• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.117-132
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• 2007

In a $2\times2$ table showing binary agreement between two raters, it is known that Cohen's $\kappa$, a chance-corrected measure of agreement, has two paradoxes. $\kappa$ is substantially sensitive to raters' classification probabilities(marginal probabilities) and does not satisfy conditions as a chance-corrected measure of agreement. However, $\kappa$ and other established measures have a reasonable and similar value when each marginal distribution is close to 0.5. The objectives of this paper are to present a new measure of agreement, H, which resolves paradoxes of $\kappa$ by adjusting unbalanced marginal distributions and to compare the proposed measure with established measures through some examples.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1073-1084
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• 2009

For ordinal categorical $R{\times}R$ tables, a weighted measure of association, $H_{\omega}$, was proposed and its maximum likelihood estimator and asymptotic variance were drived. We redefined the last paradox of ${\kappa}$ and proved its relation to marginal distributions. We also introduced the new paradox of ${\kappa}$ and summaried the general relationships between ${\kappa}$ and marginal distributions.