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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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The impact of measurement error on Ferguson's δ. Graphical representation of the same 30 subjects, and their mutual comparisons, as in Figure 2, but now with a little measurement error added to their scores, resulting in different frequencies (fi) per score category.
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Figure 3: The impact of measurement error on Ferguson's δ. Graphical representation of the same 30 subjects, and their mutual comparisons, as in Figure 2, but now with a little measurement error added to their scores, resulting in different frequencies (fi) per score category.

Mentions: So far, we assumed an instrument without measurement error, an unrealistic situation. What will happen with Ferguson's δ when we introduce some error into the scores? We will continue with the sample of Example 2, and assume the scale is ordinal. In Example 3, however, we add some measurement error. In order to obtain scores between 1 and 10 with a 'good' reliability coefficient between 0.80 and 0.90, we add to the perfectly reliable (true) score of the subjects a normally distributed random (error) score with a mean of 0 and a standard deviation of 1. After summating the true score and the error score, we need to 'force' the scores into the score categories by rounding to the nearest integer and subsequently recode scores <1 into 1 and scores >10 into 10. The resulting total score turns out to have a variance of 9.91. The variance of the true score is 8.53, and the variance of the error score thus is 9.91 – 8.53 = 1.38. Hence, the reliability coefficient of the score is 8.53/9.91 = 0.86. The situation is shown in Figure 3. The number of non-different comparisons, (within the shaded cells), is 108. Using formula (2), Ferguson's δ is:


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

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

The impact of measurement error on Ferguson's δ. Graphical representation of the same 30 subjects, and their mutual comparisons, as in Figure 2, but now with a little measurement error added to their scores, resulting in different frequencies (fi) per score category.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: The impact of measurement error on Ferguson's δ. Graphical representation of the same 30 subjects, and their mutual comparisons, as in Figure 2, but now with a little measurement error added to their scores, resulting in different frequencies (fi) per score category.
Mentions: So far, we assumed an instrument without measurement error, an unrealistic situation. What will happen with Ferguson's δ when we introduce some error into the scores? We will continue with the sample of Example 2, and assume the scale is ordinal. In Example 3, however, we add some measurement error. In order to obtain scores between 1 and 10 with a 'good' reliability coefficient between 0.80 and 0.90, we add to the perfectly reliable (true) score of the subjects a normally distributed random (error) score with a mean of 0 and a standard deviation of 1. After summating the true score and the error score, we need to 'force' the scores into the score categories by rounding to the nearest integer and subsequently recode scores <1 into 1 and scores >10 into 10. The resulting total score turns out to have a variance of 9.91. The variance of the true score is 8.53, and the variance of the error score thus is 9.91 – 8.53 = 1.38. Hence, the reliability coefficient of the score is 8.53/9.91 = 0.86. The situation is shown in Figure 3. The number of non-different comparisons, (within the shaded cells), is 108. Using formula (2), Ferguson's δ is:

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