Football managers get sacked all the time. There’s near-constant speculation in the media about which manager will be the next to go. Bookies even run an annual “sack race”, with punters betting on which Premier League manager will get sacked first in the season. It’s difficult to think of a profession with worse job security.

Right now, Sam Allardyce’s job at Newcastle is looking vulnerable. He’s only been at the club for seven months, but the team are playing ugly football and losing, so there are calls for his head.

One of his senior players, Nicky Butt, has backed him using an argument that always comes up on these occasions: stability leads to success.

If you look at all the big teams, like United and Arsenal, they’re the clubs that have stood by managers for a long time. If we do that, I’m sure we’ll do it right.

[Source: BBC Sport: Allardyce has to stay, says Butt]

So the argument is that the big clubs have stood by their managers for a long time, so standing by their managers must be what made them successful.

The first concern with this argument is that it there may be some selective sampling going on. Man Utd and Arsenal may have had the same manager for years, but Chelsea have done fairly well recently despite sacking two successful managers since Abramovich bought the club a few years ago: Ranieri and Mourinho. Not all the big clubs have had stability. That’s a minor quibble though.

The real problem with the argument is that it seems to get the causal order wrong. Plausibly, it’s not standing by your manager that makes you successful; it’s being successful that makes you (more likely to) stand by your manager.

Sure, a few managers have been sacked when things have been going well on the pitch, but it’s much more normal for managers to get sacked when things are going badly. Even if stability didn’t lead to success, then, we would expect to see a correlation between teams doing well and their managers keeping their jobs.

Perhaps Man Utd and Arsenal don’t keep on winning because they’ve stuck by their managers; perhaps they’ve stuck by their managers because they keep on winning.

Mobile phones have changed our lives. Within a decade or so, mobile phones have gone from rarities to, for many people, necessities; a lot of people now depend on them.

Because of the rapid rise of mobile phones, there was little opportunity to prove them safe before their use became widespread. Concerns remain. One worry is that the radiation emitted by mobile phones might damage the brain. Another is that it might have a negative impact on fertility.

A correlation has now been found between the amount of time that men spend using phones and reduced fertility. A study in Ohio found that men who use phones for four or more hours per day have fewer and lower quality sperm than men who use phones for between two and four hours per day, who in turn have fewer and lower quality sperm than men who use phones still less. Men who do not use mobile phones at all were found to be the most fertile of all.

The conclusion drawn by the scientists in Ohio was that mobile phone use does seem to damage fertility. However, a BBC article on the subject included the views of Dr Allan Pacey, who was more cautious in his response to the data.

Most of the concerns about mobile phone use damaging fertility relate to the use of hands-free kits. These allow people to leave their phones in their pockets while using their phones, meaning that some of the radiation emitted by the phone is absorbed by the testes.

As Dr Pacey pointed out, though, the men studied in the survey were not using hands-free kits. It is therefore unclear how mobile phone use could damage their fertility.

Dr Pacey suggested several alternative explanations of the data: men who use mobile phones a lot might tend to lead more sedantry lives, or be more stressed, or have poorer diets, each of which might in turn affect fertility.

If any of these is the correct explanation of the data, then there is no direct causal connection between mobile phone use and reduced fertility. Dr Pacey’s point is that mere correlation does not prove causation; to be sure that using a mobile phone can damage men’s fertility, we would need to have a clearer idea of the causal mechanism by which the damage might be done.

Back in May 2002, the BBC ran a story affirming that breast-milk boosts babies’ brainpower. The central claim of the article was this: “The longer a baby is breast-fed the more intelligent it is likely to be.”

This claim was supported by a statistical analysis. Danish and American researchers had recorded how individuals were fed as babies, measured their IQs as adults, and found a connection.

Statistically, babies that were breast-fed for less than a month had below-average IQs. IQ increased proportionally to how long babies were breast-fed up to nine months, after which it tapered off.

On this basis, the conclusion was drawn: breast-feeding for the first nine-months of a baby’s life increases its intelligence.

Four years later, the flaw in this reasoning has been spotted, and a new story has been run. This time the headline is “Breast Milk does not Boost IQ”.

The more recent article explains that the breast-fed babies are not more intelligent because they are breast-fed, but because breast-feeding mothers tend to be more intelligent, educated, and affluent. These qualities are passed on to the children through genetic and other means, but there is no evidence to indicate that they are passed on by breast-feeding.

In other words, the original study committed the correlation not causation fallacy, mistaking a statistical correlation for a causal link.