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Here's the thing about IQ curves. Let's assume, for the moment, that we create a new "WQ" (waps quotient). It is 1000 random questions that you either know or d
by waps 11y ago
Here's the thing about IQ curves. Let's assume, for the moment, that we create a new "WQ" (waps quotient). It is 1000 random questions that you either know or don't know, which have absolutely nothing to do with eachother (who is the beatles' lead singer, what is the 7th prime number, did Mr. Garrison ever kill Kenny, is Spam searching related to Bayes' rule ? (nope, it's Bayes theorem), ...
For every question you have right you get +0.1, for every wrong answer you get 0. Obviously this proves nothing about you, except that you've at some point looked up the beatles, or actually looked up history of Thomas Bayes, or ... In other words it's a long list of "do you know trick X" bits.
What would the division of WQ in the population look like ? Exactly like the division of IQ in the population. [1] [2]
Here's a supposition : the IQ stat is exactly that. It's measuring of how many of the "little tricks" known by a test maker you know. The better you match the test maker, the better your score (think mostly cultural, but also whether your parents are academics or not, ...)
Although I must say, teaching kids "tricks" with numbers (e.g. how to tell if a number is divisible by 9 by looking at individual digits) and symbols is a good way to make them good at math over time.
[1] http://en.wikipedia.org/wiki/Binomial_distribution http://en.wikipedia.org/wiki/Binomial_distribution (read top paragraph, note that n will be a relatively large 1000)
[2] http://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation http://en.wikipedia.org/wiki/Binomial_distribution#Normal_ap...
- gohrt 11y agoYour theory would also need to explain correlations between scores on different IQ tests taken by the same test-taker. And knowing the answers to more or less questions than someone else is suggestive of something, if the questions are broad enough. Especially if someone else grew up in the same culture as you
- mturmon 11y ago"Your theory would also need to explain correlations between scores on different IQ tests taken by the same test-taker." I think that one is easy: In fact, @waps has a bag of M questions, where M > 1000. To compose a new WQ test, he draws 1000 questions, without replacement, from his bag. Then the series of tests has some similar or even same questions. In such a case the scores must be correlated. This is not too far off-base. Especially when you consider that many questions are superficially different, but really the same. E.g., those "name the next number in the series" questions.
- Jach 11y agoBetter to explain the correlation with job performance, and why the correlation improves with more complex jobs. http://www.udel.edu/educ/gottfredson/reprints/1997whygmatters.pdf http://www.udel.edu/educ/gottfredson/reprints/1997whygmatter...
- rawnlq 11y agoHmm, is it still binomial if each individual question has different p of being correct? Also you will have to shift and rescale the binomial distribution to get it to have a mean of 100 and a std dev of 15 (which iq is defined as). But you did answer my question on why IQ is normally distributed: the IIDs being averaged are the test questions themselves! (although I don't fully understand if those questions are bernoullis?)
- rawnlq 11y agoThinking about it more I think it makes more sense to have N as the number of test takers. That way you can model it as a question x having a probability p_x of being correct. Then the total grade on problem x will be a binomial(N, p_x), which will converge to a normal distribution for large number of test takers. Then you are simply summing up a small number of normal approximations to get the final grade (and sum of normals is normal). Did I model that correctly?
- agumonkey 11y agoIf intelligence is about seeing the invisible, Rorschach tests would fare better. I'd love to see 'pioneering quotient' tests, when someone envision something out of a blurry mess; just like a pioneer stumbling on a new idea.