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V_V comments on 2012 Survey Results - Less Wrong
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I don't think you could really apply any 'algorithmic' method to that question (other than looking it up, but that would be cheating). It was a test on how much confidence you put in your heuristics. (BTW, It seems that I've underestimated mine, or I've been lucky, since I've got the date off by one year but estimated my confidence at 50% IIRC). Still, it was a valuable test, since most of human reasoning is necessarily heuristic.
Really? What probability do you assign to that statement being true? :D
I'm under the impression that Bayes' theorem is included in the high school math programs of most developed countries, and I'm certain it is included in any science and engineering college program.
I assign about 80% probability to less than 25% of adults knowing Bayes theorem and how to use it. I took physics and calculus and other such advanced courses in high school, and graduated never having heard of Bayes' Theorem. I didn't learn about it in university, either–granted, I was in 'Statistics for Nursing', it's possible that the 'Statistics for Engineering' syllabus included it.
Only 80%?
In the USA, about 30% of adults have a bachelor's degree or higher, and about 44% of those have done a degree where I can slightly conceive that they might possibly meet Bayes' theorem (those in the science & engineering and science- & engineering-related categories (includes economics), p. 3), i.e. as a very loose bound 13% of US adults may have met Bayes' theorem.
Even bumping the 30% up to the 56% who have "some college" and using the 44% for a estimate of the true ratio of possible-Bayes'-knowledge, that's only just 25% of the US adult population.
(I've no idea how this extends to the rest of the world, the US data was easiest to find.)
You did your research and earned your confidence level. I didn't look anything up, just based an estimate on anecdotal evidence (the fact that I didn't learn it in school despite taking lots of sciences). Knowing what you just told me, I would update my confidence level a little–I'm probably 90% sure that less than 25% of adults know Bayes Theorem. (I should clarify that=adults living in the US, Canada, Britain, and other countries with similar school systems. The percentage for the whole world is likely significantly lower.)
I hear Britain's school system is much better than the US's.
Once you control for demographics, the US public school system actually performs relatively well.
Good point.
The UK high school system does not cover Bayes Theorem.
If you choose maths as one of your A-levels, there's a good chance you will cover stats 1 which includes the formula for Bayes' Theorem and how to apply it to calculate medical test false positives/false negatives (and equivalent problems). However it isn't named and the significance to science/rationality is not explained, so it's just seen as "one more formula to learn".
Offhand, 1/2 young people do A levels, 1/4 of those do maths, and 2/3 of those do stats, giving us 1/12 of young people. I don't think any of these numbers are off by enough to push the fraction over 25%
Maybe you guys could solve that problem by publishing some results demonstrating its exteme significance
As far as I know, it's been formally demonstrated to be the absolutely mathematically-optimal method of achieving maximal hypothesis accuracy in an environment with obscured, limited or unreliable information.
That's basically saying: "There is no possible way to do better than this using mathematics, and as far as we know there doesn't yet exist anything more powerful than mathematics."
What more could you want? A theorem proving that any optimal decision theory must necessarily use Bayesian updating? ETA: It has been pointed out that there already exists such a theorem. I could've found that out by looking it up. Oops.
There already is such a theorem. From Wikipedia:
It's not great by international standards, but I have heard that the US system is particularly bad for an advanced country.
In terms of outcomes, the US does pretty terribly when considered 1 country, but when split into several countries it appears at the top of each class. Really, the EU is cheating by considering itself multiple countries.
The EU arguably is more heterogeneous than the US. But then, India is even more so.
How's it being split?
I actually thought someone would dig up and provide the relevant link by now. I'll have to find it.
You mean comparing poorer states to poorer countries?
Actually it is quite good (even for an "advanced country") if you compare the test scores of, say, Swedes and Swedish-Americans rather than Swedes and Americans as a whole.
I wonder what that's controlling for? Cultural tendencies to have different levels of work ethic?
Hmmm. So it's "good" but people with the wrong genes are spoiling the average somehow.
Must be a problem of the American school system, I suppose.
Did they teach you about conditional probability? Usually Bayes' theorem is introduced right after the definition of conditional probability.
Well, it's certainly not included in the US high school curriculum.
There are national and international surveys of quantitative literacy in adults. The U.S. does reasonably well in these, but in general the level of knowledge is appalling to math teachers. See this pdf (page 118 of the pdf, the in-text page number is "Section III, 93") for the quantitative literacy questions, and the percentage of the general population attaining each level of skill. less than a fifth of the population can handle basic arithmetic operations to perform tasks like this:
People who haven't learned and retained basic arithmetic are not going to have a grasp of Bayes' theorem.
I'm pretty sure Ireland doesn't have it on our curriculum, not sure how typical we are.
It was in my high school curriculum (in Italy, in the mid-2000s), but the teacher spent probably only 5 minutes on it, so I would be surprised if a nontrivial number of my classmates who haven't also heard of it somewhere else remember it from there. IIRC it was also briefly mentioned in the part about probability and statistics of my "introduction to physics" course in my first year of university, but that's it. I wouldn't be surprised if more than 50% of physics graduates remember hardly anything about it other than its name.