5 ms·

I don’t think so. They also said: > Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size ... less than 3.5

by ken 6y ago

I don’t think so. They also said: > Even more astonishing, Daniels discovered that if you picked out just three of the ten dimensions of size ... less than 3.5 per cent of pilots would be average sized on all three dimensions.

Someone 6y ago
FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“ 0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.
- Retric 6y ago
  I think the general assumption is arm length and height for example are strongly correlated.
- Worker32850 6y ago
  Human dimensions are closer to a normal distribution. (Not quite normal, but let's pretend.) In that distribution then 46% of subjects should be in the middle 30% of 3 dimensions. [0] [0] With 4000 subjects they presumably have all sizes within ~3.5 stddevs represented. The middle ~1.2 stddevs should hold ~77% of the population. 0.77^3 = ~46%
  - dragonwriter 6y ago
    > Human dimensions are closer to a normal distribution Human height is (it's the textbook example of a real, intuitive_that is, using the normal linear scale—physical measure that is a good fit for a normal distribution) plenty of other human dimensions are not.
    - smabie 6y ago
      Human height should be a negative binomial distribution, since human height can't be negative.
      - dragonwriter 6y ago
        > Human height should be a negative binomial distribution, since human height can't be negative. That's a sensible analytical speculation, but it empirically fits very well with a normal distribution. The fact that zero is, for adult male height (the typical cited example for fitting a nor Al distribution, though adult female height also works), around 17 standard deviations below the mean helps: I won't bother to calculate how little should be below that, since below 7σ in a normal distribution is 1/780 billion.

by ken 6y ago

Someone 6y ago

FTA: ”These formed the dimensions of the “average pilot,” which Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values for each dimension.“ 0.3³ = 0.0027 = 2.7%, so if those measurements are independent of each other, it isn’t surprising that he found “less than 3.5 percent”.

Retric 6y ago
I think the general assumption is arm length and height for example are strongly correlated.
Worker32850 6y ago
Human dimensions are closer to a normal distribution. (Not quite normal, but let's pretend.) In that distribution then 46% of subjects should be in the middle 30% of 3 dimensions. [0] [0] With 4000 subjects they presumably have all sizes within ~3.5 stddevs represented. The middle ~1.2 stddevs should hold ~77% of the population. 0.77^3 = ~46%
- dragonwriter 6y ago
  > Human dimensions are closer to a normal distribution Human height is (it's the textbook example of a real, intuitive_that is, using the normal linear scale—physical measure that is a good fit for a normal distribution) plenty of other human dimensions are not.
  - smabie 6y ago
    Human height should be a negative binomial distribution, since human height can't be negative.
    - dragonwriter 6y ago
      > Human height should be a negative binomial distribution, since human height can't be negative. That's a sensible analytical speculation, but it empirically fits very well with a normal distribution. The fact that zero is, for adult male height (the typical cited example for fitting a nor Al distribution, though adult female height also works), around 17 standard deviations below the mean helps: I won't bother to calculate how little should be below that, since below 7σ in a normal distribution is 1/780 billion.