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Cohen's kappa measures the agreement between two raters who each classify N items into C mutually exclusive categories. The definition of is =, where p o is the relative observed agreement among raters, and p e is the hypothetical probability of chance agreement, using the observed data to calculate the probabilities of each observer randomly selecting each category.
Samples from the cosine variant of the bivariate von Mises distribution. The green points are sampled from a distribution with high concentration and no correlation (= =, =), the blue points are sampled from a distribution with high concentration and negative correlation (= =, =), and the red points are sampled from a distribution with low concentration and no correlation (= =, =).
Fleiss' kappa is a generalisation of Scott's pi statistic, [2] a statistical measure of inter-rater reliability. [3] It is also related to Cohen's kappa statistic and Youden's J statistic which may be more appropriate in certain instances. [4]
For finite >, the length of the expected value is strictly between zero and one and is a monotonic rising function of . The empirical mean ( arithmetic average ) of a collection of points on the unit hypersphere behaves in a similar manner, being close to the origin for widely spread data and close to the sphere for concentrated data.
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The von Mises probability density function for the angle x is given by: [2] (,) = ( ()) ()where I 0 is the modified Bessel function of the first kind of order 0, with this scaling constant chosen so that the distribution sums to unity: () = ().
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