Here is an abstract of an enormously interesting and already famous 2002 study of the effect of better nutrition on the behavior of prison inmates. The supplements included omega-3 fats.
The study was very innovative and no doubt extremely difficult. About as far from studying lab rats or college students as you can get. Here are the key results:
Those who received the active capsules committed on average 11.8 infringements per 1000 person-days, a reduction of 26.3% (95% CI 8.3-44.3%) compared to those who received placebos. This difference between groups was statistically significant at P<0.03 (two-tailed).
In spite of a huge effect — huge at least in practical terms — the statistical significance was marginal. There isn’t anything wrong with that, it indicates that we need a way of studying these very important issues that isn’t incredibly hard. Of course the “easy” method will be “deficient” (according to overly critical critics) in a dozen ways; that’s the price you pay. The authors of this article don’t entirely understand this point. “Further investigations should include assessments of nutritional status from blood before and during supplementation,” they write. Uh, no, you don’t always follow a very difficult thing by trying to do an even more difficult thing.
Nothing is said about the difficulty of the study, which is extremely important, in this report. The difficulty of a scientific study is always important but almost always goes unmentioned in scientific articles. If you (the reader) have done similar studies you can guess okay but with an innovative study like this few readers could have any clear idea.