Earlier quoted context omitted.
Post hoc ergo propter hoc is one of the classic logical fallacies[1]. You persist in the assumption that poverty causes lower IQ, rather than the possibility that both poverty and lower IQ are correlated because they share a common cause. [1] See http://www.skepdic.com/posthoc.html
The way you do a controlled experiment in science is that you have a number of subjects, you subject only some of them to some new condition, and then you look for statistically significant differences between the group subject to the condition and the one that wasn't. That was what happened in the study I mentioned. Now, you can say that this wasn't absolute proof and you'd be right, because science doesn't provide…
No, what needs to be thrown out is armchair scientists who don't properly understand the scientific method. Just because you've shown a statistically-significant correlation between two phenomenon, there really is very little reason to expect that shoring up one of those phenomenon will actually have an effect on the other.
Let's look at the question at hand, the correlation between (low) IQ and childhood poverty. Observing that the poor are more likely to be undernourished and at the same time, children in poverty show fewer signs of inherited high intelligence, there is very little (one might even say zero) reason to believe that giving poor kids food will improve their intelligence.
People seem to nod their heads and say "yeah, whatever" when challenged on the difference between causation and correlation, but in fact there's a world of difference.
Here's an alternative speculation about the real causation of the observation. Being a single-parent household causes poverty because a smaller income must be spread across the same fixed expenses (rent, etc.) and nearly the same variable expenses (say, 3/4 the food, medical care, etc.), and thus the money "runs out" sooner. Being a single-parent household also causes lower IQ, because there is less parental involvement available to the child (helping with homework and the like), because a single parent must be consuming at least as much time working, more (per family member) doing necessary household chores, and thus less remains for the kid.
Through this chain of causation, throwing food at the problem may fix the malnutrition, but that's not the identified cause of the lower IQ, so if our goal is to improve IQs, then the investment was entirely wasted. We've still got as many single-parent households who can't invest as much time interacting with the child, and since the actual cause is still out there, there will be just as many lower-IQ kids. Your un-scientific jump to conclusions about the causation has wasted what you've invested to fix it, and worse, because you believed you were fixing it, you've actually blocked more legitimate efforts to fix the real cause.
Really: seeing a correlation is no reason to believe that there's causation in effect. This is true in philosophy, but just as true in science!