Putting percentages in context

Percentages might make news stories stand out, but without a connection to the human experience, can become meaningless. Wouldn't it be good to have the mental agility to separate the wheat from the chaff? In his third lesson of a weekly series, author Michael Blastland gives some hints for percentages.

Lesson Three: Percentages

The story: Vitamin E can kill. Supplements cause a 14% increase in mortality, said the man on telly, standing in front of a huge "14%", propped up on a number like the bar of the local.

The flaw: Funny, but wasn't my risk of mortality quite high already? Like, 100%? But no, it's even worse than that. Vitamin E supplements apparently make the end more than certain. For death has become like a footballer, giving it 114% out there today, Brian.

The lesson: Journalists and percentages mix like ball bearings in souffle. They say their preference is for real life over boring, abstract figures. Not with percentages, it's not.

Often these digits become no more than that: digits, fetishised, but separate from human meaning and, in the case of risk, frequently reported only if they can be made to look big or scary.

We need to reconnect them with human experience. Here are two ways.

First, we need to remember that not much in life is either/or. According to the research, there's something in the claim that Vitamin E supplements can be harmful. But, as with the consumption of salt, or even water, much that can kill is also essential to good health.

The world does not divide easily into what's toxic and what's not, what's safe and what isn't. Risk is simply a way of measuring where we stand on the messy middle ground - which is almost everywhere.

A 100% increase in the number of bullets in a revolver - if you are playing Russian roulette - well, that makes a difference Lesson One: Surveys Lesson Two: Counting

What matters in that messy middle is the relevant human quantity: how much supplementary vitamin E? A little won't do any harm (or, probably, much good). A lot, especially if you are getting on in life, might.

So a 14% increase in risk of death does mean something, but only if you say at what dose (high), for which group (the elderly), over what period (a single year, not in a lifetime).

The second common problem with any percentage increase like this, also crying out for a dose of real life is: what's it increased from? Because 14% might be a lot if you start somewhere big, next to nothing if you start somewhere small.

A 100% increase from one in a million becomes two in a million. So what?

A 100% increase in the number of bullets in a revolver - if you are playing Russian roulette - well, that makes a difference.

How can supplements cause a 14% increase in mortality?

So let's get human again and ask where we begin. What is the risk of dying, this year, for a 75-year-old man? And let's keep percentages out of it, as far as we can.

The answer is that in every 100 men aged 75, four or more will typically die in the next year. If all 100 of them tuck heartily into Vitamin E, maybe five will.

That is, according to this research, there'll be less than one (actually 0.6) extra death per 100 people if all are on high doses of vitamin E. At low doses, there's almost no change.

That's what 14% turns out to mean: 0.6 of a death per 100, or six deaths per 1,000. I wonder if a large daily dose of salt is any worse?

For 60-year-olds, the risk of death this year is so much smaller to begin with that even an extra 14% risk (from a high dose of Vitamin E) makes almost no difference at all.

Junk rating: Four out of five. There's some salvation in the fact that this was part of a report on all kinds of teenage cancers, some of which are a real concern, but this was the one that had the attention. Yet the human numbers are so small they might well be the result of nothing more than random variation.

A little context can make a lot of difference to a percentage. Another simple example is the story that young Americans can't afford to move out and are all now stuck with the folks.

Since 1970, when 12.5 million 18-34 year olds lived with their parents, the number has apparently risen by 48%, to more than 18.6 million.

Except that the American population has also risen in that time - by about 32%, or roughly 75 million people. So, in figures easier to translate to real life, the number of 18-34 year olds still living with the folks has gone from a bit more than one in five to not quite one in four. Still a real increase, but nothing like 48%.

The biggest part (though not all) of the explanation for increasing numbers of Americans living with their parents is... that there are increasing numbers of Americans.

Or take what it means to be 99.9% effective. In the NHS it might mean 135 botched operations and 13 babies given to the wrong parents, every week. (Thanks to writer Anne Miller for that example).

