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The Kappa statistic was defined as following: $\kappa = \displaystyle\frac{p_o-p_e}{1-p_e}$, where $ p_o = \displaystyle\sum_{i=1}^{k} p_{ii}$ is the observed agreement, and $p_c = \displaystyle\sum_{i=1}^{k} p_{i.} p_{.i}$ is the chance agreement.

I saw the following conclusion from a reference book: $Var(\kappa)=\frac{1}{N(1-p_e)^2}[p_e+p_e^2-\sum_{i=1}^{k} p_{i.}p_{.i}(p_{i.}+p_{.i})]$ and the mean $E(\kappa)$ of $\kappa$ is 0.

How to compute the variance of $\kappa$

math112358
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  • I am not sure what your question is but does this Q&A help? https://stats.stackexchange.com/questions/30604/computing-cohens-kappa-variance-and-standard-errors?rq=1 – mdewey Dec 10 '21 at 13:33
  • No, I want to prove the above conclusion. – math112358 Dec 10 '21 at 13:47

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