As David Cameron explained in a recent speech, the basic cause of Britain's obesity epidemic is pretty straightforward. People put on weight because they consume more calories than they burn through exercise. Another explanation, however, was advanced this week by several newspapers: the British weather, they claimed, is to blame.

Their evidence was a new study from Aberdeen University, which found that obesity is associated with low levels of vitamin D, an essential nutrient that our bodies synthesise through exposure to sunlight. From this, the newspapers concluded that the nation's notoriously inclement climate must be implicated in our expanding waistlines.

“Scotland's dismal weather makes it more difficult for people to shed those extra pounds,” declared one headline. The Daily Telegraph decided, more simply still, that “heavy weather makes you fat”. There is nothing wrong with the research on which these reports were based. The same cannot be said for the way in which it has been reported, for the study simply did not show that grey skies encourage obesity.

These accounts have made a classic howler. As so often happens with health statistics, correlation has been confused with causation.

The Aberdeen study did indeed find that obese people had lower levels of vitamin D than those of healthy weight, even after other controlling for factors such as diet and social class. It is also true that sunlight is the primary source of vitamin D (though it is also found in foods such as oily fish and eggs). This association led much of the media to make the jump to a simple headline that absolves obese people from some responsibility for their shape, while indulging our national obsession with the weather.

Yet as the NHS Choices website (www.nhs.uk ) explained in an analysis of the coverage, the design of the research had no way of establishing which effect came first. It could be, as the newspapers claimed, that lack of sunlight is making people fat. Or it could be that obesity somehow lowers the concentration of vitamin D in people's bodies. Equally, both observations may be manifestations of a third, as yet unknown, phenomenon.

It is quite possible that vitamin D has an influence on obesity. The researchers suggested, for instance, that the vitamin might affect levels of the appetite hormone leptin, which is known to be involved in weight gain and loss. But at least two other explanations for the link might strike you as more probable.

Perhaps people who are very overweight spend more time watching television, playing computer games and on other indoor activities than do those with healthier bodies? Or perhaps, when they do venture out into the sunshine, they tend to cover up more of their bodies? The available data only allow us to guess which is correct.

If vitamin D deficiency does have a causative effect on obesity, it is probably a small one. Diet, lifestyle and genetic factors are always likely to be greater. For evidence, you need look only at the “fat map” of the United States, which was recently featured in the Comment Central blog (timesonline. typepad.com/comment/ ). The states with the highest rates of obesity, such as Mississippi, are all in the sun-kissed Deep South. Northern states that get less sunshine, such as Vermont, are the leanest.

The causes of obesity are fairly easy to understand and misreporting of perfectly respectable studies like this does little apart from muddy the waters. While there are genetic variations in our propensity to put on weight, and we should avoid blaming people for their obesity, the condition is at root a matter of addition and subtraction. Consume more energy than you use and you will put on pounds. Whether the weather be fine, or whether the weather be not, makes no difference to anyone's weight.

Mark Henderson is Science Editor of The Times

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