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Understanding Ferguson's delta: time to say good-bye?

Terluin B, Knol DL, Terwee CB, de Vet HC - Health Qual Life Outcomes (2009)

Bottom Line: A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.

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ABSTRACT
A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.

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Graphical representation of how Ferguson's δ 'works'. Ferguson's δ counts comparisons between subjects. In this sample 10 subjects are mutually compared. The subjects have scores 1, 2, ... 9, 10 on an instrument with 10 score categories (i). The frequency (fi) is 1 for all i scores. The subjects are placed in a 10 × 10 matrix in which each cell comprises 1 comparison of 1 subject with another subject (white cells) or with itself (shaded cells). Ferguson's δ relates the number of discriminating comparisons between subjects (white cells) to all comparisons (all cells). See the text for the actual calculation of δ.
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Figure 1: Graphical representation of how Ferguson's δ 'works'. Ferguson's δ counts comparisons between subjects. In this sample 10 subjects are mutually compared. The subjects have scores 1, 2, ... 9, 10 on an instrument with 10 score categories (i). The frequency (fi) is 1 for all i scores. The subjects are placed in a 10 × 10 matrix in which each cell comprises 1 comparison of 1 subject with another subject (white cells) or with itself (shaded cells). Ferguson's δ relates the number of discriminating comparisons between subjects (white cells) to all comparisons (all cells). See the text for the actual calculation of δ.

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


Understanding Ferguson's delta: time to say good-bye?

Terluin B, Knol DL, Terwee CB, de Vet HC - Health Qual Life Outcomes (2009)

Graphical representation of how Ferguson's δ 'works'. Ferguson's δ counts comparisons between subjects. In this sample 10 subjects are mutually compared. The subjects have scores 1, 2, ... 9, 10 on an instrument with 10 score categories (i). The frequency (fi) is 1 for all i scores. The subjects are placed in a 10 × 10 matrix in which each cell comprises 1 comparison of 1 subject with another subject (white cells) or with itself (shaded cells). Ferguson's δ relates the number of discriminating comparisons between subjects (white cells) to all comparisons (all cells). See the text for the actual calculation of δ.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2691398&req=5

Figure 1: Graphical representation of how Ferguson's δ 'works'. Ferguson's δ counts comparisons between subjects. In this sample 10 subjects are mutually compared. The subjects have scores 1, 2, ... 9, 10 on an instrument with 10 score categories (i). The frequency (fi) is 1 for all i scores. The subjects are placed in a 10 × 10 matrix in which each cell comprises 1 comparison of 1 subject with another subject (white cells) or with itself (shaded cells). Ferguson's δ relates the number of discriminating comparisons between subjects (white cells) to all comparisons (all cells). See the text for the actual calculation of δ.
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

Bottom Line: A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.

View Article: PubMed Central - HTML - PubMed

ABSTRACT
A critique of Hankins, M: 'How discriminating are discriminative instruments?' Health and Quality of Life Outcomes 2008, 6:36.

Show MeSH