## 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.

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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).

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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. **

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* 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.

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** 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 ...

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More bad science from The Times.