Imagine this newspaper reports that cuts in the dairy industry mean there will now be “four times fewer” maids a-milking on the eighth day of Christmas. How many do you imagine will be at work? We’ll come back to that question later.
The handling of numbers is something that readers regularly make contact about, and 2022 has been no different. But with the bountiful optimism of an approaching new year, we can hope that a review of some repeat offences brings down the 2023 tally by a fraction.
First, a percentage increase is not the same as a percentage point increase. So, for example, national insurance contributions in the UK were not “set to increase by 1.25% in April”, as a January article said, but by 1.25 percentage points.
Calculations involving percentages can also trap the unwary. If five gold rings bought last Christmas for £1,200 had this year become exempt from 20% VAT, it would be wrong to say the cost had “fallen by 20%”; a decrease from £1,200 to £1,000 (without the sales tax) is 16.67%.
Meanwhile, megawatts (MW) and megawatt hours (MWh) get variously muddled. The first is a measure of power or capacity, while the second expresses the amount of energy produced. Hence a correction in an article that spoke of tidal power projects “upping the amount generated” from 10.4 megawatts to 51.2 megawatts; those numbers were for installed capacity, not output. Think of 12 drummers drumming, but not all together and not all night.
Speaking of energy, a hefty blanket might be stitched from complaints relating to expressions of temperature. An article about the likelihood of snow on Christmas Day slipped up, resulting in a footnote explaining that celsius is a relative, not an absolute, scale and “it is therefore incorrect to say that an increase from 10C to 15C, for example, is a rise in temperature of 50%”.
Errors in converting rises or falls in temperature from celsius to fahrenheit always attract heat. In fact, the Guardian’s style guide rather forlornly advises to “be extremely wary (or don’t bother) converting temperature changes”. We do bother, but not always warily. In reporting on vanishing polar ice sheets, an article gave a temperature increase of 1.5C as equivalent to 34F, when that figure should have been 2.7F. As readers were quick to remind us, the way to convert temperature changes (rather than absolute temperatures, which was the mistake here) is to multiply by 1.8, or by 9/5 if you prefer.
But there is a mathematical matter beyond the plain mistake that continually irks some readers: the formulation of “times less” or “times smaller” or its close cousin the “fold decrease”. This, they complain, produces a negative number.
“It is a mathematical nonsense,” wrote one reader. “I realise that ‘x times lower’ is being used to mean ‘1/x of’ – but this really is a horrible way of describing it, and really tough on children and less numerate adults wanting to understand maths.”
Another said: “I presume ‘three times less than’ actually means a third of – but I’m never sure when I see or hear it used.”
A reader in Canada wrote that while one item might cost x times more than the other, “math does not allow the comparison to just be flipped”. She suggested saying the item costs only 1/67th, rather than “67 times less”. It was a very common “error”, she said. “I rail against it constantly.”
Is it an error? I have left “times less” unamended on many occasions on the basis that it is so widely seen, including in academic papers, that it is likely to be understood even if it meets with some disapproval. I imagine most readers picture two maids a-milking in the example at the top.
But I asked Sir David Spiegelhalter, former president of the Royal Statistical Society, for his view. He told me that while he tries “not to be pedantic about numerical expressions”, he has come to the conclusion that expressions such as “five times less” are “just wrong”. The word “times”, he said, “means multiplication – no argument. And nothing is being multiplied by five, it is being divided.”
There is no new rule on this, but some of the Guardian’s science journalists told me they do tend to avoid “times” when writing about a fall. A “fold decrease” can be additionally vexed with regard to meaning; if 10 lords a-leaping become five, would you expect to see this described as a twofold or 0.5-fold decrease?
We live more than ever in a world where numbers matter, from the cost of living crisis, to Covid to climate change. The Guardian does superb work involving stats, and specialist reporters are typically adept, but every area of a newspaper at some point relies on mathematical expressions. And while a dangling participle may occasionally mislead, a mistake with the “grammar of numbers” is in my experience much more likely to do so.
I have sympathy with journalists who are not natural number-wranglers (I switched out of an economics degree when the maths became too much), but it is not necessary to remember all concepts and conversions, only to remember when to stop and enlist help. As Einstein may or may not have put it: “Never memorise something that you can look up.”
Elisabeth Ribbans is the Guardian and Observer’s global readers’ editor. She can be contacted at this email address
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