Archive for category Maths

The Sun, 20 mph speed limits, and a lot of nonsense

CONTROVERSIAL 20mph speed limits designed to cut road casualties are not working, official figures show.

So says The Sun anyway*. So, what’s the problem?

A report from the Department for Transport shows there were 2,262 fatalities and injuries in 2011 on 20mph roads in built-up areas — 24 per cent more than in 2010 when 1,827 were recorded.

That compares to a one per cent reduction in casualties on 30mph roads in built-up areas.

How many people died or were injured on roads with a 30 mph speed limit then? The Sun doesn’t say, but the official data is easy enough to find. In 2010, 127,377 people were killed or injured on a road with a 30 mph speed limit. In 2011, it was 125,494.

In other words, that “1% drop” corresponds to almost 2000 fewer people were injured on 30 mph roads, while 400 more people were injured on 20 mph roads. That is a net decrease of 1448 injuries/deaths.

Just looking at the number of injuries on 20 mph roads is not going to tell you about how effective 20 mph speed limits are. You have to compare them with other speed limits. Data about how many 20 mph zones there are is hard to find, which makes making sense of the Sun‘s data difficult, but it certainly looks like a lot of them have been springing up lately, so an increase in injuries is to be expected – if there are more roads, there will always be more accidents!

Studies of 20 mph zones consistently find that the same stretch of road will see fewer accidents and fewer injuries if the speed limit decreases from 30 mph to 20 mph, especially if this decrease is enforced by speed bumps and other traffic calming measures.

* Incidentally, far from being “controversial”, surveys consistently find around 74% in favour of 20 mph speed limits and just 12% against them.

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50 Shades of Babies

Baby boom predicted next year thanks to success of Fifty Shades of Grey books, says theDaily Mail today. It’s such nonsense that I don’t really know where to be being. Let’s have a quick rundown of the problems.

  1. Fifty Shades of Grey did not invent sex, nor did it invent porn. There have been plenty of erotic books written for women before Fifty Shades came along. People like Jilly Cooper were best sellers decades ago, and somehow these authors didn’t inspire baby booms of their own.
  2. The sort of sex Fifty Shades of Grey is credited with inspiring – again, according to the Daily Mail, quoting a poll by a dating website – is going to tend to be controlled and organised. The Twilight fanfic book does after all focus heavily on contracts between sexual partners. It stands to reason that people would be more likely to use contraception if acting out scenes from the book.
  3. There’s no real evidence that Fifty Shades of Grey has led to people having more sex – a few people posting “I had so much sex after reading this!” on Mumsnet isn’t really enough. Fifty Shades of Grey didn’t just magically materialise in people’s houses, they had to go out and buy it. Presumably most of these people would have bought a similar book if Fifty Shades was not available, especially if they were looking to “spice things up in the bedroom”.
  4. The story comes, ultimately, from one Professor Ellis Cashmore (the only professor I know of whose website has an intro video). I’m sure he’s a smart guy, but he’s professor of culture, media and sport, not demography or statistics or anything else that you might expect someone making predictions about the birth rate to be grounded in. He’s in the papers quite a lot too, for sometimes quite disconnected stories. In the past month alone, he’s explained the psychology behind penalty shootouts, the meanings of footballers tattoos, homosexuality in sport, the place of Wimbledon in British culture and the reasons Madame Tussauds is so successful. It’s not proof he’s wrong, of course, just a reason to be a bit wary that he’s suddenly leapt out of his department to give the Daily Mail a juicy story about a particularly popular book.
  5. Come on, seriously, this story is nonsense meant solely to drive traffic to the Daily Mail and boost Professor Cashmore’s profile. In 2010, 723,165 babies were born in England & Wales. To be statistically significant, you’d need the book to lead to tens of thousands of extra births – i.e., ones that were not planned. Even for a book that’s sold a million or so copies, that’s a lot of babies.

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Did GM soy cause allergies to soar? Probably not.

So, California’s planning a referendum on the labelling of genetically modified food. The Guardian has covered this not in it’s regular news pages, but in its Comment is Free section, under the title “How California’s GM food referendum may change what America eats“.

The article is mostly an opinion piece – fair enough – but there’s one statistic buried in there that leapt out at me.

While researchers have not yet found a “smoking gun”, which would prove that GM foods as a class are dangerous, there are troubling signs that they may be a factor in the recent epidemic of food allergies. Soon after GM soy was introduced to the UK, for example, soy allergies escalated by 50%.

The link there doesn’t go to a scientific paper, but to a piece on “News. Controversy. Opinion.” site Opposing Views, and their figures seem to come, ultimately, from American Academy of Environmental Medicine, a group that has some decidedly quackish views on topics like water fluoridation, vaccines and “Multiple Chemical Sensitivity” (a scientifically unfounded belief that everything in modern society contains toxins). It’s not impossible to support some outlandish ideas while being right about things, of course, but it does ring some alarm bells.

