FBI Testimony on Microscopic Hair Analysis Contained Errors in at least 90% of Cases in Ongoing Review
https://www.documentcloud.org/documents/1996772-joint-press-...
Ditto bite-mark analysis:
https://phys.org/news/2015-05-fbi-hair-analysis-problems-rev...
Yet, this kind of "expert" testimony was accepted for years and years. People went to jail on the basis of flim-flam.
"Our facial recognition has over 90% accuracy" from the prosecution's expert can easily become "clearly guilty" in the jury room.
I found this article helpful to understand why 90% accurate isn't as good as it sounds: https://www.badscience.net/2009/02/datamining-would-be-lovel...
He goes I to more detail in his book, bad science with a more detailed explanation. It fools everyone because it is counterintuitive.
Most juries will have around half, perhaps more, who've done nothing at all mathematical since school 10-45 years previously and think percentages are in the difficult part of maths (ie it's more than basic arithmetic). HN is going to be very unrepresentative for numeracy. :)
You want them to achieve "beyond reasonable doubt" conclusions from probabilities, percentages, false positive rates and perhaps standard deviations, well you may as well be making your case in French or Ancient Greek that they can pick a few part-understood bits from.
Or hope for an eloquent statistician on the jury!
Often these numbers are given as percentages, and he says that most people (even the doctors and nurses administering the tests) don't really understand them, and that we should use natural numbers (as Ben Goldacre does in the example you provide).
He uses examples from cancer screening and HIV testing.
This. You will have a hard time contending with pretty graphs, confusing numbers and a guy with an impressive title/badge/degree explaining why you're guilty.
My point is that you get some bad evidence, some bad eye witnesses or profiles and you get convicted, especially if the judge or jury gets tricked by the media in general on how good the forensic science actually is.