# Kappa Level of Agreement

It should be noted that for measurements of unusual conditions, the value of kappa is lower than that of common conditions, although the values of specificity and sensitivity remain the same. This property must be taken into account when interpreting kappa values. Again, this is just a fair level agreement. Note that although pathologists agree in 70% of cases, they are expected to have almost as high levels of agreement (62%) by chance only. We can look at the data in Table III with kappa (remember that N = 100): I have many references for kappa and the intraclass correlation coefficient that I have to sort. Interpretation of kappa value Landis & Koch (1977):<0 No correspondence0 — .20 Light.21 — .40 Fair.41 — .60 Moderate.61 — .80 Essential.81–1.0 Perfect If statistical significance is not a useful guide, what order of magnitude does kappa reflect an appropriate agreement? 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.

:261-262 If two binary variables are attempts by two individuals to measure the same thing, Cohen`s kappa (often simply called kappa) can be used as a measure of agreement between the two individuals. Once the kappa is calculated, the researcher will probably want to assess the importance of the kappa obtained by calculating the confidence intervals for the kappa obtained. Percentage match statistics are a direct measure, not an estimate. So there is no need for confidence intervals. However, kappa is an estimate of the reliability of the intervaluor and the confidence intervals are therefore of greater interest. Cohen`s kappa (κ) statistics are a randomly corrected method for assessing agreement (rather than association) between evaluators. Kappa is defined as: (19.3_agreement_Cohen.sas): Two radiologists evaluated 85 patients in terms of liver damage. The ratings were labeled on an ordinal scale as follows: The value for kappa is 0.16, indicating a low level of agreement. To better understand the conditional interpretation of the Cohen-Kappa coefficient, I followed the method of calculating the Cohen-Kappa coefficient proposed by Bakeman et al. (1997). The calculations make the simplistic assumption that both observers were equally accurate and impartial, that the codes were recognized with the same accuracy, that disagreements were equally likely, and that when prevalence varied, it was done with uniformly noted probabilities (Bakeman and Quera, 2011).

Note that Cohen`s kappa only measures the agreement between two evaluators. For a similar measure of agreement (Fleiss kappa) used when there are more than two evaluators, see Fleiss (1971). However, fleiss kappa is a multi-evaluator generalization of Scott`s Pi statistics, not Cohen`s kappa. Kappa is also used to compare machine learning performance, but the directional version known as Informedness or Youden`s J Statistics is considered better suited for supervised learning.  But how do you know if you have a high degree of agreement? To get the kappa standard error (SEκ), the following formula must be used: it is rare that we get a perfect match. Different people have different interpretations of what a good level of agreement is. At the bottom of this page is an interpretation provided on page 404 of DG Altman. Practical statistics for medical research. (1991) London England: Chapman and Hall. To calculate Kappa, you must first calculate the degree of agreement observed 20 disagreements come from Rater B, who chooses Yes and Rater A chooses No.

15 Disagreements come from Rater A, who chooses Yes and Councillor B votes No. The compliance value for interobserver assessments, expressed as the coefficient κ, was 0.9 for histological diagnosis and ranged from 0.7 to 0.75 for semi-quantitative immunohistochemical staining for all antibodies used in the study. Kappa measures the percentage of data values in the main diagonal of the table, and then adjusts those values for the match that one might expect by chance alone. where (f_{i+}) is the sum of the row (i^{th}) and (f_{+i}) is the sum of the column (i^{th}). Kappa`s statistic reads as follows: The groundbreaking work that introduces Kappa as a new technique was published in 1960 by Jacob Cohen in the journal Educational and Psychological Measurement.  The higher the prevalence, the lower the overall level of compliance. The level of agreement tends to decrease as prevalence increases. At the observer accuracy level .90, there are 33, 32 and 29 perfect match for equiprobability, moderately variable and extremely variable. 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 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.  For more information, see Restrictions. Cohen`s kappa, symbolized by the Greek lowercase letter κ (7), is a robust statistic useful for interrater or intrarater reliability tests. Similar to correlation coefficients, it can range from −1 to +1, where 0 represents the amount of correspondence that can be expected from chance, and 1 represents the perfect match between evaluators. Although kappa levels below 0 are possible, Cohen notes that they are unlikely in practice (8). As with all correlation statistics, kappa is a standardised value and is therefore interpreted in the same way in several studies. where fO is the number of chords observed between evaluators, fE is the number of chords expected at random, and N is the total number of observations. In essence, kappa answers the following question: What proportion of values that are not supposed to be chords (accidentally) are actually chords? What have we learned about Kappa? Kappa statistics are a measure of inter-evaluator reliability.

There is no absolute value for a good match and depends on the type of study. Be aware that in certain circumstances it is possible to have a good match, but a weak kappa. .