5 ms·

Common sense and statistics

23 points by jaimebuelta 12y ago

shanacarp 12y ago
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.
onion2k 12y ago
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.
- misframer 12y ago
  If you keep the units in mind, they are performing better on average per salesperson.
  - onion2k 12y ago
    To clarify, I meant 'both stores' as a whole. I should have made that clearer.
    - kaoD 12y ago
      That's not fair. A mean is a way to group values, in this case per salesman. Both stores are doing better per salesman! You're the one ignoring the per salesman part, which might or might not be due to "common sense". If you want to compare both stores per se, the operator you want is sum, not average.
      - jiggy2011 12y ago
        The point , I think is that it's an easy way to mislead, "Average employee productivity is up in all our stores!". Of course in reality it's a good idea to mix high performers in with low performers to teach them to improve.
        shanacarp 12y ago
        But that goes back to the original point of the article.
        shanacarp 12y ago
        But that goes back to the original point of the article.
- nodata 12y ago
  Each store is performing better: the successful store lost its weakest sales person, the unsuccessful store gained a (comparatively) excellent sales person.
  - robrenaud 12y ago
    What if that worst salesman in the good store was costing the store $50K, and making it $100K? Average is the wrong metric here. Something like profit is the right one.
    - nodata 12y ago
      Sure, that's another metric.
- yummyfajitas 12y ago
  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.
  - sogen 12y ago
    'Vinod' doesn't sound too american btw And aren't there studies that confirm inmigrants are more likely to contribute to the wealth of a country?
    - yummyfajitas 12y ago
      Khosla is a PIO, but as I recall from his debate with Bryan Caplan (they were both supposed to be on the same side!) he only favors immigration of highly skilled individuals. I'm having trouble finding it, but he had very little substance behind his arguments - just a cheap slogan ("import prosperity, not poverty" or something like that). Overall it was very disappointing. There are good arguments to be made both for and against immigration - the particular one I describe here just isn't one of them.
  - spindritf 12y ago
    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 12y ago
      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.
- brazzy 12y ago
  I think that's just another form of Simpson's paradox.
- iconjack 12y ago
  I believe this is an example of Simpson's Paradox mentioned in the article.
GFK_of_xmaspast 12y ago
"common sense" is just data that agrees with your priors.

23 points by jaimebuelta 12y ago

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.

onion2k 12y ago

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.

misframer 12y ago
If you keep the units in mind, they are performing better on average per salesperson.
- onion2k 12y ago
  To clarify, I meant 'both stores' as a whole. I should have made that clearer.
  - kaoD 12y ago
    That's not fair. A mean is a way to group values, in this case per salesman. Both stores are doing better per salesman! You're the one ignoring the per salesman part, which might or might not be due to "common sense". If you want to compare both stores per se, the operator you want is sum, not average.
    - jiggy2011 12y ago
      The point , I think is that it's an easy way to mislead, "Average employee productivity is up in all our stores!". Of course in reality it's a good idea to mix high performers in with low performers to teach them to improve.
      - shanacarp 12y ago
        But that goes back to the original point of the article.
      - shanacarp 12y ago
        But that goes back to the original point of the article.
nodata 12y ago
Each store is performing better: the successful store lost its weakest sales person, the unsuccessful store gained a (comparatively) excellent sales person.
- robrenaud 12y ago
  What if that worst salesman in the good store was costing the store $50K, and making it $100K? Average is the wrong metric here. Something like profit is the right one.
  - nodata 12y ago
    Sure, that's another metric.
yummyfajitas 12y ago
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.
- sogen 12y ago
  'Vinod' doesn't sound too american btw And aren't there studies that confirm inmigrants are more likely to contribute to the wealth of a country?
  - yummyfajitas 12y ago
    Khosla is a PIO, but as I recall from his debate with Bryan Caplan (they were both supposed to be on the same side!) he only favors immigration of highly skilled individuals. I'm having trouble finding it, but he had very little substance behind his arguments - just a cheap slogan ("import prosperity, not poverty" or something like that). Overall it was very disappointing. There are good arguments to be made both for and against immigration - the particular one I describe here just isn't one of them.
- spindritf 12y ago
  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 12y ago
    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.
brazzy 12y ago
I think that's just another form of Simpson's paradox.
iconjack 12y ago
I believe this is an example of Simpson's Paradox mentioned in the article.

GFK_of_xmaspast 12y ago

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