Second, the researcher must indicate whether a good IRR should be characterized by absolute agreement or consistency in the evaluations. If it is important for evaluators to specify similar values in absolute value, then absolute correspondence should be used, while if it is more important for evaluators to provide values that are similar in priority, then consistency should be used. For example, imagine a programmer who typically provides low scores (e.B 1 to 5 on an 8-point Likert scale) and another coder who typically offers high scores (e.B. 4 to 8 on the same scale). The absolute consistency of these ratings could be expected to be low, as there were large discrepancies in the actual values of the ratings; However, it is possible that the consistency of these notations would be high if the ranking of these notations was similar between the two encoders. Lin`s concordance correlation coefficient (CCC) measures the correspondence between two variables as a deviation from the perfect linearity of the type y = x. Iota is an index of agreement between evaluators of quantitative or nominal multivariate observations. In the case of a categorical variable (a single list item), iota is reduced to the exact kappa coefficient of diligence (see above). Kappa`s statistics measure the degree of agreement observed between programmers for a series of nominal ratings and correct the expected match at random, providing a standardized IRR index that can be generalized to all studies. The degree of correspondence observed is determined by cross-tabulation dimensions for two encoders, and the expected random match is determined by the limit frequencies of the dimensions of each encoder. Kappa is calculated on the basis of the equation beforehand, we describe many statistical metrics, such as Cohen`s kappa @ref (cohen-s-kappa) and @ref-weighted kappa (weighted-kappa) to evaluate the agreement or concordance between two evaluators (judges, observers, clinicians) or two measurement methods.

Possible values for kappa statistics range from −1 to 1, where 1 indicates a perfect match, 0 indicates a completely random match, and −1 indicates a « perfect » match. Landis and Koch (1977) provide guidelines for the interpretation of kappa values, with values ranging from 0.0 to 0.2 indicating slight agreement, 0.21 to 0.40 indicating fair agreement, 0.41 to 0.60 indicating moderate agreement, 0.61 to 0.80 indicating substantial agreement, and 0.81 to 1.0 indicating near-perfect or perfect match. However, the use of these qualitative thresholds is discussed, and Krippendorff (1980) provides a more conservative interpretation suggesting that conclusions should be discarded for variables with values below 0.67, that conclusions should be provisionally drawn for values between 0.67 and 0.80, and that final conclusions should be drawn for values above 0.80. In practice, however, kappa coefficients are often kept in research studies below Krippendorff`s conservative threshold values, and Krippendorff proposes these thresholds based on his own content analysis work, recognizing that acceptable IRR estimates vary depending on the study methods and research question. CCC is also an inter-assessor measure called « compliance match » rather than « reliability » with inter-assessors. Numerically, however, ICC and CCC can be quite close to each other and sometimes differ to the third decimal place. For fully cross-bred designs with three or more encoders, Light (1971) proposes to calculate kappa for all pairs of encoders, and then use the arithmetic mean of these estimates to obtain an overall matching index. Davies and Fleiss (1982) propose a similar solution that uses the average P(e) between all encoder pairs to calculate kappa-like statistics for multiple encoders. Light and Davies and Fleiss solutions are not available in most statistics packages. However, Light`s solution can be easily implemented by calculating kappa for all pairs of encoders using statistical software and then manually calculating the arithmetic mean. In statistics, reliability between evaluators, agreement between evaluators or concordance is the degree of agreement between evaluators. There is an assessment of the homogeneity or consensus that there is in the assessments given by the judges.

Kappa statistics are used to assess the agreement between two or more evaluators if the measurement scale is categorical. In this brief summary, we discuss and interpret the main features of kappa statistics, the influence of prevalence on kappa statistics and their usefulness in clinical research. We also introduce weighted kappa if the result is ordinal, and intraclass correlation to assess the match in a case where the data is measured on a continuous scale. Although it was definitively rejected as an adequate measure for IRR (Cohen, 1960; Krippendorff, 1980), many researchers continue to report the percentage that programmers accept in their evaluations as an index of encoder correspondence. For categorical data, this can be expressed as the number of matches in the observations divided by the total number of observations. For ordinal, interval, or ratio data where a close but imperfect match may be acceptable, the percentages of the match are sometimes expressed as a percentage of the scores that correspond in a given interval. Perhaps the biggest criticism of match percentages is that they do not correct agreements that one would expect by chance, and therefore overestimate the level of agreement. For example, if programmers randomly rated 50% of subjects as « depressed » and 50% as « not depressed », regardless of the actual characteristics of the subject, the expected percentage of match would be 50%, although all overlapping grades are due to chance. If programmers randomly rated 10% of subjects as depressed and 90% as non-depressed, the expected percentage of match would be 82%, although this seemingly high level of agreement is still solely due to chance.

Kendall`s W ranges from 0 (no chord) to 1 (full chord). Kendall`s W does not assume normally distributed values and can handle an unlimited number of different results. .