What Does Agreement Mean in Statistics

The agreement`s limit approach was introduced in 1983 by English statisticians Martin Bland and Douglas Altman. The method became popular after the authors` 1986 article in The Lancet. This second article is one of the most cited statistical articles, cited more than 30,000 times. Kalantri et al. investigated the accuracy and reliability of Pallor as a tool for detecting anemia. [5] They concluded that “clinical evaluation of pallor may exclude and modestly regulate severe anemia.” However, inter-observer agreement for the detection of pallor was very low (kappa values = 0.07 for conjunctival pallor and 0.20 for pallor of the tongue), meaning that pallor is an unreliable sign of the diagnosis of anemia. Weighted kappa allows for different weighting of disagreements[21] and is especially useful when ordering codes. [8]:66 These are three matrices, the observed score matrix, the expected score matrix based on random matching, and the weight matrix. The cells of the weight matrix located on the diagonal (from top left to bottom right) represent the correspondence and therefore contain zeros.

Cells outside the diagonal contain weights that indicate the severity of this disagreement. Often, the one cells outside the diagonal are weighted with 1, these two with 2, etc. For example, studies on rating agreements are often used to evaluate a new rating system or instrument. If such a study is conducted during the development phase of the device, the data may be analyzed using methods that identify how the device could be modified to improve compliance. However, if an instrument is already in a final format, the same methods may not be useful. Since differences of opinion on the definition of characteristics and disagreements on the extent of evaluation categories are different components of disagreements with different practical implications, a statistical approach to the data should ideally quantify each individually. Click here for a list of statistical links, including links to pages related to agreement analysis. Cohen`s Kappa measures the agreement between two evaluators, each dividing N elements into C that divide mutually exclusive categories. The definition of κ {textstyle kappa } is: To calculate pe (the probability of a random match), we note that: Cohen`s κ can also be used when the same assessor assesses the same patients at two points in time (e.B.

at intervals of 2 weeks) or, in the example above, reassesses the same response sheets after 2 weeks. Its limitations are as follows: (i) it does not take into account the extent of the differences, which makes it unsuitable for ordinal data, (ii) it cannot be used if there are more than two evaluators, and (iii) it does not distinguish between agreement for positive and negative results – which can be important in clinical situations (for example. B, misdiagnosis of a disease or wrong exclusion may have different consequences). Category definitions, on the other hand, differ because evaluators divide the characteristic into different intervals. For example, an evaluator with “low qualifications” may mean subjects from the 1st to the 20th percentile. However, another evaluator may understand that they are subjects from the 1st to the 10th percentile. In this case, the assessor`s thresholds can generally be adjusted to improve compliance. The similarity of category definitions results in marginal homogeneity among evaluators.

Marginal homogeneity means that the frequencies (or the equivalent of “base interest rates”) at which two appraisers use different valuation categories are the same. The statistic κ can take values from − 1 to 1 and is interpreted somewhat arbitrarily as follows: 0 = correspondence which corresponds to chance; 0.10–0.20 = slight chord; 0.21–0.40 = fair agreement; 0.41–0.60 = moderate chord; 0.61–0.80 = essential agreement; 0.81–0.99 = near-perfect match; and 1.00 = perfect chord. 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 level of disagreement. We find that in the second case, it has a greater similarity between A and B than in the first. Indeed, although the percentage of agreement is the same, the percentage of agreement that would occur “randomly” is significantly higher in the first case (0.54 compared to 0.46). There is little consensus on the most suitable statistical methods for analyzing evaluator correspondence (here we will use the generic words “evaluators” and “evaluations” to provide observers, judges, diagnostic tests, etc. and include their evaluations/results.) For the non-statistician, the number of alternatives and the lack of consistency in the literature are undoubtedly worrying. This website aims to avoid confusion and help researchers choose appropriate methods for their applications. The statistical methods used to assess conformity vary according to the type of variable to be studied and the number of observers between whom a match is to be assessed. These are summarized in Table 2 and are explained below.

Of course, they could theoretically have done worse than was randomly expected. For example, in situation 3 [Table 1], although each of them passed 50% of the students, their grades corresponded to only 4 of the 20 students – much less than expected at random! Compliance limits = mean difference observed ± 1.96 × standard deviation of observed differences. For the three situations presented in Table 1, the use of the McNemar test (which aims to compare matched categorical data) would show no difference. However, this cannot be interpreted as evidence of an agreement. The McNemar test compares total percentages; Therefore, any situation in which the overall proportion of the two examiners passed/failed (e.B situations 1, 2 and 3 of Table 1) would lead to an absence of differences. Similarly, the matched t-test compares the mean difference between two observations in a group. It cannot therefore be significant if the mean difference between the matched values is small, although the differences between two observers are important for individuals. A characteristic definition can be considered as a weighted composition of several variables. Different evaluators may define or understand the characteristic as different weighted combinations.

For example, for an evaluator, intelligence can mean 50% verbal skills and 50% mathematical skills; On the other hand, it can mean 33% verbal skills, 33% math skills and 33% motor skills. Therefore, their essential definitions of what characteristic means differ. Similarity in the characteristic definitions of evaluators can be assessed using different estimates of the correlation of their ratings or similar measures of association. Kappa assumes its theoretical maximum value of 1 only if the two observers distribute the codes equally, that is, if the corresponding row and column totals are identical. Everything else is less than a perfect match. Nevertheless, the maximum value that kappa could achieve with uneven distributions helps to interpret the value actually obtained from kappa. The equation for κ maximum is as follows:[16] It is important to note that in each of the three situations in Table 1, the success rates of the two examiners are the same, and if both examiners are compared to a common test 2 × 2 for the matched data (mcNemar test), there would be no difference between their performance; On the other hand, the agreement between the observers is very different in the 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 total percentage of points passed between the examiners.

where po is the observed relative agreement between the evaluators (identical to the accuracy) and pe is the hypothetical probability of the random match, using the observed data to calculate the probabilities of each observer who randomly sees each category. If the evaluators completely match, then κ = 1 {textstyle kappa =1}. If there is no match between the evaluators other than what is expected randomly (as given by pe), κ = 0 {textstyle kappa =0}. It is possible that the statistic is negative[6], implying that there is no effective match between the two evaluators or that the match is worse than random. Some researchers have expressed concern about the tendency of κ to take for granted the frequencies of the observed categories, which can make the agreement unreliable 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 degree of agreement. [18] Others[19] dispute the claim that kappa “takes into account” a random 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 evaluators, if they are not quite sure, 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 the data on the number of disagreements are as follows, where A and B are readers, the data on the main diagonal of the matrix (a and d) the number of matches and the data outside the diagonal (b and c) count the number of disagreements: Imagine two ophthalmologists measuring intraocular pressure with a tonometer. Each patient thus receives two measured values – one from each observer. CCI provides an estimate of the overall concordance between these measures. It is similar in some respects to “analysis of variance” in that it examines differences between pairs expressed as a proportion of the overall variance of observations (i.e., the total variability of “2n” observations, which should be the sum of variances within and between pairs). .