11 Plus Exams Forum

This might be a hopelessly naive question, and apologies if it is, but are the pass marks for Tiffin equivalent to standardised IQ/GL-type scores, i.e. mean 100 (for all children of the age taking the test), standard deviation 15?

So with a cut-off of 229, this is equivalent to a score of 115 and 114 in both VR and NVR, i.e. only 1 sd above the mean?

Do I have this wrong? It doesn't seem terribly 'super-selective' if so.

twelveminus wrote:This might be a hopelessly naive question, and apologies if it is, but are the pass marks for Tiffin equivalent to standardised IQ/GL-type scores, i.e. mean 100 (for all children of the age taking the test), standard deviation 15?

So with a cut-off of 229, this is equivalent to a score of 115 and 114 in both VR and NVR, i.e. only 1 sd above the mean?

Do I have this wrong? It doesn't seem terribly 'super-selective' if so.

You may be right. And it would be lovely if more parents from distant areas share this view. That will help Tiffins rebuilt its roots in local community.

tiffinboys wrote:

twelveminus wrote:This might be a hopelessly naive question, and apologies if it is, but are the pass marks for Tiffin equivalent to standardised IQ/GL-type scores, i.e. mean 100 (for all children of the age taking the test), standard deviation 15?

So with a cut-off of 229, this is equivalent to a score of 115 and 114 in both VR and NVR, i.e. only 1 sd above the mean?

Do I have this wrong? It doesn't seem terribly 'super-selective' if so.

You may be right. And it would be lovely if more parents from distant areas share this view. That will help Tiffins rebuilt its roots in local community.

I suspect it would mean more distant parents applying, if more children have a chance of getting in. It's not like there is a great selection of more selective schools around and about is there.

The children taking the exam will be above average ability. Let's hypothesis the average IQ of applicants as 110-115.

Lets assume to get an offer you would have to have an IQ score above the average of the -applicants say minimum 125 IQ.

This is almost top 3% IQ of the whole school population-so it is very selective.

Well I don't really want to hypothesise anything.

If the cut-off is 229, then I'm wondering if that means an VR 'IQ' of 115 and a NVR 'IQ' of 114, for example.

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 expect the distribution of NVR ability for a given VR score to follow a normal distribution (bell curve) around the VR score, so if you get 115.00 for VR, there would be a 50% chance that you would have a VR score of 115.00 or over, and 50% chance of it being 115.00 or less.

If you got 130 for VR then with a cut-off of 229 then you would need only 99 on NVR, and assuming a normal distribution of NVR around 130, then that's 2 standard deviations below the mean for someone with a NVR score of 130, so only a 2% chance of not making the grade.

Based on this, I came up with an estimated chance of success of 0.19 for a randomly selected child (by multiplying together the chance of 88 on one exam 141 on the other, 89 on one exam, 140+ on the other etc., based on a standard deviation of 15 and mean of 100 for the first score, and then a mean of the first score (e.g., 88, 89 in the examples I've given) and a standard deviation of 15 for the second score).

Of course with so much tutoring etc. going on meaning the tests are not truly an indication of ability, the chance for a randomly selected child should be way lower than that, given that the children sitting the test are already a selected sample excluding most of the children in the bottom part of the ability range.

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.

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" onclick="window.open(this.href);return false; 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.....

Good explanation, thank you.

So it must not be very difficult to get into Tiffins. After all, it is not as super selective as most people would have us believed. What a relief..

Well as I said I might have this wrong.

But if their marks are standardised using the standard mean of the population = 100, standard deviation = 15, used by GL, etc., then 229 is obviously bright, but by no means exceptional.

If however the mean of 100 represents the cohort taking the exams (which would make sense if you intend to reject roughly five in six of applicants), that is another thing entirely. If the median 'Verbal Reasoning/Non Verbal Reasoning IQ' of the cohort is 115 (to take an entirely arbitrary figure), and for the purpose of Tiffin testing a person with GL CAT VR score equal to the median of the exam-taking cohort (115 as we are arbitrarily assuming here) is given a score of 100, then a score of 229 on the Tiffin would most likely translate to a score on GLs standard tests of somewhere around 250-260, a score that is indeed 'super-selective'.

twelveminus wrote:
If however the mean of 100 represents the cohort taking the exams (which would make sense if you intend to reject roughly five in six of applicants), that is another thing entirely. ...................... then a score of 229 on the Tiffin would most likely translate to a score on GLs standard tests of somewhere around 250-260, a score that is indeed 'super-selective'.

From Tiffin Girls faq.

The profile of the group of children entered for the Tiffin Girls' School selection test is generally of higher than average ability.

Ok so that settles it. Tiffins are super-selectives.