# What Is Overall Agreement

October 15, 2021 3:43 amIt is important to note that in each of the three situations in Table 1, the pass percentages are the same for both examiners, and if both examiners are compared to a usual 2 × 2 test for matched data (McNemar test), there would be no difference between their performance; on the other hand, the agreement between the observers in the three situations is very different. The basic concept to understand is that the “agreement” quantifies the agreement between the two examiners for each of the “pairs” of marks and not the similarity of the overall percentage of success between the examiners. Some researchers have expressed concern about the tendency of κ to take for granted the frequencies of the observed categories, which may make them unreliable for measuring agreement in situations such as the diagnosis of rare diseases. In these situations, κ tends to underestimate the agreement on the rare category. [17] For this reason, κ is considered too conservative a measure of agreement. [18] Others[19][citation required] dispute the assertion that kappa “takes into account” the accidental agreement. To do this, an explicit model of how chance affects evaluators` decisions would be needed. The so-called random adjustment of kappa statistics presupposes that if it is not entirely certain, evaluators simply guess – a very unrealistic scenario. For example, suppose you are analyzing data from a group of 50 people applying for a grant. Each grant application was read by two readers and each reader said “yes” or “no” to the proposal. Suppose that the data to count disagreements are as follows, where A and B are readers, the data on the main diagonal of the matrix (a and d) count the number of matches, and the non-diagonal data (b and c) count the number of disagreements: the agreement between the measures refers to the degree of concordance between two (or more) sets of measures. Statistical methods to verify compliance are used to assess variability between evaluators or to decide whether one technique for measuring one variable can replace another. In this article, we look at the agreed statistical measures for different types of data and discuss the differences between these and those used to assess correlation.

If statistical significance is not a useful guide, what size of kappa reflects an appropriate match? Guidelines would be helpful, but factors other than matching can affect their size, making interpretation of a certain magnitude problematic. As Sim and Wright noted, two important factors are prevalence (are the codes equiprobable or do they vary their probabilities) and bias (are the marginal probabilities similar or different for both observers). When other things are the same, kappas are higher when the codes are equiprobable. On the other hand, kappas are higher when codes are distributed asymmetrically by both observers. Unlike variations in probability, the distorting effect is greater when the kappa is small than when it is large. [11]:261–262 Methods for evaluating the agreement between observers as a function of the type of variable measured and the number of observers Kappa assumes its theoretical maximum value of 1 only if the two observers distribute the codes equally, i.e. if the corresponding row and column totals are identical. . . .

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