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Good_Burning_Plastic comments on Open Thread, Apr. 20 - Apr. 26, 2015 - Less Wrong
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That's a good point, but on the other hand, even thinking that everything is a Gaussian would be a vast improvement over thinking that everything is a Dirac delta and it is therefore not ludicrous to speculate about why some politician's approval rating went down from 42.8% last week to 42.3% today when both figures come from surveys with a sample size of 1600.
A well trained mathematician or physicist who never took a formal course on statistics likely isn't going to make that error, just as a well trained statistician isn't going to make that error.
I would think that the mathematician is more likely to get this right than the medical doctor who got statistics lessons at med school.