# Agreement Calculation

The basic measure for Inter-Rater`s reliability is a percentage agreement between advisors. Another factor is the number of codes. As the number of codes increases, kappas become higher. Based on a simulation study, Bakeman and colleagues concluded that for fallible observers, Kappa values were lower when codes were lower. And in accordance with Sim-Wright`s claim on prevalence, kappas were higher than the codes were about equal. Thus Bakeman et al. concluded that no Kappa value could be considered universally acceptable. [12]:357 They also provide a computer program that allows users to calculate values for Kappa that indicate the number of codes, their probability and the accuracy of the observer. If, for example, the codes and observers of the same probability, which are 85% accurate, are 0.49, 0.60, 0.66 and 0.69 if the number of codes 2, 3, 5 and 10 is 2, 3, 5 and 10. A serious error in this type of reliability between boards is that the random agreement does not take into account and overestimates the level of agreement. This is the main reason why the percentage of consent should not be used for scientific work (i.e. doctoral theses or scientific publications).

where in is the relative correspondence observed between advisors (identical to accuracy), and pe is the hypothetical probability of a random agreement, the observed data being used to calculate the probabilities of each observer who sees each category at random. If the advisors are in complete agreement, it`s the option “ 1″ „textstyle“ „kappa – 1.“ If there is no agreement between advisors who are not expected at random (as indicated by pe), the „textstyle“ option is given by the name „. The statistics may be negative,[6] which implies that there is no effective agreement between the two advisers or that the agreement is worse than by chance. Kappa is always smaller or equal to 1. A value of 1 implies a perfect match and values below 1 mean less than a perfect match. 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 of:[16] Suppose you have analyzed data about a group of 50 people applying for an allowance. Each grant proposal was read by two readers, and each reader said „yes“ or „no“ to the proposal. Suppose the data for the tally of disagreements were as follows, A and B being readers, the data on the main diagonal of the matrix (a and d) the number of agreements and the non-diagonal data (b and c) the number of disagreements count: we find that in the second case, they show a greater similarity between A and B , compared to the first. Indeed, if the percentage of agreement is the same, the percentage of agreement that would occur „by chance“ is much higher in the first case (0.54 vs. 0.46). Some researchers have expressed concern about the tendency to take into account the frequency of observed categories as circumstances, which may make it unreliable for measuring matches in situations such as the diagnosis of rare diseases. In these situations, the S tends to underestimate the agreement on the rare category. [17] This is why the degree of convergence is considered too conservative. [18] Others[19][citation necessary] dispute the assertion that kappa „takes into consideration“ the coincidence agreement. To do this effectively, an explicit model of the impact of chance on councillors` decisions would be needed.

The so-called random adjustment of Kappa`s statistics assumes that, if they are not entirely sure, the advisors simply guess – a very unrealistic scenario.