Neither article links to any of the studies it referenced, but with a bit of digging, I found this piece at Academics Review which seems to be dealing with the same statistic. Go there if you want the full takedown, but in a nutshell, it refers to marketing information from a group called “York Nutritional Laboratories” (which sell food allergy testing kits) the rise was in people with a particular antibody, not those who reported allergies and the study didn’t find any connection (the rise simply happened at a similar time to the introduction of GM, although it actually took place before GM soy became mainstream).*

I decided to have a look on Google Scholar for papers looking in the allergenicity of GM soy. There are plenty of studies and review papers looking into this – one, two, three, four, five – and all the ones I’ve found so far suggest that genetic soybeans and GM soybeans pose exactly the same risk of allergy (though as far as I can tell, these are all animal trials. There isn’t much data on human soy allergies out there).

In this case, the claim that GM soy may be responsible for a rise in allergies seems to be simply wrong.

* For the other major claim in Opposing View’s piece, about baby rats dying from eating GM soy, see this peer review of the paper, originally from Nature Biotechnology , which expresses grave concerns about the unusually high numbers of deaths in the control group – it looks like bad care killed the rats, not the soy)

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Will driving at 80 mph help the economy? Statistics say… probably not

Last week, the Transport Secretary Phillip Hammond announced plans to raise the speed limits on motorways from 70 mph to 80 mph. This, he claimed, would:

“generate economic benefits of hundreds of millions of pounds through shorter journey times.”

Never mind the debates about safety and the environment, let’s look at this one argument. So, does a shorter journey equal a more economic journey? The problem is that cars need more fuel to travel faster, and so the faster you go, the worse your fuel efficiency is. Statistics that go right up to 80 mph are hard to find for some reason – the big US government study for example only went up to 75 mph – but according to the calculator at MPG for speed (better sources always appreciated), driving at 80 mph uses about 15% more fuel per mile than driving at 70 mph.

So, lets do some maths! For the sake of simplicity, we’ll assume every single journey on the motorways is work-related. The actual figures will be lower, especially on weekends and holidays.

At 70 mph, it takes 51 seconds to drive 1 mile. In this time, a car with a claimed “highway” fuel efficiency of 40 miles per gallon (roughly as efficient as a modern hatchback like a Ford Fiesta) will use about 0.11 litres of petrol. At the current average pump price, that’s 15 pence of petrol.

At 80 mph, you cover that same mile in 45 seconds, saving you 6 seconds. On the other hand, your car is now 15% less efficient. According to the calculator, your 40 MPG car is now doing just 28.8 MPG, using around 0.13 litres of petrol to cover that mile, so the fuel to travel that distance cost you about 18 pence.

Spending 3 pence to save 6 seconds is equivalent to spending £18 to save 1 hour. The average median wage in the UK is far lower than £18 an hour (currently, it’s £12.50 per hour for full-time workers (PDF))* – in other words, if you drove at the speed limit to get to/from work, the money you’d be spending on petrol would mean most people would actually lose out (people who car-share would be in a better position, but few people car-share to work).

All the extra pay taken home by workers would simply end up going straight to the petrol companies – and when the government is trying to increase consumer spending, that’s the last thing the economy needs.

(Oops, forgot to mention that this post bears a debt of inspiration to this xkcd comic.)

* Thanks to Lukeablancas in the comments for pointing out that I’ve gone for the median wage. The median wage is good for working out what this means for the average person, since it’s unaffected by extremes, but if we’re looking at the country as a whole, the mean wage might be better – this will take high-earners like company bosses into account, as well as people who work in short but intense shifts, like some freelancers. In 2010, the mean wage for men was £16.00 per hour and for women it was £12.92 per hour (annoyingly the government hasn’t released the combined figures for men and women, but assuming there are roughly equal numbers of both in work the average wage overall is £14.46 per hour). Either way, on average people will end up losing out.

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The Daily Mail blames “brain chemicals” for riots… the research they cite doesn’t

Daily Mail headline: Rioters have ‘lower levels’ of brain chemical that keeps impulsive behaviour under control

Do they? Well, some of them might, but the research in question wasn’t about rioters at all.

Researchers from the University of Cardiff uncovered a link between impulsiveness and levels of the neurotransmitter GABA in a key brain region.

… Around 30 male university students had their levels of GABA measured using a specialised type of brain scan.

They were also asked to complete questionnaires that assessed different aspects of impulsiveness, a trait known to influence self-control.

Participants with more GABA in the pre-frontal brain region had lower scores for ‘urgency’ – the tendency to behave rashly in response to distress or strong emotions and urges.

There was no connection to rioting in the study. Any connection made in the article is being made by journalists – this article has no by-line, being published solely under the Daily Mail Reporter name, but I think it came from the Press Association originally – and it’s a tenuous connection. You see, The Mail is working completely backwards here – they’ve decided that since people who have less GABA tend to behave more rashly, people who they think behaved rashly must have less GABA. You might as well assume that since every MP is in London right now, everyone in London is an MP.

