Stop Working & Start Thinking by Jack Cohen & Graham Medley

Author:Jack Cohen & Graham Medley
Language: eng
Format: epub
Publisher: Taylor & Francis

8.2 Bayesian thinking

We are indebted to Gigerenzer’s book Adaptive Thinking1 for the first two examples in this section – and indeed for the realisation that we needed to put in a section about how statistics are easily misunderstood. We found two of the examples that he gives very persuasive, and have used them here. For more of the same, go to his book. Here we are concerned to show you that, even – perhaps especially – in the very important clinical areas he presents, the counsellors get their advice very seriously wrong. It’s like the contestant and the goats example in Ian Stewart’s introduction: it feels just as good when you’re sure and wrong.

The first example concerns young German men who, despite not having many sexual partners or injecting drugs, were diagnosed as HIV positive at a public clinic. They were deeply shocked, of course, and attended the post-test counselling. The counsellor told them that the test has a very low false-positive rate, about 1/20,000 – so they had a 99.99995% chance, virtually a certainty, of having the disease. A significant proportion of these young men then attempted to commit suicide, and a few succeeded. This was a very serious matter, all the more so in that the counsellors were misinterpreting the measurement.

There is another measurement, an important source of data: ‘How many men in this low-prevalence group actually had the disease?’ About 1/20,000. About the same rate as the false-positive, note. So the question was not ‘How likely is the test to have failed to be correct, this time, for you, Hans?’ as the counsellor believed. It was much more ‘Now let us think, Hans; are you the 1/20,000 of your peers who has the disease, or are you the 1/20,000 false-positive? I would say, as you stand before me, that you have about a 50% chance either way.’ And that would have made a great difference to what the men then did. Gigerenzer sent some of his young colleagues to these counsellors, claiming to have a positive HIV test, and asking for advice. All were told that their infection was ‘virtually certain’. They were then instructed to ask, ‘But what about the incidence in the general population?’ and were answered, ‘What has that got to do with your case?’ The counsellors couldn’t, for the most part, see that they were wrong in their assessments. It can’t make any difference to the odds of getting a goat or a car (Chapter 2, Section 2.3) to change your choice, can it? And the soldiers in the First War War (Chapter 3.4, Section 3.4) must have been more reckless, to increase the number of head injuries?

Here is another clinical example, about breast-cancer clinics. A woman goes to a clinic and a suspicious lump is found. A biopsy is taken, and she is told that it is ‘positive’. She is very worried, of course, and she gets counselling. ‘There are many kinds of lumps: cysts, and benign and malignant growths in the

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