CDBC/BCAAN Education Bite – originally emailed April 12, 2024
I hope this could be helpful for trainees, or those who like a review of statistical concepts.
It seems counter-intuitive when index scores of 70, 71, and 72 lead to an overall composite score of 67. This has been called the composite score extremity effect. This effect accounts for the fact that imperfectly correlated scores are always more extreme (further from the population mean) than if you were to simply average the scores. As explained in Schneider (2016) –
Composite scores are more extreme when:
- The composite is made up of a higher number of individual scores
- The individual scores have a lower correlation with each other
- The individual scores are farther away from the mean
Schneider explains this in simple terms: “though it is unusual to have a particular deficit, it is even more unusual to have that deficit and several more. A composite score that summarizes all of these deficits would have to take this comparative rarity into account. It is for this reason that a composite score that consists of many low scores is lower than the average of those scores” (p. 8)
An important concept in this is regression to the mean. For a composite comprised of two similar subtests, where there is a low score on subtest A (70), the predicted score for subtest B might 78, due to regression to the mean. If the person scored 70 on both A and B, the composite would be under 70, as it is unusual for people to be equally extreme on both subtests. The technical/mathematical explanation can be found here starting on page 10.
References
Barnett, A.G., van der Pols, J.C., & Dobson, A.J. (2005). Regression to the mean: what it is and how to deal with it, International Journal of Epidemiology, 34(1), 215–220. https://doi.org/10.1093/ije/dyh299