4 ms·

[The bell curve] crops up a lot when talking about traits in a population, such as intelligence. The reason for this is well understood (see central limit theor

[The bell curve] crops up a lot when talking about traits in a population, such as intelligence. The reason for this is well understood (see central limit theorem) and won’t concern us here. No! The Central Limit Theorem states that the average of the values in the distribution creates a bell curve -- not that it starts out that way. Traits in a population do not follow a bell curve and the CLT doesn't give any reason why they should.

myg204 12y ago
If one considers intelligence (or other features) as the sum of many random sources, then it makes sense again to invoke the CLT. Maybe that's what the article implied. [edit: see other replies saying the same thing below]
- leni536 11y ago
  "Intelligence" itself is not a well defined quantity like height or weight. IQ is well defined but it is defined to follow a bell curve, it has nothing to do with CLT.
  - gwern 11y ago
    Intelligence is a well-defined quantity like temperature, and it follows a genetic architecture like height: thousands of genetic variants of small effect size. Which setup does indeed give you a binomial or normal sort of distribution, justifying the norming as more than a mathematical convenience.
    - leni536 11y ago
      >Which setup does indeed give you a binomial or normal sort of distribution distribution of what? Still no quantity defined. >Intelligence is a well-defined quantity like temperature As a physicist it sounds about right. Temperature is tricky to define in non-stationary systems (aka. "real world").
      - deleted 11y ago
        [deleted]
  - myg204 11y ago
    As per wikipedia: "An intelligence quotient, or IQ, is a score derived from one of several standardized tests designed to assess human intelligence. " I fail to see how IQ is "defined to follow a bell curve" as you wrote. The tests were designed so the answers distribution is a bell curve? In my statement above, just replace "Intelligence" by "IQ", I believe that's what being discussed. In any case, "Intelligence" can takes a thousand forms that I don't think IQ tests or even our vocabulary can really pin down.
    - leni536 11y ago
      As per wikipedia: "When current IQ tests are developed, the median raw score of the norming sample is defined as IQ 100 and scores each standard deviation (SD) up or down are defined as 15 IQ points greater or less" Raw test scores are transformed so the test results distribute on a bell curve. Can't find a more precise definition though.

myg204 12y ago

If one considers intelligence (or other features) as the sum of many random sources, then it makes sense again to invoke the CLT. Maybe that's what the article implied. [edit: see other replies saying the same thing below]

leni536 11y ago
"Intelligence" itself is not a well defined quantity like height or weight. IQ is well defined but it is defined to follow a bell curve, it has nothing to do with CLT.
- gwern 11y ago
  Intelligence is a well-defined quantity like temperature, and it follows a genetic architecture like height: thousands of genetic variants of small effect size. Which setup does indeed give you a binomial or normal sort of distribution, justifying the norming as more than a mathematical convenience.
  - leni536 11y ago
    >Which setup does indeed give you a binomial or normal sort of distribution distribution of what? Still no quantity defined. >Intelligence is a well-defined quantity like temperature As a physicist it sounds about right. Temperature is tricky to define in non-stationary systems (aka. "real world").
    - deleted 11y ago
      [deleted]
- myg204 11y ago
  As per wikipedia: "An intelligence quotient, or IQ, is a score derived from one of several standardized tests designed to assess human intelligence. " I fail to see how IQ is "defined to follow a bell curve" as you wrote. The tests were designed so the answers distribution is a bell curve? In my statement above, just replace "Intelligence" by "IQ", I believe that's what being discussed. In any case, "Intelligence" can takes a thousand forms that I don't think IQ tests or even our vocabulary can really pin down.
  - leni536 11y ago
    As per wikipedia: "When current IQ tests are developed, the median raw score of the norming sample is defined as IQ 100 and scores each standard deviation (SD) up or down are defined as 15 IQ points greater or less" Raw test scores are transformed so the test results distribute on a bell curve. Can't find a more precise definition though.