4 ms·

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per

by keenerd 11y ago

While hindsight is 20:20, parts of this should have been more obvious. > Daniels generously defined as someone whose measurements were within the middle 30 per cent of the range of values > 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. 30% raised to the third power is 2.7%. Basic probability. I guess everyone assumed there would be heavy clustering instead of largely independent variables?

muddyrivers 11y ago
That is over-simplification. First, the samples are not randomly selected. The selection process tended to lean toward means, based on the article. Second, the variables are not independent. They are strongly correlated. The selection process indicated that the probability of having a pilot with long legs but short arms was close to zero.
- cowsandmilk 11y ago
  > They are strongly correlated Uh, no. What the study shows is that people assumed these measurements would be strongly correlated, but they were not. When only 3.5% of people fall into the middle 30% on 3 variables, that is strong evidence that they are mostly independent.
sparky_z 11y ago
Assuming a normal distribution instead of a uniform one isn't that outlandishly unreasonable.
- keenerd 11y ago
  He didn't assume a normal distribution. It wasn't "within ±15% of the mean". It was "the middle 30% of the range". This means excluding 70% of the population for each factor, regardless of the distribution. Finding a "normal person" was impossible from the beginning with that approach.
  - dgemm 11y ago
    The original assumption before Daniels was that the data would follow a normal distribution and so there was an "average" pilot. He showed that was wrong.
    - thaumasiotes 11y ago
      I can't tell what you mean. In some sense (not a very good one), the data must follow a normal distribution, as the sum of normal distributions is itself a normal distribution. But that would imply that you could sensibly add values like "circumference of upper arm" and "length, ankle to knee", which you really shouldn't be doing. - If you measure values from a 10-dimensional space, what would it mean for them to be "normally distributed"? Do we norm them by distance to the center of the space, or what? Does that approach preserve the nice properties of normals? - If this concept exists, did Daniels or anyone related to the project know that? Is it really what they were looking for? - If this concept exists, were the pilots in fact normally distributed? Saying "the data should follow a normal distribution" without having a definition of "normal distribution" that allows for multidimensional points immediately implies that all body measurements are correlated with all other body measurements at plus or minus 1, which I'm certain nobody believed. And the individual measurements are normally distributed.
      - JupiterMoon 11y ago
        I this case they may not have been. Given the US Airforce was selecting pilots with measurements within certain bounds their measurements were probably a truncated normal.
      - eru 11y ago
        You are looking for https://en.wikipedia.org/wiki/Multivariate_normal_distribution https://en.wikipedia.org/wiki/Multivariate_normal_distributi...
  - Dylan16807 11y ago
    "the middle 30% of the range" is ambiguous. I interpreted it as mean ± .15 * [max - min] Also it's only impossible from the beginning if you assume the values are uncorrelated. That's an even worse thing to assume than the existence of an 'average person'.
tomjen3 11y ago
Only if the variables are independent, right? Because I would expect a tall guy to have longer arms than I have.
andrewfong 11y ago
> The Aero Medical Laboratory hired Daniels because he had majored in physical anthropology, a field that specialized in the anatomy of humans, as an undergraduate at Harvard. During the first half of the 20th century, this field focused heavily on trying to classify the personalities of groups of people according to their average body shapes — a practice known as “typing.” For example, many physical anthropologists believed a short and heavy body was indicative of a merry and fun-loving personality, while receding hairlines and fleshy lips reflected a “criminal type.” Also, for what's it worth, this was during (or at least not too far removed from) a time period where researchers were trying to ascribe all sorts of random characteristics to people based on whether they were "Negroids", "Caucasoids", or "Mongoloids". This says a lot to me about how people thought about physical characteristics back then. If researchers assumed male-pattern baldness was associated with a "criminal type", then it's not a huge stretch to imagine that researchers assumed there was a "pilot type" with a large number of clustered or heavily correlated characteristics.
- foolrush 11y ago
  Lombroso et al. Worth noting that this phenomenon is typically described as “medicalization.” Othered groups medicalized include women, African Americans, homosexuals, and many other groups. The medicalization of Jewish ancestry cropped up and was amplified during a not-too-distant past.
- deleted 11y ago
  [deleted]

by keenerd 11y ago

muddyrivers 11y ago

That is over-simplification. First, the samples are not randomly selected. The selection process tended to lean toward means, based on the article. Second, the variables are not independent. They are strongly correlated. The selection process indicated that the probability of having a pilot with long legs but short arms was close to zero.

