

Whenever ice cream sales rise, so do shark attacks. As more economists are recruited to the Treasury, inflation rises. In his fifth lesson of a weekly series, author Michael Blastland gives hints about reading too much into "correlated" facts. Lesson Five: Causation The story: The smoking ban in Wales "caused" a 13% fall in heart attacks from October to December 2007, compared with the same period in 2006. The flaw: The ban began in April. So did it also "cause" the rise in heart attacks in the first few months after the ban? And presumably it "caused" me to spill my tea. For that happened during the smoking ban too. Grand claims for the smoking ban The lesson: This is a foolish case of a simple error - the assumption that things happening after an event must be caused by it. Everyone examines data for evidence that their side is right. If a statistical morsel seems to our taste, the temptation is to swallow it. Such zeal produces, in this case, the following logic: Here's event A - a smoking ban.

Here's event B - a selective fall in heart attacks.

Therefore, A caused B. And if the earlier months for which data is available show an inconvenient rise, the logic presumably staggers on - why, it simply proves that it took a few months for the effect to appear, surely? It's the kind of logic that ought to wilt with embarrassment. In the event, no one even blushed. Is it serious? Well, it passed for broadsheet news, political and medical establishment opinion. The problem here is that neither media nor politicians like to acknowledge the power of chance. The numbers must mean something, they think. If there was a fall last month, it must mean this. If a rise, it must be explained by that. And we can all stretch our imaginations to suggest that explanation, as some readers will be itching to do. Something must have done it. Someone deserves credit, or blame. MISSED PAST LESSONS?

Lesson One: Our survey says Lesson Two: Myth of counting Lesson Three: Percentages Lesson Four: Averages But brace yourself for a remarkable fact: numbers go up and down. Does it need to be said that people in Wales do not have heart attacks with perfect regularity, 180 a day, 7.5 every hour? Sometimes the numbers go up, sometimes down. If you simply take the period, or the place, in which the numbers go the way you want, but disregard the rest, you are likely to read meaning into nothing. Over the whole period, there seems to have been a fall no faster (so far) than the steady falls of previous years. The ban can't (yet) be shown to have had any effect on the fall, or the rise, or my tea. Junk Rating: Five out of five. I am a non-smoker and dislike smoky places. But those preferences can't blind me to the statistical weaknesses of the benefits to my health in this, as in many reports of the effect on heart attacks of smoking bans. That there will be some benefit with time seems plausible. That it is as great or quick as claimed does not. This is one problem with arguments about causality, the belief that any change must have a principal cause, when it may be the result of the many causes that produce nothing more meaningful than random variation. There's another variety of the problem, which is to mistake one cause for another. Take a look at this chart, released last month. It appears to show that trade unions secure substantially better pay for their members. One thing leads to another, membership brings more money.

But is it the union what done it? Because other things tend to go with union membership too, as the ONS points out. It seems that being longer in a job, or older, means you are more likely to have joined a union. But age and experience also often bring seniority. So these people would earn more on average (see lesson four), whether in the union or not. Another of what are known as confounding factors is education. Union members apparently tend to have more formal education. More education tends to go with higher pay. So is it the union, or the other things that tend to be true of union members that are the main cause of the pay premium? Ice cream sales up, ditto shark attacks The key is not to stop looking for the cause with the first plausible link you find. Keep your imagination restless for other causes, or the possibility of chance, and it will serve you well. So finally, here's a game based on reading absurd causation into correlated facts. Let's call it "dimputations." The idea is to find two facts that genuinely do change in tandem, then work out what's really going on. Here are a few examples, some new, some old, and all true except for the explanation. Work out the more likely chain of causation then think of some examples of your own. Whenever ice cream sales rise, so do shark attacks (eating ice cream makes you tastier?)

As more economists are recruited to the Treasury, inflation rises (economists cause inflation?)

In Scandinavia, storks appear more often on the rooftops of families with more babies (storks bring babies?)

As vocabulary increases in infancy, so does appetite (words make you hungry?) Have fun. Next week, Lesson Six: Doubt Michael Blastland is the author, with Andrew Dilnot, of The Tiger That Isn't. Add your comments on this story, using the form below. Ice cream sales rise in hotter weather, which also forces sharks to get their Aircon serviced. This is very expensive and angers the shark. Angry shark equals more attacks. Instances of drunkenness in those below 18 years of age are significantly lower than for those above. Clearly children can hold their drink better than adults.

