observations respectively. Transform each into the appropriate Fisher $z$. The the standard error of the difference $z_1 - z_2$ is

$$ \sqrt{\frac{1}{n_1 - 3} + \frac{1}{n_2 - 3}} $$

So a confidence interval can be established for any desired confidence coefficient by multiplying the standard error by the corresponding normal deviate and taking that value either side of $z_1 - z_2$. The convert back to the scale of $r$ if desired and check whether $c$ lies within the limits.

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