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

Multi tool use
Multi tool use

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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












    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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 30 at 6:52

























      asked Aug 30 at 6:40









      Slavskii Sergei

      112




      112

























          active

          oldest

          votes











          Your Answer




          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













           

          draft saved


          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2899209%2fsampling-error-of-correlation-coefficient-phi-coefficient-for-binary-variables%23new-answer', 'question_page');

          );

          Post as a guest



































          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















           

          draft saved


          draft discarded















































           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2899209%2fsampling-error-of-correlation-coefficient-phi-coefficient-for-binary-variables%23new-answer', 'question_page');

          );

          Post as a guest













































































          p8gYIGxTbMQlQ
          z0RRP3eWTWGca7vQfThyQM whSSzccdb8tPZUXeZF5D IQ,8J V,M3L,oV,Nh QPKl

          這個網誌中的熱門文章

          How to combine Bézier curves to a surface?

          Propositional logic and tautologies

          Distribution of Stopped Wiener Process with Stochastic Volatility