

Common sense and statistics - jaimebuelta
http://www.johndcook.com/blog/2014/09/18/common-sense/

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onion2k
My favourite example of why common sense is pretty useless in maths is an
example of comparing averages;

There are two shops, each with 5 salespeople. One shop performs very well,
each of the salespeople selling 50, 40, 40, 40 and 30 widgets respectively.
The other performs very badly, as the staff selling 20, 10, 10, 10 and 0
widgets each.

    
    
        The average monthly sales for the first shop is (50+40+40+40+30)/5 = 40 widgets.
    
        The average monthly sales for the second shop is (20+10+10+10+0)/5 = 10 widgets.
    

As an experiment the worst salesperson from Shop 1 is moved to Shop 2.

    
    
        The average monthly sales for the first shop is (50+40+40+40)/4 = 42.5 widgets.
    
        The average monthly sales for the second shop is (30+20+10+10+10+0)/6 = 13.3 widgets.
    

Common sense says that both stores are now performing 'better', but quite
obviously that is nonsense.

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yummyfajitas
Conversely, this also illustrates a fallacy in many arguments against
immigration. Suppose Mexicans/Indians/whoever are all (or predominantly) worse
than Americans on whatever scale you choose to measure them. When you allow
immigration you'll cause averages to go down in both countries by the converse
of the mechanism you describe above.

Various people (Vinod Khosla, Steve Sailer) fallaciously use this statistical
truism as an argument against immigration by people without a PhD.

The only way I can think of to steelman arguments like this are by combining
Steve Sailer style nationalism with fairly extreme "redistribute all the
things" liberalism.

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spindritf
I don't get the fallacy. If you believe that there are positive externalities
from living in a country with people who are better on whatever scale you
choose to measure them, then migration benefits a (relatively) small number of
migrants and hurts everyone else, both in their country of origin and
destination.

Whether this should prevail over freedom of individuals is another matter.

~~~
yummyfajitas
Externalities is a separate argument, and requires doing more than simply
looking at average qualities.

If you want to make that argument you need to start by drawing the line
between people who are positive and people who are negative. This is a more
compelling argument, but it's not the one I described.

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shanacarp
Actually, this is pretty good advice. For everyday problems, if it doesn't
line up with common sense, usually it ends up meaning I need to ask more
questions. Models that tend to not be close enough to reality means I need to
observe reality more.

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GFK_of_xmaspast
"common sense" is just data that agrees with your priors.

