To calculate pe (the probability of a random match), we find the following: If you have multiple evaluators, calculate the percentage match as follows: Suppose you analyze the data relating to 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. Assuming that the data on the number of disagreements were 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 data outside the diagonal (b and c) count the number of disagreements: it is important to note that in each of the three situations in Table 1, the pass percentages for both examiners are the same, and if both examiners were compared to a common test of 2 × 2 for the matched data (McNemar test), no difference between their performance would be found; On the other hand, the agreement between observers is very different in all three situations. The basic concept to understand here is that the “agreement” quantifies the concordance between the two examiners for each of the “pairs” of notes, rather than the similarity of the overall percentage of success between the examiners. The statistic κ can take values from − 1 to 1 and is interpreted somewhat arbitrarily as follows: 0 = correspondence equivalent to chance; 0.10–0.20 = slight chord; 0.21–0.40 = fair agreement; 0.41–0.60 = moderate approval; 0.61 to 0.80 = substantial agreement; 0.81–0.99 = near-perfect match; and 1.00 = perfect match. Negative values indicate that the observed match is worse than might be expected by chance. Another interpretation is that kappa levels below 0.60 indicate a significant degree of disagreement. Consider a situation in which we want to evaluate the correspondence between hemoglobin measurements (in g/dl) with a bedside hemoglobinometer and formal photometric laboratory technique in ten people [Table 3]. The Bland-Altman graph for these data shows the difference between the two methods for each person [Figure 1].
The mean difference between the values is 1.07 g/dL (with a standard deviation of 0.36 g/dL) and the compliance limits of 95% are 0.35 to 1.79. This implies that a particular person`s hemoglobin level, measured by photometry, can vary from the bedside hemoglobin level measured by the method from as low as 0.35 g/dl higher to 1.79 g/dl higher (this is the case in 95% of individuals; in 5% of individuals, variations could be outside these limits). This, of course, means that the two techniques cannot be used as a substitute for each other. It is important to note that there is no single criterion for what constitutes acceptable limits of agreement; This is a clinical decision that depends on the variable to be measured. where po is the observed relative agreement between the evaluators (identical to accuracy) and pe is the hypothetical probability of random matching, using the observed data to calculate the probabilities of each observer who randomly sees each category. If the evaluators completely agree, then κ = 1 {textstyle kappa =1}. If there is no correspondence between the evaluators, except for what would be expected by chance (as given by pe), κ = 0 {textstyle kappa =0}. It is possible that the statistics are negative[6], which means that there is no effective agreement between the two evaluators or that the match is worse than random. The statistical methods used to assess conformity vary according to the type of variable studied and the number of observers between whom agreement is sought. These are summarized in Table 2 and are explained below.
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 equipped or do they vary their probabilities) and bias (are the marginal probabilities similar or different for the two observers). When other things are the same, the kappas are higher when the codes are equipped. 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 Compliance limits = mean difference observed ± 1.96 × standard deviation of observed differences. The Cohen-Kappa coefficient (κ) is a statistic used to measure inter-evaluator reliability (and also intra-evaluator reliability) for qualitative (categorical) elements. [1] It is generally thought that this is a more robust measure than simply calculating the percentage of agreement, since κ takes into account the possibility that the agreement will occur randomly. There is controversy around Cohen`s kappa due to the difficulty of interpreting correspondence clues. Some researchers have suggested that it is conceptually easier to assess disagreements between elements.
[2] For more information, see Restrictions. For the three situations presented in Table 1, the use of the McNemar test (which is intended to compare the matched categorical data) would show no difference. However, this cannot be interpreted as evidence of a match. The McNemar test compares overall proportions; Therefore, any situation in which the overall proportion of the two examiners (e.B situations 1, 2 and 3 of Table 1) is similar would result in no difference. Similarly, the matched t-test compares the mean difference between two observations in a group. It can therefore be insignificant if the mean difference between the matched values is small, although the differences between two observers are important for individuals. There is often interest in whether measurements by two (sometimes more than two) different observers or two different techniques lead to similar results. .