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Is this common sense and by definition of what an average is?


It seems to be a textbook example of the Simpson's paradox.


In a sense, but it is a bit more devious. It basically invalidates all past fMRI studies. Not that anyone should have taken those seriously, but it looks like another nail in the coffin. fMRI analysis is (was?) basically: squeeze each brain scan into a standard box, then average the BOLD responses (that's roughly oxygen usage between 3s and 9s after activity). This abstract says that --at least in some cases-- those averages are wrong. Not just hiding information through aggregation, but flat-out lying.

Just from reading the link, I do see an objection: they studied repetitions, which are known to be different from the initial response, so this may not be the fMRI's eulogy.


What cases was it saying it was lying? An average and a median can be drastically different without the average being false, right?


The averages a "standard" fMRI analysis produces highlights brain areas which may not even have been involved in the majority of subjects, because the pattern is so wide spread. That is in contrast with your usual average or median over e.g. height. It's a bit like averaging squares on a chess board and concluding that the opening is played in the middle two columns.


I mean.. it kind of is, and even more about control of these two columns..




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