tiffinboys wrote:

Disclaimer: Not a mathematician or statistician, so excuse me if I get this wrong.

twelveminus wrote:

If verbal reasoning and non-verbal reasoning scores were independent of each other then with 115 equal to one in six of the population, then overall that would be roughly one-in-thirty-six of the population (the top 2.5%), which is indeed 'super-selective'.

However clearly VR and NVR scores are significantly correlated, so given that a student has VR of 115 or over, the top 16% of the population, then the chance that they also have a NVR score of 114 or over, is self-evidently much, much greater than one-in-six.

I would have thought that if only 2.5% would achieve 115 or more in VR

or NVR, then the children scoring 115 or above in

both VR and NVR would not be more than 2.5%; rather would be much less.

Well, I stand to be corrected.

No, as I said, a score of 115 or greater on a given standardised test will be attained by roughly one in six of the population.

So if we have every child in the country sit a NVR and a VR test, and we randomly pick a test from either pile, then there is roughly one-in-six chance that it will be 115 or above (see this graph:

http://upload.wikimedia.org/wikipedia/c ... am.svg.png 115 is 1 σ for modern IQ tests, GL CAT tests, etc., so you are looking at the area to the right of that, roughly 1 in 6).

If we then randomly select a test from the other pile, the chance is again approximately one-in-six.

The chance of both randomly selected tests being 115 or above is therefore (approximately) 1/6 * 1/6, which is 1/36, or, slightly more accurately, 2.5%.

However this is not what we are doing - we are not randomly selecting two unrelated tests (by different candidates) from the whole population, we are actually selecting from a population that is already above average (since most of the weakest won't waste their time entering), AND the two tests are by the same candidates and are therefore scores should be highly correlated between the two tests by the same candidate.

If you were asked to guess what a randomly chosen IQ test score would be out of the whole country, then you should say '100', as this is the most common value. But if you were told that a given child has a score of 115 for verbal-reasoning, and wanted to guess what their NVR score was, you certainly wouldn't guess '100', because children with high VR scores are likely to have high NVR scores also. I guess the most likely score given the information we have would actually be '115'.

Conditional probability.....