Volume 61, Issue 1 p. 29-48

Computing inter-rater reliability and its variance in the presence of high agreement

Kilem Li Gwet

Corresponding Author

Kilem Li Gwet

STATAXIS Consulting, Gaithersburg, USA

Correspondence should be addressed to Dr Kilem Li Gwet, Statistical Consultant, STATAXIS Consulting, PO Box 2696, Gaithersburg, MD 20886-2696, USA (e-mail: [email protected]).Search for more papers by this author
First published: 24 December 2010
Citations: 994


Pi (π) and kappa (κ) statistics are widely used in the areas of psychiatry and psychological testing to compute the extent of agreement between raters on nominally scaled data. It is a fact that these coefficients occasionally yield unexpected results in situations known as the paradoxes of kappa. This paper explores the origin of these limitations, and introduces an alternative and more stable agreement coefficient referred to as the AC1 coefficient. Also proposed are new variance estimators for the multiple-rater generalized π and AC1 statistics, whose validity does not depend upon the hypothesis of independence between raters. This is an improvement over existing alternative variances, which depend on the independence assumption. A Monte-Carlo simulation study demonstrates the validity of these variance estimators for confidence interval construction, and confirms the value of AC1 as an improved alternative to existing inter-rater reliability statistics.