# The Inter-Annotator Agreement

Kappa will only address its maximum theoretical value of 1 if the two observers distribute codes in the same way, i.e. if the corresponding totals are the same. Everything else is less than a perfect match. Nevertheless, the maximum value Kappa could achieve helps, as uneven distributions help interpret the actual value received from Kappa. The equation for the maximum is:[16] Fleiss` kappa is a statistical measure for assessing the reliability of compliance between a fixed number of advisors when categorical evaluations are assigned to multiple positions or classified articles. This is a generalization of the Scotts pi (π) assessment metric for two annotators that have been extended to several annotators. While Scotts pi and Cohens Kappa work for only two advisors, Fleiss` Kappa works for any number of advisors who give categorical ratings for a fixed number of articles. In addition, not all advisors are required to comment on all articles. Therefore, the common probability of an agreement will remain high, even in the absence of an „intrinsic“ agreement between the councillors. A useful interrater reliability coefficient (a) is expected to be close to 0 if there is no „intrinsic“ agreement and (b) increased if the „intrinsic“ agreement rate improves.

Most probability-adjusted match coefficients achieve the first objective. However, the second objective is not achieved by many well-known measures that correct the odds. [4] kappa2 () is the function that gives you the actual inter-annotator chord. But it`s often a good idea to also draw a cross chart of annotators, so you get a perspective on the actual numbers: There are a number of statistics that can be used to determine interrater reliability. Different statistics are adapted to different types of measurement. Some options are the common probability of an agreement, Cohens Kappa, Scott`s pi and the Fleiss`Kappa associated with it, inter-rate correlation, correlation coefficient, intra-class correlation and Krippendorff alpha. If the number of categories used is small (z.B. 2 or 3), the probability of 2 advisors agreeing by pure coincidence increases considerably. This is because the two advisors must limit themselves to the limited number of options available, which affects the overall agreement rate, not necessarily their propensity to enter into an „intrinsic“ agreement (an agreement is considered „intrinsic“ if not due to chance). Cohens Kappa measures the agreement between two advisors who classify each of the N elements into exclusion categories C. The definition of „textstyle“ is as follows: the value of Kappa is therefore 0.826, which is actually quite high. Although the Kappa should always be interpreted with respect to the levels available in the category for which an intermediate note agreement is calculated, the basic rule is that there is no value above 0.8.

The weighted Kappa allows differences of opinion to be weighted differently[21] and is particularly useful when codes are ordered. [8]:66 Three matrixes are involved, the matrix of observed scores, the matrix of expected values based on random tuning and the weight matrix.