To calculate pe (the probability of a random agreement), we find that: Graham P, Bull B. Approximate standard errors and confidence intervals for positive and negative match indices. J Clin Epidemiol, 1998, 51(9), 763-771. In Table 2, the share of Category I-specific agreements is 2nii ps (i) – ———. (6) nor. Values a, b, c and here indicate the observed frequencies for each possible combination of ratings by Rater 1 and Rater 2. The overall agreement, for example, consider an epidemiological application in which a positive rating corresponds to a positive diagnosis for a very rare disease – one, say, with a prevalence of 1 in 1,000,000. Here, we may not be very impressed when Po is very high — even above .99. This result is almost exclusively due to an agreement on the absence of disease; We are not informed directly if the diagnosticians agree on the occurrence of diseases. Before continuing the completely general case, it will help to consider the simpler situation of estimating a specific positive agreement for several binary valuations. 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). Suppose you analyze data for a group of 50 people applying for a grant. 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) count the number of agreements and the non-diagonal data (b and c) the number of disagreements: in this contest, the judges agreed on 3 out of 5 points. The approval percentage is 3/5 – 60%. We find that it shows a greater resemblance between A and B in the second case, 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). Eq. (6) is like collapsing Table C × C in a table of 2×2 relative to category i, if this category is considered a “positive” rating, and then calculating Eq`s Positive Agreement Index (PA).