Ever since the Stewart report into mobile phone safety was published in 2000, many parents have been nervous about their children's fondness for fashionable handsets. While this expert inquiry found no evidence of harm, it recommended a precautionary approach for children, citing uncertainties about their developing brains.

Those fears have been heightened this week by a spate of alarming headlines, triggered by a story in the Independent on Sunday. “Children and teenagers are five times more likely to get brain cancer if they use mobile phones,” it declared.

A study by Lennart Hardell, a Swedish scientist, had found an increased risk of two types of tumour, acoustic neuroma and glioma, among under-16s who used mobile phones. Here, it appeared, was evidence that concern was justified.

The story, however, was not quite what it seemed. In fact, it is an object lesson in how not to report risk.

A five-fold risk sounds extremely frightening. But it is what is known in statistics as a relative risk, and on its own, it is meaningless for judging health hazards. The question you need to ask is: “Five times what?” If the original risk is reasonably high, a five-fold rise might be worth worrying about, but a tiny risk multiplied five times will still be tiny. It is absolute risks - the overall chance of getting a condition - that matter for health. The Independent on Sunday did not supply them.

As it happens, both cancers are rare. They primarily affect adults, at rates of about one in 100,000 for acoustic neuroma and one in 30,000 for glioma. Among children, they are still less common. Even if Hardell's research proves to be copper-bottomed, mobile phones will not be causing more than a handful of these tumours. It is also uncertain that the figures even stack up, for they have not been published. Hardell's finding was presented at a conference, but his full data have yet to reach the public domain. They are not available for scrutiny, and we have only his word for it that his interpretation is correct.

This is especially important because his results concern a sub-group - children - of a much bigger data set. Look at enough sub-groups, and some will always appear to have an elevated risk through chance alone. It is essential that independent experts can pore over the data if we are to establish whether this effect is real or illusory.

The misuse of statistics is a common media problem even when published data are available. A good example is a link between painkillers and heart attacks that was widely reported in 2005. Most stories stated that ibuprofen raised the risk of heart attacks by 25 per cent. Yet few pointed out that this would mean just one extra heart attack per year for every 1,000 people taking the drugs - a much less frightening figure.

A Daily Telegraph story this week was similarly confusing. It reported that swimming in chlorinated pools raises children's risk of asthma by a factor of five, without saying what the background risk was to begin with.

The public isn't being given the information it needs to assess risks. To provide it, the media should take a different approach to reporting risk. Instead of using confusing percentages and probabilities, it is better to explain in terms of “natural frequencies”, which describe actual numbers of people who are affected.

If four out of every 1,000 people will normally have a heart attack each year, and the rate for ibuprofen users is five in 1,000, that is a relative risk increase of 25 per cent. The natural frequencies, however, are at once more comprehensible and convey a more meaningful message. They make it clear that the vast majority of people on painkillers will not have a heart attack as a result, which the relative risk does not.

Study after study has shown that natural frequencies are by far the best way to communicate risk. All of us who report medicine should make more effort to use them.

Mark Henderson is science editor of The Times