What Is Chance-Corrected Agreement
where fO is the number of agreements observed between evaluators, fE is the number of expected chords at random, and N is the total number of observations. Essentially, kappa answers the following question: What proportion of values that should not be (accidental) chords are actually chords? To calculate pe (the probability of a random match), we note the following: Nevertheless, size guidelines have appeared in the literature. The first were perhaps Landis and Koch, who characterized the values < 0 as no agreement and 0–0.20 as easy, 0.21–0.40 as fair, 0.41–0.60 as moderate, 0.61–0.80 as substantial, and 0.81–1 as near-perfect match. However, these guidelines are by no means generally accepted; Landis and Koch did not provide any supporting evidence, but instead based it on personal opinions. It has been found that these guidelines can be harmful rather than useful.  Diligence:218 Equally arbitrary guidelines characterize Kappas above 0.75 as excellent, 0.40 to 0.75 as just to good, and below 0.40 as bad. Gwet`s AC1 provides a reasonable chance-adjusted match coefficient equal to the degree of agreement as a percentage. Gwet  explained that one problem with Cohen`s kappa is that there is a very wide range for e(K) – from 0 to 1, depending on the marginal probability, despite the fact that e(K) values should not exceed 0.5. Gwet attributed this to the incorrect methods used in calculating the probability of random match for kappa . A randomly corrected chord measure takes into account the possibility of a random chord. The characteristic prevalence was calculated here based on the number of positive cases assessed by both assessors and then calculated as a percentage of the total number of cases and the reliability between the assessors (Tables 3, 4 and 5).
For example, when calculating the prevalence of avoidant PD in the VU-MN pair (Table 3), the number of cases in which the assessors matched was 5, which was calculated as a percentage of the total number of cases (19), resulting in a prevalence rate of 26.32%. Table 6 provided a summary of the comparison between Cohen`s kappa and Gwets AC1 values based on the prevalence rate for each PM. When the prevalence rate was higher, so was kappa and Cohen`s degree of agreement; In contrast, Gwet`s AC1 values did not change dramatically with prevalence compared to Cohen`s kappa, but remained close to the percentage of agreement. Clinicians must ensure that the measures they use are valid, and low reliability between evaluators leads to a lack of trust; For example, in this study, schizoid had a high percentage of match (88% – 100%) between 4 pairs of assessors; Therefore, a high level of reliability between evaluators is to be expected. However, Cohen`s kappa gave values of .565, .600, .737 and 1,000, while Gwets AC1 provided values of .757, .840, .820 and 1,000, documenting that a different level of agreement can be achieved when these different measurements are applied to the same data set. For example, according to landis and Koch`s criteria, Cohen`s Kappa value of 0.565 falls into the Moderate category, while Gwet`s AC1 value of 0.757 falls into the Substantial category (Table 7). A good level of agreement, regardless of the criteria used, is important for clinicians because it promotes confidence in the diagnoses made. To solve this problem, most clinical trials now express agreement among observers using kappa (κ-) statistics, which usually have values between 0 and 1. (The appendix at the end of this chapter shows how the statistics κ are calculated.) A κ value of 0 indicates that the observed match is the same as randomly expected, and a κ value of 1 indicates a perfect match. According to the convention, a value κ from 0 to 0.2 indicates a slight correspondence; 0.2 to 0.4 fair agreement; 0.4 to 0.6 moderate chord; 0.6 to 0.8 essential agreements; and 0.8 to 1.0 almost perfect match.† Rarely do physical signs have κ values below 0 (theoretically as low as -1), suggesting that the observed match was worse than the random chord. The overall probability of a random match is the probability that they accepted yes or no, i.e.
the Cohen-kappa coefficient (κ) is a statistic used to measure inter-evaluator reliability (and also intra-evaluator reliability) for qualitative (categorical) elements.  It is generally thought that this is a more robust measure than the simple calculation of the percentage of agreement, since κ takes into account the possibility that the agreement is concluded by chance. There is controversy around Cohen`s kappa because it is difficult to interpret the corresponding clues. Some researchers have suggested that it is conceptually easier to assess disagreements between elements.  For more information, see Restrictions. The structured clinical interview, based on the Diagnostic and Statistical Manual of Mental Disorders-IV – for Axis II Personality Disorders (SCID II) , is one of the standard tools for diagnosing personality disorders. Because this assessment leads to dichotomous outcomes, Cohen`s kappa [2, 3] is often used to assess the reliability of evaluators. Few studies have assessed cross-rater reliability with SCID II, but our recent report  found that the total kappa for the Thai version of SCID II is 0.80, ranging from 0.70 for depressive personality disorder to 0.90 for obsessive-compulsive personality disorder. However, some researchers have raised concerns about the low levels of kappa found for certain outcomes despite the high percentage of matching [4-6].
This problem was called the “kappa paradox” by Feinstein and Cicchetti , who noted: “In a paradox, a high observed chord value (in) can be significantly reduced by a significant imbalance in the limit sums of the table, vertically or horizontally. In the second paradox, the kappa will be more unbalanced with an asymmetric imbalance instead symmetrical in marginal sums and with imperfect rather than perfect symmetry in imbalance. A custom kappa solves neither problem and seems to make the second one worse. Di Eugenio and Glass  explained that κ is influenced by distorted distributions of categories (the problem of prevalence) and the extent to which coders disagree (the problem of bias). .