8 ms·

> What are the independent and identically distributed random variables that are being averaged in this case? The random variable is simply whether you answere

by waps 11y ago

> What are the independent and identically distributed random variables that are being averaged in this case? The random variable is simply whether you answered question N on the test correctly or not. For every question there is a probability Pn that any given test taker answers it correctly, and that probability is relatively uniform per-question. (so scores on any test, where the same test is administered to a large numbers of test takers, will be normally distributed. Yes, even if the questions are nonsensical and the answers random) So an IQ score simply indicates the probability, relative to the general population, whether a test taker will answer simple abstract mathematical questions correctly (where correctly should be understood to have cultural biases).

panic 11y ago
The most important condition of the central limit theorem is that the variables are independent. In an IQ test, you'd hope the probability of answering a question correctly depends on your intelligence. Therefore these variables can't be independent from one another.
- waps 11y ago
  The thing about the central limit theorem is that violating it's assumptions doesn't really make it no longer apply. There's simply a few pathological cases where it totally breaks down, which violate that assumption and are very hard to state otherwise. But taking 2 variables that correlate 80% or 20% or even more will not change the outcome. It's just very near the edge that it totally breaks down, or if the number of variables that correlate is really too high, or if they're really chaotic variables, or ... So one the one hand you're right. But it's not a point that a statistician would make, only a logicist or a rather pedantic mathematician. In the graphs, even if things correlate it will "look okay". Therefore the statement that intelligence is normally distributed along a bell curve is technically correct, but good look finding a large piece of data that doesn't look like a bell curve.

by waps 11y ago

panic 11y ago

The most important condition of the central limit theorem is that the variables are independent. In an IQ test, you'd hope the probability of answering a question correctly depends on your intelligence. Therefore these variables can't be independent from one another.

waps 11y ago
The thing about the central limit theorem is that violating it's assumptions doesn't really make it no longer apply. There's simply a few pathological cases where it totally breaks down, which violate that assumption and are very hard to state otherwise. But taking 2 variables that correlate 80% or 20% or even more will not change the outcome. It's just very near the edge that it totally breaks down, or if the number of variables that correlate is really too high, or if they're really chaotic variables, or ... So one the one hand you're right. But it's not a point that a statistician would make, only a logicist or a rather pedantic mathematician. In the graphs, even if things correlate it will "look okay". Therefore the statement that intelligence is normally distributed along a bell curve is technically correct, but good look finding a large piece of data that doesn't look like a bell curve.