Damned Statistics

Statistically speaking, far too few people have read the excellent book called How We Know What Isn’t So by Thomas Gilovich, Professor of Psychology at Cornell University. The book deals with the way that people are easily deceived into thinking that things are different to the way that they actually are, basically because people are very bad at interpreting statistics.
It’s very strong on certain types of ‘statistical illusion’ (my phrase, not the book’s).
This illusion is brought about because people fail to realise the statistical phenomenon of regression to the mean – a law that states that the further a quality or statistic drifts from its average or mean position the more likely it is to turn around and move back in the direction of the norm (as though itís on the end of a piece of elastic that tugs harder as it’s stretched further from the average position).
This has interesting consequences when analysing the effectiveness of such things as alternative medical treatments such as homeopathy or herbal medicine.
It works like this.
If a person has a chronic illness in which the symptoms periodically gets much worse, then the worse the symptoms are at any one moment the more likely the illness is to be nearing a peak – and thus the nearer it is to turning around and improving somewhat, simply because it has reached the extreme of how bad it’s going to get at present. Now it just happens that it’s when the symptoms of chronic illnesses get particularly bad that people are motivated to seek alternative forms of remedy for the illness. Once the alternative remedy has been administered the symptoms of the illness start to recede. The improvement is interpreted as being a direct result of the alternative treatment, while it is probably due to nothing more than the fact that the illness was at a peak and was about to recede anyway.
This doesn’t mean that alternative medicine doesn’t work, I must add – it simply means that the statistics that are gathered when the medicines are administered to patients who are undergoing a flair-up of their illness should be treated with extreme caution, or probably discarded.
It occurs to me that this tendency for administering alternative medicines specifically when an illness is peaking may explain a phenomenon that has puzzled me for some time – the alleged improvement in the health of animals when treated with homeopathic remedies (The argument goes that homeopathy must have a valid basis due to the fact that it works on animals which are immune to the suggestive powers of the placebo effect).
As a non-believer when it comes to homeopathy I often have arguments with friends who are advocates of the treatment – and these arguments inevitably involve the point that animals respond to homeopathic treatment. My usual response has always been that I don’t know why animals seem to respond, but that I suspect that either the statistics are faulty or that the animals are responding to something else that’s been overlooked. The next time I have the argument I’ll just say that the animals’ symptoms are simply regressing towards the mean. That’ll stump them!

Due to my scepticism when it comes to alternative remedies this explanation invoking regression to the mean is very appealing to me. However, as I mentioned, this point doesn’t necessarily invalidate alternative therapies, it simply means that statistics that are obtained when an illness is peaking should be ignored. My gleeful embracing of the argument may fall into one of the other categories of deception that the book deals with – the deception of believing arguments that tell you what you want to hear and that reinforce your own prejudices. Needless to say, I don’t believe that I’m falling into this trap, just as everyone else thinks they’re not.

Prompted by the book, I’ve noticed a statistical fallacy that applies in my own household, and that no doubt probably applies to domestic situations everywhere else too. You may be able to recognise it in your own life.
Here it is.
My partner is much more concerned about eating healthy food than I am.
As a result we eat a lot of salads and vegetables.
On the rare occasions that she’s away at mealtime I cook myself a lovely fry-up.
She has noticed this phenomenon, naturally (even though I open all of the windows to try to dissipate the smell long before she gets home).
As a result she thinks that if it wasn’t for her guidance over of my dietary habits I’d be eating unhealthy fry-ups all of the time. The statistics bear this out. When she’s not around I eat fry-ups 100% of the time.
Of course, I only eat fry-ups when she’s out specifically because it’s such a relatively rare occurrence, and it’s therefore a bit of a transgressive treat. I’d soon revert to salads and vegetables if she was away for more than a day.
But the statistics don’t show this underlying fact. They only show the 100% fry-up diet.
The statistics are absolutely correct, but they are also grossly misleading.
Damned Statistics


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