Re:The Nobel Prize in Physics 2019
by soVeryTired on Tuesday October 08, 2019 @10:19AM
(#21192574)
> Statistically, averages work only if distributions are symmetric.
I'm not really sure what you mean by that but I don't think you're correct. The law of large numbers applies to any distribution with finite first moment.
You're probably right in that factors like wealth (and wealth distribution rather than per-capita wealth) affect a country's scientific output. But your stats argument is a bit wobbly :)
It’s a more general statement that applies to say orange production as various plants only grow well in specific climates. Basically, if you’re looking at total calories consumed that is mostly a function of population size, but large samples don’t average out inherent differences.
Re:The Nobel Prize in Physics 2019
by denzil_correa on Tuesday October 08, 2019 @10:40AM
(#21192814)
> I'm not really sure what you mean by that but I don't think you're correct.
Can you explain, in context to what I said - what exactly is incorrect? I am very well versed with the theory of Law of Large numbers. The question is - "Why does the Law of Large Numbers tell us that per capita is a the right metric to compare Nobel Prize output of different countries?"
All he’s saying that the further mean and median are from each, the more importsnt it is that we think about what an average implies about the sample.
Re:The Nobel Prize in Physics 2019
by soVeryTired on Tuesday October 08, 2019 @07:02PM
(#21198230)
Well the median number of nobel prizes in any country is pretty obviously zero...
Be wary of any "per-capita" statistics. Statistically, averages work only if distributions are symmetric. Mean is a poor indicator of an asymmetric distribution.
So, the question is - Do we have symmetric distributions for talent within each geographical area? We see similar arguments in sport but the assumption of symmetrical (normal) distributions for talent within a geographical area is most likely not the case [0]. There are many other factors like income, population density and "coaching" centers that lead to existence of asymmetric distributions. Hence, "per capita" statistics are quite meaningless and mask the real factors that contribute to Nobel Prize winners.
Primarily, the proportion of GDP to research and scientific activity are a better measure to compare countries against [1]. That ensures that most predictive factors are accounted for.
[0] https://www.frontiersin.org/articles/10.3389/fpsyg.2018.0274...
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3968020/