Fish oil helps schoolchildren to concentrate ran a headline in the Observer. Regular readers will remember the omega-3 fish oil pill issue. The entire British news media has been claiming for several years now that there are trials showing that the pill improves school performance and behaviour in mainstream children, despite the fact that no such trial has ever been published.

There is something very attractive about the idea that solutions to complex problems in education lie in a pill.

So have things changed? The Observer's health correspondent, Denis Campbell, is on the case, and it certainly sounds as if they have. "Boys aged 8-11 who were given doses once or twice a day of docosahexaenoic acid, an essential fatty acid known as DHA, showed big improvements in their performance during tasks involving attention."

Great. "The researchers gave 33 US schoolboys 400mg or 1,200mg doses of DHA, or a placebo every day for eight weeks. Those who had received the high doses did much better in mental tasks involving mathematical challenges."

Brilliant news. Is it true? After some effort, I tracked down the academic paper. The first thing to note is that this study was not a trial of whether fish oil pills improve children's performance; it was a brain imaging study. They took 33 children, split them into three groups (of 9, 10 and 12 children) and gave them either: no omega-3, a small dose, or a big dose. The children performed some attention tasks in a brain scanner, to see if bits of their brains lit up differently.

Why am I saying omega-3? Because it wasn't a study of fish oil, as the Observer says, but of omega-3 fatty acids derived from algae. Small print.

If this had been a trial to detect whether omega-3 improves performance, it would be laughably small: a dozen children in each group.

While small studies aren't entirely useless, as amateurs often claim, you do have a very small number of observations to work from, so your study is much more prone to error from the simple play of chance. A study with 11 children in each arm could conceivably detect an effect, but only if the fish oil caused a gigantic and unambiguous improvement in all the children who got it, and none of those youngsters taking the placebo improved.

This paper showed no difference in performance at all. Since it was a brain imaging study, not a trial, the results of the children's actual performance in the attention task was only reported in a single paragraph. But these results were clear: "There were no significant group differences in percentage correct, commission errors, discriminability, or reaction time."

So this is all looking pretty wrong. Are we even talking about the same academic paper? I've a long-standing campaign to get mainstream media to link to original academic papers when they write about them, at least online, with some limited success on the BBC website. I asked the writer Campbell which academic paper he was referring to, but he declined to answer, and passed me on the Stephen Pritchard, the readers' editor for the Observer, who answered a couple of days later to say he did not understand why he was being involved. Eventually Campbell confirmed, but through Pritchard, that it was indeed a paper from the April edition of the American Journal of Clinical Nutrition.

If we are very generous, is it informative, in any sense, that a brain area lights up differently in a scanner after some pills? Intellectually, it may be. But doctors get very accustomed to drug company sales reps and enthusiastic researchers who approach them with an exciting theoretical reason as to why one treatment should be better than another (or better than life as usual without the miracle treatment): maybe their intervention works selectively on only one kind of receptor molecule, for example, so it should therefore have fewer side effects.

Similarly, drug reps and researchers will often announce that their intervention has some kind of effect on some kind of elaborate measure of some kind of surrogate outcome: maybe a molecule in the blood goes up in concentration, or down, in a way that suggests the intervention might be effective.

This is all very well. But it's not the same as showing that something really does actually work back here in the real world. Medicine is overflowing with unfulfilled promises from this kind of early theoretical research. It's not even in the same ballpark as showing that something works.

Oddly enough, someone has now finally conducted a proper trial of fish oil pills, in mainstream children, to see if they work: a well-conducted, randomised, double-blind, placebo-controlled trial, in 450 children aged 8–10 years from a mainstream school population. It was published in full this year – and the researchers found no improvement. Show me the news headlines about that paper.

Meanwhile, Euromonitor estimates global sales for fish oil pills to be at $2bn, having doubled in five years, with sales projected to reach $2.5bn by 2012. The pills are now the single best-selling product in the UK food supplement market. This has only been possible with the kind assistance of the British media, and their eagerness for stories about the magic intelligence pill.

• This article was amended on Wednesday 9 June 2010 to remove a link to an article in the Observer which is no longer available online