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RichardKennaway comments on The Universal Medical Journal Article Error - Less Wrong Discussion
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Are you intending the irony there?
BTW, it seems to me that your point is about an error of statistical inference, not first-order logic. Specifically, experimenters not noticing their assumption that the population is homogeneous. When the assumption is wrong, wrong inferences can follow. That is, inferences which correctly follow from the assumption and the experimental results, but which are nevertheless false.
No; the difference is that in your interpretation, we would say "wrong assumption, hence discard results." In my interpretation, if they had found a significant effect, they would have been able to correctly conclude that there was an effect; and finding no significant effect, they could have correctly concluded the negation of that.
I don't know what irony you refer to.
I am confused. In your article you said that researchers on food colouring and hyperactivity found no significant effect and concluded there was none, and criticised them for doing that since, according to later work, there is a significant effect among a small subpopulation. Now you are saying that they correctly concluded that there was no significant effect ("no significant effect" being the negation of "significant effect").
What I said in my comment above is misleading. If they had found an effect, it would have meant something, although they would have again stated it as stronger than it really was: "For all children, food dye affects behavior." There could in fact have been one food dye monster child whose behavior was radically altered by food dye. Having failed to find an effect, they can conclude that they failed to find an effect on all children, which is still useful information but in practice would be very difficult to use correctly.