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dspeyer comments on The Universal Medical Journal Article Error - Less Wrong
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If 11 out of 11 children studied have a property (no food coloring hyperactivity response), that's a bit stronger than "there exist 11 children with this property", though perhaps not quite "all children have this property".
That's not how it works. You measure the magnitude of an effect, then do a statistical test of the hypothesis that all of the children have a response, which gives a cutoff that the effect magnitude must reach to accept that hypothesis with 95% confidence. If only 10% of the children have such a response, you won't reach that cutoff. If 10% have a positive response and 10% have a negative response, you will detect nothing, no matter how big your sample is.