Bad Science

Now that you appreciate the value of statistics – the benefits and risks of intuition – we can look at how these numbers and calculations are repeatedly misused and misunderstood. Our first examples will come from the world of journalism, but the true horror is that journalists are not the only ones to make basic errors of reasoning.

Numbers, as we will see, can ruin lives. The biggest statistic

Newspapers like big numbers and eye-catching headlines. They need miracle cures and hidden scares, and small percentage shifts in risk will never be enough for them to sell readers to advertisers (because that is the business model). To this end they pick the single most melodramatic and misleading way of describing any statistical increase in risk, which is called the ‘relative risk increase’.

Let’s say the risk of having a heart attack in your fifties is 50 per cent higher if you have high cholesterol. That sounds pretty bad. Let’s say the extra risk of having a heart attack if you have high cholesterol is only 2 per cent. That sounds OK to me. But they’re the same (hypothetical) figures. Let’s try this. Out of a hundred men in their fifties with normal cholesterol, four will be expected to have a heart attack; whereas out of a hundred men with high cholesterol, six will be expected to have a heart attack. That’s two extra heart attacks per hundred. Those are called ‘natural frequencies’.

Natural frequencies are readily understandable, because instead of using probabilities, or percentages, or anything even slightly technical or difficult, they use concrete numbers, just like the ones you use every day to check if you’ve lost a kid on a coach trip, or got the right change in a shop. Lots of people have argued that we evolved to reason and do maths with concrete numbers like these, and not with probabilities, so we find them more intuitive. Simple numbers are simple.

The other methods of describing the increase have names too. From our example above, with high cholesterol, you could have a 50 per cent increase in risk (the ‘relative risk increase’); or a 2 per cent increase in risk (the ‘absolute risk increase’); or, let me ram it home, the easy one, the informative one, an extra two heart attacks for every hundred men, the natural frequency.

As well as being the most comprehensible option, natural frequencies also contain more information than the journalists’ ‘relative risk increase’. Recently, for example, we were told that red meat causes bowel cancer, and ibuprofen increases the risk of heart attacks: but if you followed the news reports, you would be no wiser. Try this, on bowel cancer, from the Today programme on Radio 4: ‘A bigger risk meaning what, Professor Bingham?’ ‘A third higher risk.’ ‘That sounds an awful lot, a third higher risk; what are we talking about in terms of numbers here?’ ‘A difference … of around about twenty people per year.’ ‘So it’s still a small number?’ ‘Umm … per 10,000 …’

These things are hard to communicate if you step outside of the simplest format. Professor Sheila Bingham is Director of the MRC Centre for Nutrition in Cancer Epidemiology Prevention and Survival at the University of Cambridge, and deals with these numbers for a living, but in this (entirely forgivable) fumbling on a live radio show she is not alone: there are studies of doctors, and commissioning committees for local health authorities, and members of the legal profession, which show that people who interpret and manage risk for a living often have huge difficulties expressing what they mean on the spot. They are also much more likely to make the right decision when information about risk is presented as natural frequencies, rather than as probabilities or percentages.

For painkillers and heart attacks, another front-page story, the desperate urge to choose the biggest possible number led to the figures being completely inaccurate, in many newspapers. The reports were based on a study that had observed participants over four years, and the results suggested, using natural frequencies, that you would expect one extra heart attack for every 1,005 people taking ibuprofen. Or as the Daily Mail, in an article titled ‘How Pills for Your Headache Could Kill’, reported: ‘British research revealed that patients taking ibuprofen to treat arthritis face a 24 per cent increased risk of suffering a heart attack.’ Feel the fear.

Almost everyone reported the relative risk increases: diclofenac increases the risk of heart attack by 55 per cent, ibuprofen by 24 per cent. Only the Daily Telegraph and the Evening Standard reported the natural frequencies: one extra heart attack in 1,005 people on ibuprofen. The Mirror, meanwhile, tried and failed, reporting that one in 1,005 people on ibuprofen ‘will suffer heart failure over the following year’. No. It’s heart attack, not heart failure, and it’s one extra person in 1,005, on top of the heart attacks you’d get anyway. Several other papers repeated the same mistake.

Often it’s the fault of the press releases, and academics can themselves be as guilty as the rest when it comes to overdramatising their research (there are excellent best-practice guidelines from the Royal Society on communicating research, if you are interested). But if anyone in a position of power is reading this, here is the information I would like from a newspaper, to help me make decisions about my health, when reporting on a risk: I want to know who you’re talking about (e.g. men in their fifties); I want to know what the baseline risk is (e.g. four men out of a hundred will have a heart attack over ten years); and I want to know what the increase in risk is, as a natural frequency (two extra men out of that hundred will have a heart attack over ten years). I also want to know exactly what’s causing that increase in risk – an occasional headache pill or a daily tub full of pain-relieving medication for arthritis. Then I will consider reading your newspapers again, instead of blogs which are written by people who understand research, and which link reliably back to the original academic paper, so that I can double- check their precis when I wish.

Over a hundred years ago, H.G. Wells said that statistical thinking would one day be as important as the ability to read and write in a modern technological society. I disagree; probabilistic reasoning is difficult for everyone, but everyone understands normal numbers. This is why ‘natural frequencies’ are the only sensible way to communicate risk. Choosing your figures

Sometimes the mispresentation of figures goes so far beyond reality that you can only assume mendacity. Often these situations seem to involve morality: drugs, abortion and the rest. With very careful selection of numbers, in what some might consider to be a cynical and immoral manipulation of the facts for personal gain, you can sometimes make figures say anything you want.

The Independent was in favour of legalising cannabis for many years, but in March 2007 it decided to change its stance. One option would have been simply to explain this as a change of heart, or a reconsideration of the moral issues. Instead it was decorated with science – as cowardly zealots have done from eugenics through to prohibition – and justified with a fictitious change in the facts. ‘Cannabis – An Apology’ was the headline for their front-page splash.

In 1997, this newspaper launched a campaign to decriminalise the drug. If only we had known then what we can reveal today … Record numbers of teenagers are requiring drug treatment as a result of smoking skunk, the highly potent cannabis strain that is 25 times stronger than resin sold a decade ago.

Twice in this story we are told that cannabis is twenty-five times stronger than it was a decade ago. For the paper’s former editor Rosie Boycott, in her melodramatic recantation, skunk was ‘thirty times stronger’. In one inside feature the strength issue was briefly downgraded to a ‘can be’. The paper even referenced its figures: ‘The Forensic Science Service says that in the early Nineties cannabis would contain around 1 per cent tetrahydrocannabidinol (THC), the mind-altering compound, but can now have up to 25 per cent.’

This is all sheer fantasy.

I’ve got the Forensic Science Service data right here in front of me, and the earlier data from the Laboratory of the Government Chemist, the United Nations Drug Control Program, and the European Union’s Monitoring Centre for Drugs and Drug Addiction. I’m going to share it with you, because I happen to think that people are very well able to make their own minds up about important social and moral issues when given the facts.

The data from the Laboratory of the Government Chemist goes from 1975 to 1989. Cannabis resin pootles around between 6 per cent and 10 per cent THC, herbal between 4 per cent and 6 per cent. There is no clear trend.

The Forensic Science Service data then takes over to produce the more modern figures, showing not much change in resin,

Mean potency (% THC) of cannabis products examined in the UK (Laboratory of the Government Chemist, 1975–89)

and domestically produced indoor herbal cannabis doubling in potency from 6 per cent to around 12 or 14 per