Understanding Ferguson's delta: time to say good-bye?
Bottom Line: A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.
A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.
Mentions: Intuitively, it may already have been apparent that this example presents a maximally discriminative instrument: each subject is perfectly distinguished from all other subjects. Therefore, it comes as no surprise that δ is 1 (the maximum value). Figure 1 illustrates how δ is calculated: in a matrix n subjects (rows) are compared with the same n subjects (columns). In every cell of the matrix, one subject (from the rows) is compared to one subject (from the columns). Ferguson's δ classifies these comparisons as either the same (when i = j) or as different (when i ≠ j). In formula (1) we see n2 in the denominator: all possible (n × n) comparisons between the n subjects, all cells in Figure 1. In the numerator we see the expression , the sum of comparisons of each subject with his or her self: the shaded cells in Figure 1. The expression represents the between-subjects comparisons of different subjects: the white cells in Figure 1. If we re-write the formula of δ as