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Observation: Cohen’s kappa takes into account disagreement between the two raters, but not the degree of disagreement. Since the figures are the same as in Example 1, once again kappa is. Determine how closely their answers agree. The following table shows their responses. On another occasion, the same group of students was asked the same question in an interview. The raters could also be two different measurement instruments, as in the next example.Įxample 3: A group of 50 college students are given a self-administered questionnaire and asked how often they have used recreational drugs in the past year: Often (more than 5 times), Seldom (1 to 4 times) and Never (0 times). Observation: In Example 1, ratings were made by people. 10625 (cell M9), and so the 95% confidence interval for kappa is (.28767. We see that the standard error of kappa is. The calculation of the standard error is shown in Figure 5.įigure 5 – Calculation of standard error and confidence interval The standard error is given by the formulaĮxample 2: Calculate the standard error for Cohen’s kappa of Example 1, and use this value to create a 95% confidence interval for kappa. Let n i = the number of subjects for which rater A chooses category i and m j = the number of subjects for which rater B chooses category j. Let n ij = the number of subjects for which rater A chooses category i and rater B chooses category j and p ij = n ij/ n. Observation: Provided and np a and n(1 –p a) are large enough (usually > 5), κ is normally distributed with an estimated standard error calculated as follows. There isn’t clear-cut agreement on what constitutes good or poor levels of agreement based on Cohen’s kappa, although a common, although not always so useful, set of criteria is: less than 0% no agreement, 0-20% poor, 20-40% fair, 40-60% moderate, 60-80% good, 80% or higher very good.Ī key assumption is that the judges act independently, an assumption that isn’t easy to satisfy completely in the real world. Thus, κ can take any negative value, although we are generally interested only in values of kappa between 0 and 1. Cohen’s kappa of 1 indicates perfect agreement between the raters and 0 indicates that any agreement is totally due to chance. Observation: Another way to calculate Cohen’s kappa is illustrated in Figure 4, which recalculates kappa for Example 1. Some key formulas in Figure 2 are shown in Figure 3.įigure 3 – Key formulas for worksheet in Figure 2ĭefinition 1: If p a = the proportion of observations in agreement and p ε = the proportion in agreement due to chance, then Cohen’s kappa isĪlternatively where n = number of subjects, n a = number of agreements and n ε = number of agreements due to chance. Subtracting out the agreement due to chance, we get that there is agreement 49.6% of the time, where
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In a similar way, we see that 11.04 of the Borderline agreements and 2.42 of the Neither agreements are due to chance, which means that a total of 18.26 of the diagnoses are due to chance. Thus 32% ∙ 30% = 9.6% of the agreement about this diagnosis is due to chance, i.e. Psychoses represents 16/50 = 32% of Judge 1’s diagnoses and 15/50 = 30% of Judge 2’s diagnoses.
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But this figure includes agreement that is due to chance. Thus the percentage of agreement is 34/50 = 68%. The diagnoses in agreement are located on the main diagonal of the table in Figure 1. We use Cohen’s kappa to measure the reliability of the diagnosis by measuring the agreement between the two judges, subtracting out agreement due to chance, as shown in Figure 2. We illustrate the technique via the following example.Įxample 1: Two psychologists (judges) evaluate 50 patients as to whether they are psychotic, borderline or neither. the category that a subject is assigned to) or they disagree there are no degrees of disagreement (i.e. The two raters either agree in their rating (i.e. Cohen’s kappa is a measure of the agreement between two raters who determine which category a finite number of subjects belong to whereby agreement due to chance is factored out.