Media reports this week that some speed cameras have failed to reduce accidents - even in places and led to an increase - you ignore the power of random variation

"Speed ??cameras do not cut too many accidents on roads and in fact led to an increase in losses on some routes," says the The Telegraph.

Can this be true? Did Blitzer "failed", to reduce accidents? Did they 'out' an increase in accidents? A little careful consideration shows that these two bold assertions may be wrong.

When considering a large number of speed and works, we would expect by chance alone, that there are some places where the number of accidents after the installation will have increased by a speed camera. This will also happen if the probabilities of an accident actually declined.

Any analysis must take into account randomness. The figures provided by the councils must also allow the people the whole picture that the public information about how variable data are means to get. For example, the City Council Humberside data are only three years on average for victims and collisions, and no indication of the fluctuations around these values.

Whether or not a particular accident will occur is a mathematically random event - it can't be predicted. The number of accidents that happen each hour or each day or each year is a random number that will depend on all sorts of factors, such as the speed limit on the stretch of road on which a particular camera is placed, how busy the road is and the weather. We cannot predict exactly how many accidents there will be in any given time, but we can estimate it with some degree of certainty.

The key to understanding the speed camera data is a value estimate for this measure of security. Statisticians call this number the deviation - how spread out are the numbers. In the case of speed cameras, this is a measure of the variability in the number of accidents. For example, if the number of accidents was about the same every year, then this is a small variance, and if the number of accidents will change dramatically every year, this is a large variance.

Imagine that, whether it be an accident, such as tossing a coin. Is this a fair coin, then the probability of an accident with a car would be half or 50:50. This is the same as saying that it is equally likely that a car does not have an accident or have an accident.

Against this background, we can look at the speed camera claims in the Telegraph. These claims are an example of the prosecutor 's fallacy that occurs when you can have multiple comparisons - for example, over years or between works.

When we trade a 100-coin test, by throwing 10 times each, were the chance to head will naturally be a half. Thus one would expect that if 100 mirrors fair coin 10 times each, chosen on a particular coin coming up heads before would see nine or 10 times, most unlikely.

However, if we are not concerned about the special coin could behave so, then see some coin heads are 9 or 10 times more likely than not would be by chance alone.

As a result, tossing 100 coins would more likely than not lead us to the false conclusion that at least one coin is not fair. We would totally come to the wrong conclusion that some of the coins have a higher probability of landing heads than tails.

When a car accident always corresponds to a head with a coin simply by chance alone, we would expect to see an increase in the number of accidents at some points, although the installation of a radar device.