Besides, although the paper in question, “Dorso-lateral prefrontal gamma-amino butyric acid in men predicts individual differences in rash impulsivity” (in Biological Psychiatry not Biological Society, despite what The Mail claims) did find a connection between GABA and impulsiveness, it wasn’t as strong as The Mail claims:

Figure 1 from the paper

Figure 1 from the paper (highlights my own)

That’s a graph from the paper, showing the connection between the amount of GABA in one particular part of the brain (along the bottom axis) and how strong the individual’s feeling of urgency was (along the side axis) in two groups (cohorts). There does appear to be a correlation (the R number is a measure of how strong this correlation is; R = -0.7 is a reasonable correlation) but look at the two I’ve highlighted with red dots in cohort 2. These two people have the same amount of GABA in their brains, but one of them was incredibly impulsive while the other was one of the calmest people in the study. Likewise, in cohort 1, while there was a definite tendency for people with more GABA to be less impulsive, just look at that cluster of dots – there are impulsive people with lots of GABA, and cautious people without it.

The best you could possibly say about this article is that maybe on average a rioter* has less GABA than normal, assuming these riots are entirely impulsive and there is nothing at all planned or premeditated about them. But then, why does this study need to be connected to riots at all? The paper came out in July before the riots, it’s not about riots – or any kind of violence at all – and none of the scientists quoted mention them, and to be honest, blaming the riots entirely on brain chemistry leaves a nasty taste in my mouth. As Mindhacks has pointed out, The Daily Mail seems to be going to great lengths to avoid exploring any of the context behind the riots, and this kind of story helps bolster the Mail‘s line that there is no deeper cause of these riots than “criminality pure and simple”.

Wales Online originally ran this story too (here’s the Google cache, and if that stops working, here’s a screenshot), but they’ve since realised there’s nothing in this proving anything about the brains of rioters and have replaced the story with an altogether more reasonable report on the research. Will The Mail follow suit? Let’s see.

* Male rioters at least – the study only looked at men, so there’s no guarantee this correlation is true in women too.

Edit: The researchers behind the study have published a scathing rebuttal in The Guardian, saying “Let us be absolutely clear. Our research has almost nothing to say about rioting, and certainly can’t be used to justify or excuse any type of behaviour.” Despite complaints from the scientists, The Mail‘s article is still online.

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A punny reply from the TaxPayers’ Alliance

A couple of days ago, Primly Stable commented on the post from last month about the false claims that the NHS was buying loaves of bread for £32 a piece, pointing out that The Express had issued a retraction of the story (though it remains available online), and Tabloid Watch followed this up with an excellent post pointing out that The Sun had quietly deleted the story too.

At Tabloid Watch’s suggestion, I emailed Emma Boon of the TaxPayers’ Alliance, who was quoted by a number of papers (including The Mail and The Telegraph) as saying

“It smacks of incompetence that the Welsh NHS is paying so much more for these goods than they are available for in the shops.

“The cost per unit prices are way above supermarket prices for gluten-free products in some cases which is really worrying.”

“This doesn’t look like taxpayers are getting value for money.”

to ask if she or the TPA would be retracting the comments, and whether the TPA would remove the claim from their website. Here, in full, is her reply:

Thank you for your e-mail. £2.82 is still an awful lot of dough for a loaf. A cursory glance around my local supermarket or online reveals gluten free loaves are sold for much less.

Whichever way you slice it I stand by every word of my comment.

Best,

Emma

The reply may not have addressed any of my concerns (for one thing, the claim that the NHS spends £32 on bread is still up on the TPA website), but those are some excellent puns, I’m sure you’ll agree. I’d say Boon should consider writing for a tabloid in her spare time, but judging by how often she and the rest of the TaxPayers’ Alliance are quoted in the papers, it seems a little redundant.

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How to inflate figures and scandalise people

A number of papers this week (Daily Express*, Daily Mail, Daily Mirror, Daily Telegraph, Wales on Sunday) have all carried the same story, claiming that, in the words of the Daily Mail, “NHS officials pay £32 for gluten-free bread that costs £2.25 in the shops”.

Though it’s not impossible that a big organisation like the NHS has inefficient bread-buying schemes, it seems a bit unlikely that something as widely prescribed as gluten-free bread is being bought for more than 10 times its shelf price. So where did the figures come from?

Well, it looks like the story comes from this Welsh government data about prescriptions. Sure enough, if you look it says that the 27 prescriptions of a particular type of bread, Lifestyle Gluten-Free High-Fibre Brown, cost £32.27 each.** But doctors aren’t prescribing one loaf of bread at a time.

The important column is the one marked “quantity”, which tells you how many grams of bread were prescribed. For Lifestyle Gluten-Free High-Fibre Brown, doctors prescribed a total of 123,600 grams. Divided between the 27 people, that’s 4,577 grams each, or about 11 loaves of bread per person. So that £32.27 figure is the cost of buying 11 loaves of bread, not 1, and as the Welsh government points out, it works out at around £2.82 per loaf.  This is still slightly more than the cheapest online cost of the bread, so I assume there is still room to bring prescription costs down, but NHS Wales is certainly not spending more than £30 on a loaf of bread.

* Turns out James Delingpole writes for The Express too. Huh.

** If you want to check for yourself, it’s in section G-O under the name “Lifestyle_G/f H/fbre Bread Brown”.

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