Tuesday, May 17, 2016

How unfair is access to university education?

The Times today has a leader, "First-Degree Burn", where they state:
"With notable exceptions, Britain’s universities are still not doing enough to attract poor students. English 18-year-olds from the most advantaged 20 per cent of backgrounds are still more than six times more likely to attend a top university than those from the least advantaged 20 per cent.

"Jo Johnson, the universities’ minister, calls this unacceptable and he is right."
In fact he is quite wrong.


Suppose 'advantage' is normally distributed in the UK population (it is not - more later) and suppose it correlates pretty well with IQ (which seems more reasonable).

Then the top 20% would have a mean IQ of 121 and their children (regressing to the mean) an average IQ of 117. *

The bottom 20% would be a symmetrical story, the left side of the bell curve. Their mean IQ would be 79 and their children's an improving 84 (83.2 but let's round up).


The Times mentions 'a top university', by which they most likely mean the Russell Group. The IQ needed to get into a Russell Group university is estimated to be 120.
 - Given a population with average IQ of 117, you would expect 42% to be eligible to meet the 120 cut-off.

 - Given a population with an average IQ of 84, you would expect 0.8% to be smart enough to meet the IQ 120 cut-off for the Russell Group.
That's a ratio of 42/0.8 = 52.5 - far worse than the lamentable six to one quoted by The Times.

The problem is with the financial-advantage model. The disadvantage-advantage distribution is far from normal; a small minority are very well off while a very large minority share a lowish level of income which is conventionally described as 'disadvantaged'.

What IQ amongst the 'disadvantaged' would replicate The Times' statistic of six to one?

A 'disadvantaged ' IQ of 98.

A population with an average child's IQ of 98 would have around 7% with an IQ at or above 120 - and thus be eligible to attend a 'top university'.

Since 98 is pretty much the average IQ of the mass of people in the UK, The Times' figures do not surprise me at all - they're exactly what we should expect.

And for that reason, despite any confected outrage or exciting new policies, I don't expect them to alter at all, short of crashing admission standards. **


* If you're wondering where all these figures came from, we're applying truncation selection ideas which were explained in detail here.

The first part of the calculation goes like this:

Talking about the top 20% of the population for IQ (mean = 100, std. dev. = 15) we have p = 20% = 0.2. This is the area we are 'breeding from', the top 20%.

The mean IQ of this group S = 100 + std. dev. * i(p) = 100 + 15 * 1.4 = 121,

... where we look up i = i(p) = i(0.2) = 1.4  in the table.

Using an IQ heritability of 0.8, the mean children's IQ = R = 100 + 0.8 * 21 = 116.8 = 117,

... reversion to the mean.

A symmetrical calculation give us the story for the bottom 20%

The rest is just putting numbers into the normal distribution.


** If pushed I'd say that the above analysis makes both the affluent and disadvantaged children too smart. As a reality check, what if we made the mean IQ of the advantaged kids 115 (1 sigma up) and the disadvantaged kids 95 (one third of a sigma down)? That sounds more like it.

Then 40% of the 'rich' kids could get into a Russell Group university, and 5% of the 'poor' kids. That's a ratio of eight to one. And The Times did hint that the ratio was worse than 6:1 ...


More bad science from The Times.

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