Measurement system analysis for categorical data: Agreement and kappa-type indices

The standard method for the assessment of the precision of measurement gauges -- the gauge R&R method -- is not applicable for measurement systems that measure on a nominal scale. For nominal measurements the agreement method can be used, which expresses precision in the form of an index named \kappa. This paper aims to provide a consistent framework for the kappa method, based on statistical modeling. The defined probability models are used to study the statistical properties of proposed estimators. Various alternative forms of \kappa are discussed, as well as their relationship to the so-called paradoxes of kappa.