Kappa is a way to measure agreements or reliability and to correct the frequency with which ratings might consent to chance. Cohens Kappa,[5] who works for two councillors, and Fleiss` Kappa,[6] an adaptation that works for any fixed number of councillors, improve the common likelihood that they would take into account the amount of agreement that could be expected by chance. The original versions suffered from the same problem as the probability of joints, as they treat the data as nominal and assume that the evaluations have no natural nature; if the data does have a rank (ordinal measurement value), this information is not fully taken into account in the measurements. Suppose we are dealing with “yes” and “no” answers and two councillors. Here are the ratings: Krippendorffs alpha[16][17] is a versatile statistic that evaluates the agreement between observers who categorize, evaluate or measure a certain number of objects against the values of a variable. It generalizes several specialized agreement coefficients by accepting any number of observers applicable to nominal, ordinal, interval and proportional levels of measurement, capable of processing missing and corrected data for small sample sizes. There are several formulas that can be used to calculate compliance limits. The simple formula that was specified in the previous paragraph and works well for sample sizes over 60,[14] is Step 5: Look for the average value for fractions in the Accord column. Average – (3/3 – 0/3 – 3/3 – 1/3 – 1/3) / 5 – 0.53 or 53%. Inter-Rater`s reliability for this example is 54%. where cj represents the degree to which the coder J systematically deviates from the average, and rcij represents the interaction between the subject gap and the code gap. The variances of the components in equations 5 and 6 are then used for the calculation of CCIs, using different combinations of these components based on the design of the study.

If the number of categories used is small (z.B. 2 or 3), the probability of 2 advisors agreeing by pure coincidence increases considerably. This is because the two advisors must limit themselves to the limited number of options available, which affects the overall agreement rate, not necessarily their propensity to enter into an “intrinsic” agreement (an agreement is considered “intrinsic” if not due to chance). Note that Cohens Kappa has only been applied to 2 advisors who evaluate exactly the same articles. As you can probably tell, calculating percentage agreements for more than a handful of advisors can quickly become tedious. For example, if you had 6 judges, you would have 16 pairs of pairs to calculate for each participant (use our combination calculator to find out how many pairs you would get for multiple judges). The resulting CCI is high, ICC – 0.96, indicating an excellent IRR for empathy assessments. Based on an incidental observation of the data in Table 5, this strong CCI is not surprising, as differences of opinion between coders in relation to the range of results observed in the study appear to be low and there does not appear to be any significant domain restrictions or serious breaches of normality.