Initial validation of an intelligent video surveillance system for automatic detection of dairy cattle lameness

Pi (pi) and kappa (kappa) 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 pi 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.

Since the introduction of Cohen's kappa as a chance-adjusted measure of agreement between two observers, several "paradoxes" in its interpretation have been pointed out. The difficulties occur because kappa not only measures agreement but is also affected in complex ways by the presence of bias between observers and by the distributions of data across the categories that are used ("prevalence"). In this paper, new indices that provide independent measures of bias and prevalence, as well as of observed agreement, are defined and a simple formula is derived that expresses kappa in terms of these three indices. When comparisons are made between agreement studies it can be misleading to report kappa values alone, and it is recommended that researchers also include quantitative indicators of bias and prevalence.