In the right-hand column, we have taken the liberty of summing the ranks for each therapist. If there were perfect agreement among the observers, then therapist A would be ranked first by everyone, and therapist F would be ranked last by all. Thus, the summed rank for A would be 1 X (number of observers)—in this case 3—and for F would be (number of therapists) X (number of observers) = 6 X 3 = 18. By contrast, if there were no association, then every summed rank would end up about the same. So one measure of the degree of association would be to determine the difference between individual rank sums and the mean rank sum. Of course, statisticians have a reflex response to square every difference they encounter, and this case is no exception. The starting point in calculating Kendall's W is to determine the summed rank for each case and the average summed rank, take the difference for each case, and add up the square of all the differences.
In our example, the average summed rank is
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