These examples may seem bizarre and improbable, but they are not the result of bad statistics. All the information is absolutely correct. Their strangeness comes from our own reasoning. We see two things changing together and our instinct is to assume that they are tied by cause and effect. Unfortunately, our instinct is often wrong. In all these examples a third "confounding" variable is actually the cause of two correlated variables.

It is absolutely true that people who play loud music are more likely to suffer from acne, but only because teenagers make up a big part of both groups. Acne and loud music are certainly correlated. But correlation is not causation. The same thing is true with the sharks and ice cream. The number of shark attacks and ice creams sold both go up during the summer, with the good weather encouraging people both to go in swimming and to eat ice cream. And as for large hands? Older children are bigger, and can read better!

But the situation is not always so clear cut. For example, it was reported recently that mobile phone use can reduce a man's sperm count by almost a third. One plausible theory is that damage caused by electromagnetic radiation makes you infertile. But what about other factors - confounding factors - that could cause both high mobile phone use and low sperm counts?

How about stress? Busy jobs? Exposure to pollution? Age - were the heavy users older? Were they more likely to be smokers? The researchers can't answer these questions; not unless they carry out a carefully designed experiment that controls for all these other variables.

And we must not forget the possibility that this was a random finding in one small study - just 221 men - which won't necessarily be replicated by other researchers. If you conduct enough studies, you will inevitably get some interesting findings just by chance.

We all draw conclusions on the basis of what we see. But it is important for us to remember that just because there is a correlation between two facts, there isn't necessarily a cause/effect relationship between them.

Chance?

My son, James was conceived by IVF. I have a photo of him when he was just seven cells big and I often look at it and think about how lucky I am to have him. Twenty years ago, the chances of a couple like us ever having a child were tiny. Fifty years ago, they were zero.

But just how lucky were we? Only about 1 IVF treatment in 7 leads to a baby, so does that mean that there was a 1 in 7 chance that we would have James? No, because that 1 in 7 is the chance of an IVF cycle leading to some child, not to that particular unique little individual. That chance is so much smaller that it's hard to even get a handle on it, because although James was conceived in a Petri dish, he still shares something with all of us: he is the result of a series of events so unlikely that you'd wonder how anyone was ever born at all.

Take yourself as an example. What if your parents had never met? What if one of them had missed the bus on their way to their first date? What if their eyes hadn't met across a crowded room because someone else was in the way? What if they'd been tired, or had had an argument the night you were conceived and had just gone to sleep instead? And that's all before we get into a biological discussion about the number of potential results arising from each single ... romantic encounter.

But of course people are born all the time. At the moment there are well over 6 billion of us, and each second we're joined by another two-and-a-half newcomers. So how can something which seems so unlikely happen so often? Well, it's all down to probability.

Before you were born, the probability of you being born was almost 0. After you were born, the probability was 1 - that is, a certainty. The point is, someone was going to be born, and if it hadn't been you, it would have been a different child. You would never have existed, and that other child would now be reading this article and asking themselves what the chances were that they were ever born.

Let's take another, sadly fictitious, example. On Saturday afternoon, you and I each buy a lottery ticket for that night's draw. Each of us has a chance of about one in 14 million of winning. A few hours later, you're tearing up your ticket in disgust and I'm running around and screaming at the top of my voice, several million pounds better off than I was that afternoon. The chance of winning the lottery with a single ticket have not changed, however; it's still 1 in 14 million. But the probability of me winning today's draw is now 1 - because I won, and the probability of you winning it is now 0 - there's no possibility you can win because you don't have the right numbers.

And this distinction, between the chances of a rare thing happening before it happens and once it has happened, is one way we're easily misled when it comes to our understanding of probability. The thing to remember is that rare things happen all the time. People do win the lottery, people do have meteorites land in their lounge, people are struck by lightning twice. These things may not have happened to you, and they may well never happen to you, but that doesn't mean that they never happen at all.

As an experiment, why not think of something unusual that's happened to you this week then imagine that someone had told you beforehand that it was going to happen. Would you have believed them? Would you have put money on it not happening? And if so, how much would you have lost?

This is a republished article by Helen Joyce with Andrew Stickland. It originally appeared on the +Plus maths website.

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