Mortality rates for pedestrians and cyclists are dramatically lower on motorways than on other roads. We urgently need to introduce a 70mph blanket speed limit.

Stewart, Basingstoke Sharks like ice cream but find it really difficult to buy them, so they resort to eating humans in the hope they will still have ice cream inside them. (Strangely this logic also applies to mosquito bites in summer.)

David, London One non-causal correlation that my Dad's fond of: Wearing a cap or hat can make men bald. If you check, the proportion of men wearing caps/hats who are bald is higher than the proportion of bald men in the population as a whole. Therefore wearing a cap makes you bald.

MarkUK, Derby I happen to understand the correlation with sharks and ice cream more deeply than most. Eating ice cream will cause people to urinate a large quantity of lipids (fats) similarly to seals and other fatty sea mammals, which happen to be the sharks' favourite prey.

Bob, London Surely no one could deny that applying for a driving test causes you to have your wisdom teeth out? Or is that the other way round?

Loops, London, UK Economists are sensitive to the earth's magnetic field. As inflation rises people require more coins to buy their ice creams. This additional metal alters the earth's magnetic field, spooking the economists who retreat to where they feel safe - Treasury. Storks fear margarine and therefore cluster near the homes of those with small children who will have gone all organic and started buying salt-free natural butter. As the children grow they can request margarine and ice cream. This upsets the sharks, storks and economists, who then feed the children burgers to give them heart disease. All quite logical really.

Phil, Birmingham It is a well known and established fact that the ice cream market is more ruthless than the oil and sugar market. Obviously Walls and Nestle train sharks to attack anyone who is eating rival products. So when your walking down London on a sunny afternoon eating your Calypso, look out for bodies of water (lake, pond, puddle, glass of water, etc...) because a Nestle shark might come and rip your arm off.

Dino Costa, London Perhaps when there is a horrible shark attack on the beach, people stay out of the water and have an ice cream instead. The moral is, if there's a big queue for Mister Whippy, stay out the water.

David Routledge, Derby, UK Clearly the author does not realise that it is easier to swim away from a shark if you are not trying to hold on to an ice cream.

The Late KingZog Speaking of storks - the decline of storks in Denmark in the 1970s followed the same trend as the Danish birth rate. Fewer storks + fewer babies = ergo storks really do bring babies.

HH, Scotland Ice cream sales rise in hot weather, people go to the beach in hot weather, there are sharks at the beach, people steal the sharks' deckchairs, the sharks attack them.

The hiring of economists is carried out according to a master plan that links the recruitment rate to inflation.

Storks have a higher concentration in regions of Scandinavia with higher human birth rate, both species benefitting from a natural abundance of food. Or people notice storks more when there has been or will be a birth.

Development of language skills happens at the same time as the growth of the infant, this is clearly because the more you need to eat, the more ways you need to describe the food you want.

Key Mika, London Talking of causality, I had a colleague at an old job who'd rant about the government allowing late Easters because, in his eyes, late Easters always caused long, cold winters and it was the timing of Easter that would control the weather in this respect.

Greg, London Storks prey on the lesser know nappy mite, meaning a higher number of storks on rooftops of those with children...

Vicky, London The ice cream/shark attack one is easy: the cause for both is obviously hotter weather - more people in the sear, the sea's warmer, the sharks come in closer to shore; hotter weather also means more people buy ice cream.

Rob, London, UK Those claiming the ice cream/shark attack connection is validated by hotter weather have missed the point - which is the attempt by some to establish a DIRECT connection between the two. That is to say, there is no evidence that people buying more ice cream brings sharks storming into shallower waters ready to bite unsuspecting bathers. If, for example, there was evidence showing sharks were attracted to chemical preservatives in ice cream, this might stand up - but there isn't. The fact that hot weather means that more ice creams are bought, and that hot weather encourages more people to swim and ergo gives sharks more people to bite, does not mean hot weather connects these two things in any way. It's clearly people who think like this that are responsible for such faulty logic in the first place.

Lorelei Lee, Leeds In Scandinavia, storks appear more often on the rooftops of families with more babies. More babies ==> bigger roofs ==> more storks.

JM, Ormskirk Warmer weather brings people to beaches, people buy ice cream at beach, sharks see ice cream, sharks become jealous. The sharks want the ice cream, and attack people to get it. The sharks will stop at nothing for a 99 with a flake.

Emily, Southampton



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