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 on placebo improved.Fish oil in the Observer: the return of a $2bn friend
This paper showed no difference in performance at all. Since it was a brain imaging study, not a trial, they only report the results of children's actual performance on the attention task in passing, in a single paragraph, but they are clear: "there were no significant group differences in percentage correct, commission errors, discriminability, or reaction time"...
And oddly enough, someone has finally now conducted a proper trial of fish oils 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 old from a mainstream school population. It was published in full this year (http://qurl.com/fish), and they found no improvement. Show me the news headlines about that paper.
(Image: Fish oil caps, a Creative Commons Attribution (2.0) image from spcummings's photostream)
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I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.