A percentage is not really a number, it is a share. The simple question to keep in mind is one that always strives to put it into a proper, human context: "A share of what? A share of a lot - or a share of a little?" Better still: "A share of who?"

Keep it real.

Next week, Lesson Four: Averages

Michael Blastland is the author, with Andrew Dilnot, of The Tiger That Isn't.

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Add your comments on this story, using the form below.

Excellent article. I remember reading a short story in the Eighties where a computer selected a "Mr Average" from the electoral register, and everything that person said was taken as general public opinion. And sometimes I wonder if we aren't getting very close to that situation now.
Steve Wehrle, Southampton, UK

simple and clear. The material each newsperson should keep at hand...
Roman, Surbiton

Brilliant - keep it coming! The reporting of statistics, percentages and risks in the news is almost always the cause to groan as the presentations lack context and a sense of how this would meaningfully effect day to day life. As a rule the larger the percentage the greater the need for context, usually as the base is very small, or the population is changing... but that seldom makes a good story!
Charlie, London

OK, you got me started. Adverts for cosmetics, shampoos and skin treatments. A fictional but representative example. "A conditioner gives 80% more shine." small print "shampoo and our conditioner compared with shampoo alone. more small print "52 women responded". How is shine measured???? Well, OF COURSE there is more shine!!!! You haven't compared two of the same things. 52? Out of (very conservatively) 10 MILLION that wash their hair. Statistically insignificant - meaningless. So, a 'scientific' measure that is not at all scientific. And is therefore meaningless. A comparison that has 2 variables and is therefore meaningless. A TINY sample group whose response is therefore meaningless.
Sandy Fox, Derby, UK

Quite right but I am afraid that you are just tilting at windmills as the population is innumerate from the top down. It's not just journalists but more importantly perhaps politicians who are unable to use numbers and you might care to note that the use of graphs and equations is banned from use in parliamentary debates, which I believe tends to explain the poor quality of decision making.
Paul j. weighell, Purley, Surrey

My favourite silly percentage is "washes 30% brighter" 30% brighter than what? Than washing you clothes with Mud for example... that's not much to brag about!
Jo Beale, Cambridge

My doctor recently told me that if I don't reduce my cholesterol, I have a 20% chance of having a heart attack in the next 10 years. Sounds frightening! Except, what she didn't tell me is what would my percentage chance be without reducing cholesterol? It is probably at least 10% anyway (aged 45-55). Plus, if I reverse it, I have an 80% chance of NOT having a heart attack. Don't get me wrong, I am exercising, dieting and taking the pills. I have never won anything and don't want this to be my first win! But it is interesting how random percentages (I am sure she had checked her facts - didn't she?) can be used to frightening effect if you don't think them through. Great article Michael, by the way.
Nick, London UK

I once read that 25% of smokers die early. I was so pleased. As a smoker myself, this logically means that I have a 75% chance of living longer. Fag anyone? (Fag=Cigarette for American readers)
James Rigby, Wickford, Essex

I love this series of articles. Very informative without being cynical. I doubt many other media organisations would do this - their sensationalist headlines depend on big numbers!
Lee, London, UK

At last! I'm sick of hearing meaningless statistics on the news with absolutely no context and no means of providing insight.
Paul Daniel, Aberdeen

I always like to see "98% fat-free" as a meaningless percentage on a food packet. Surely something is fat-free or it isn't? At least "only 2% fat" means something!
Stuart C, Cardiff, Wales

100% of people surveyed said that this was a fascinating and true article. Survey size 1 ( me )
Steve, Oxford

Very good article. I'm going to tell my boss that I'm going to give 110% this week. I was off sick yesterday, so maybe I should be giving 125% for the rest of the week. Or am I really giving only 80% because I missed a day. Now I've confused myself. That's certainly going to knock a few percentage points off my performance now ;-) I think I feel a sick day coming on....
Colin Harrison, East Grinstead

Remember also that the vitamin study was about huge doses of vitamins, many times more than you would ever find in 'supplements'. So the idea that taking supplements increases risk of death by any amount is completely bogus, as that is not what was studied.
Sarah, UK

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