Average is a human rights abuse

JME CoverThis article in the Journal of Medical Ethics was directed at Archi from the Editor of E&P, and has got me all thoughtful about how a simple understanding of statistics is essential to everyone, even those working with the judiciary.

The team writing this study reviewed the decisions of forensic physicians who were determining if the age of adolescents involved in French judicial proceedings for criminal or asylum purposes, looking to see if their decisions were supported by the best quality evidence. The key finding – that they often were not – seemed to frequently centre on the average.

Let me explain. If a wrist X-ray gives a skeletal age of 8 years 2 months … this isn’t true. It’s the average age of the folk who were x-rayed to make up the atlas. Some might have been 7 years, others 9 years 10 months. The ‘truth’ is most likely to be about 8yr 2m, but may be wildly different. The spread of ages is captured with the standard deviation, and about 95% of the ages will be within 2 standard deviations of the mean.

This is even more obvious if you take another example: the classroom. The ‘average’ mark might be 65%, but it won’t shock most to find that some pupils would score 40% and others 100%. The ‘true’ mark isn’t 65% – obviously.

So say you take a wrist X-ray, check for 3rd molars, and the average comes out at 18 years 3 months. The standard deviation might also tell you, within 95% certainty,  that the adolescent may be 15yrs 11 mth old. Is refusing asylum to this Рpotential Рchild then a human rights abuse because of a failure to understand statistics?

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