Given a set of k-tuples ( x11, x12, . . ., x1k), ( x21, x22, . . ., x2k), . . ., and ( xn1, xn2, . . ., xnk), the extent of their association, or agreement, may be measured by means of the coefficient of concordance:

Where Ri is the sum of the ranks assigned to xi1, xi2, . . ., and xik when the x€™s with the second subscript 1 are ranked among themselves and so are the x€™s with the second subscript 2, . . ., and the x€™s with the second subscript k. What are the maximum and minimum values of W, and what do they reflect with respect to the agreement, or lack of agreement, of the values of the k random variables?

n r k(n1)12 kn(n2 1)