Sampling error of correlation coefficient (Phi coefficient) for binary variables

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Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $rho$ .

Is there any analytic function for sampling error of correlation coefficient if I have finite sample from the population?



I've tried to use Fisher z-transformation, with sampling variance estimation of $1/N$ but it gives inappropriate (lower than actual) estimation of variance. As my simulations show, sampling error of Phi coefficient is a function of population correlation coefficient, frequencies of both binary variables and of course sample size.



Thanks in advance!










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    up vote
    2
    down vote

    favorite












    Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $rho$ .

    Is there any analytic function for sampling error of correlation coefficient if I have finite sample from the population?



    I've tried to use Fisher z-transformation, with sampling variance estimation of $1/N$ but it gives inappropriate (lower than actual) estimation of variance. As my simulations show, sampling error of Phi coefficient is a function of population correlation coefficient, frequencies of both binary variables and of course sample size.



    Thanks in advance!










    share|cite|improve this question

























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $rho$ .

      Is there any analytic function for sampling error of correlation coefficient if I have finite sample from the population?



      I've tried to use Fisher z-transformation, with sampling variance estimation of $1/N$ but it gives inappropriate (lower than actual) estimation of variance. As my simulations show, sampling error of Phi coefficient is a function of population correlation coefficient, frequencies of both binary variables and of course sample size.



      Thanks in advance!










      share|cite|improve this question















      Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $rho$ .

      Is there any analytic function for sampling error of correlation coefficient if I have finite sample from the population?



      I've tried to use Fisher z-transformation, with sampling variance estimation of $1/N$ but it gives inappropriate (lower than actual) estimation of variance. As my simulations show, sampling error of Phi coefficient is a function of population correlation coefficient, frequencies of both binary variables and of course sample size.



      Thanks in advance!







      statistics statistical-inference correlation






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      edited Aug 30 at 6:52

























      asked Aug 30 at 6:40









      Slavskii Sergei

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