cowsandmilk 11y ago
> They are strongly correlated Uh, no. What the study shows is that people assumed these measurements would be strongly correlated, but they were not. When only 3.5% of people fall into the middle 30% on 3 variables, that is strong evidence that they are mostly independent.

sparky_z 11y ago

Assuming a normal distribution instead of a uniform one isn't that outlandishly unreasonable.

keenerd 11y ago
He didn't assume a normal distribution. It wasn't "within ±15% of the mean". It was "the middle 30% of the range". This means excluding 70% of the population for each factor, regardless of the distribution. Finding a "normal person" was impossible from the beginning with that approach.
- dgemm 11y ago
  The original assumption before Daniels was that the data would follow a normal distribution and so there was an "average" pilot. He showed that was wrong.
  - thaumasiotes 11y ago
    I can't tell what you mean. In some sense (not a very good one), the data must follow a normal distribution, as the sum of normal distributions is itself a normal distribution. But that would imply that you could sensibly add values like "circumference of upper arm" and "length, ankle to knee", which you really shouldn't be doing. - If you measure values from a 10-dimensional space, what would it mean for them to be "normally distributed"? Do we norm them by distance to the center of the space, or what? Does that approach preserve the nice properties of normals? - If this concept exists, did Daniels or anyone related to the project know that? Is it really what they were looking for? - If this concept exists, were the pilots in fact normally distributed? Saying "the data should follow a normal distribution" without having a definition of "normal distribution" that allows for multidimensional points immediately implies that all body measurements are correlated with all other body measurements at plus or minus 1, which I'm certain nobody believed. And the individual measurements are normally distributed.
    - JupiterMoon 11y ago
      I this case they may not have been. Given the US Airforce was selecting pilots with measurements within certain bounds their measurements were probably a truncated normal.
    - eru 11y ago
      You are looking for https://en.wikipedia.org/wiki/Multivariate_normal_distribution https://en.wikipedia.org/wiki/Multivariate_normal_distributi...
- Dylan16807 11y ago
  "the middle 30% of the range" is ambiguous. I interpreted it as mean ± .15 * [max - min] Also it's only impossible from the beginning if you assume the values are uncorrelated. That's an even worse thing to assume than the existence of an 'average person'.

tomjen3 11y ago

Only if the variables are independent, right? Because I would expect a tall guy to have longer arms than I have.

andrewfong 11y ago

> The Aero Medical Laboratory hired Daniels because he had majored in physical anthropology, a field that specialized in the anatomy of humans, as an undergraduate at Harvard. During the first half of the 20th century, this field focused heavily on trying to classify the personalities of groups of people according to their average body shapes — a practice known as “typing.” For example, many physical anthropologists believed a short and heavy body was indicative of a merry and fun-loving personality, while receding hairlines and fleshy lips reflected a “criminal type.” Also, for what's it worth, this was during (or at least not too far removed from) a time period where researchers were trying to ascribe all sorts of random characteristics to people based on whether they were "Negroids", "Caucasoids", or "Mongoloids". This says a lot to me about how people thought about physical characteristics back then. If researchers assumed male-pattern baldness was associated with a "criminal type", then it's not a huge stretch to imagine that researchers assumed there was a "pilot type" with a large number of clustered or heavily correlated characteristics.

foolrush 11y ago
Lombroso et al. Worth noting that this phenomenon is typically described as “medicalization.” Othered groups medicalized include women, African Americans, homosexuals, and many other groups. The medicalization of Jewish ancestry cropped up and was amplified during a not-too-distant past.
deleted 11y ago
[deleted]