STATISTICS: EXPOSED AT LAST

Why can’t all those professors of medical statistics give governments sound, or at least consistent advice about the Covid pandemic? I am sorry to say it is because Statistics is deeply flawed in its very foundations.

I taught Statistics at university for 30 years, at first with zeal, then with growing puzzlement, finally with disillusion. Towards the end I couldn’t bring myself to teach the students “Hypothesis Testing” — the central ambition of the whole enterprise.

Collecting data is fine: the more the merrier. Analysing that data in search of useful information is essential. But turning information into a wise recommendation for action turns out to be fiendishly difficult. Why? Because the real world is far more complicated than the artificial world of card-playing, from which Probability Theory evolved long ago. And at its heart Statistics is the application of Probability Theory to real situations — like outbreaks of Corona Virus.

The problem is this: in a card game there are 52 cards so that all possible combinations of cards can be imagined — and calculated. But in the real world the combinations are infinite and so incalculable. Faced with this absolute road-block professional statisticians try to fudge their way round it by “making approximations” that is to say by pretending that arcane mathematical results drawn from card-play still apply approximately to a world of awkward germs, and bloody awkward people.

But mostly they don’t, We scientists know that there are such things in the real world as Systematic Errors, that is to say misconceptions which no amount calculation, or approximation, can ever surmount. Take one example: earthquake waves travel through the Earth arguing that it must be rigid. The great guru of geophysics at Cambridge University, Harold Jeffreys ,used it to maintain that therefore Continental Drift must be impossible — holding back the subject for 50 years. But he was making a Systematic error in assuming that because rock was rigid on a timescale of seconds (waves) it must likewise be rigid on a timescale of millions of years. Had he gone for a walk on a beach in say Pembrokeshire, and seen the dramatic folding of the rocks, he would have realised he was talking nonsense.

Ironically, in his case, one ghastly mistake led to another. Sir Harold, as he became, morphed alas into an even greater guru — on the subject of The Scientific Method, and founder of the school of “Objective Bayesian Statistics” — which is highly fashionable in academic circles today. But wrong, as Henri Poincare’ argued in the nineteenth century.

Once one knows what to look for (but only then) it’s not difficult to spot the flaws in the all-too-many (to be healthy,) text-books of Statistics, . For instance:

a) They pretend that Systematic Errors do not exist.

b) They use mathematical notions such as “The Normal Distribution”, and misapply them to the real world, justifying what they are doing by appealing to the ‘Central Limit Theorem’ — which most appear not to understand.

c) They disagree violently among themselves, and divide into many schools — which explains those all-too-numerous textbooks on the subject

d) They hardly ever come up with sound insights which couldn’t have been reached anyway using plain Common Sense (e.g. Smoking and Lung Cancer).

WHAT SHOULD WE DO ABOUT IT?

It’s all very well criticising Statistics, but what are we to do about it in the present crisis? I suggest:

1) We should listen to Statistician’s advice, but grant it only the same degree of respect we would accord to Economist’s predictions. Neither are remotely scientists.

2) We should disregard all academic titles like Professor or Doctor because they have become meaningless nowadays. Shameless grade inflation in British academe is a scam for demanding unearned respect from the public and unearned rents from the young and vulnerable. No one fails a doctorate nowadays whilst you can now become a professor by filling in a form and have your colleagues (who all want to become ‘Professors’ too of course) countersign it.

3) We should all take a crash course in Common Sense Thinking so that we could do that very needful Hypothesis Testing for ourselves, but soundly.

All these matters are covered in considerable detail in Thinking For Ourselves (described elsewhere on this site. It supplies many worked examples and some exercises with answers.) Practically anyone literate should be able to understand it while technical types will benefit from learning why they don’t need to learn Statistics.

Meanwhile there are two addenda attached to this post. A more technical survey with references, on the weaknesses of Statistics at:

https://mjdisney.org/wp-content/uploads/2020/10/statsdead.pdf

And a shortish extract from my book Thinking for Ourselves explaining why we have all, me especially, struggled so long with this tendentious and difficult subject, at :

https://mjdisney.org/wp-content/uploads/2020/10/apolstat.pdf

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