Tuesday, 28 July 2015

The Glass Floor and Frosted Glass Statistics


UK newspapers are full of a new study purporting to show that middle class parents arrange things for their children so that they get better jobs than their cognitive abilities merit, and don’t fall as far as they ought to, thus being sustained by a “glass floor”. The assertion is that middle class children do better in life than working class children of the same level of ability, because of some manipulated advantage. 

The BBC: A study by the Social Mobility and Child Poverty Commission has found that bright children from poor backgrounds are not getting highly paid jobs because of less able middle-class children. The group said a so-called "glass floor" had been created by better-off families, which stops their children falling down the social scale.

The Guardian: Children from wealthier families but with less academic ability are 35% more likely to become high earners than their more gifted counterparts from poor families, according to findings from the Social Mobility and Child Poverty Commission.

All this is based on a study: Downward mobility, opportunity hoarding and the ‘glass floor’. Research report June 2015. Abigail McKnight, Centre for Analysis of Social Exclusion (CASE), London School of Economics. Produced for the Social Mobility and Child Poverty Commission.


Anyone working at the “Centre for Analysis of Social Exclusion” is up against a moral dilemma. If they find, after due analysis, that there is no evidence for social exclusion, should they resign? I do not wish to boost their income stream from the production of government reports, but surely members of this group might be seen as more credible if they entitled it something more neutral : “Centre for Analysis of Social Class”?

By the way, I cannot find anything in the report to substantiate The Guardian’s 35% claim. Try searching for “35” in the report and see if you can produce their conclusion.

The report nails its colours to the mast immediately: “A society in which the success or failure of children with equal ability rests on the social and economic status of their parents is not a fair one” and there is a temptation to conclude that they are producing a result the Commission wants to hear. However, it is being reported as if it was an independent report, and that is how I intend to treat it. In order to meet the requirements of their findings, the authors need to show the outcomes for children of equal ability at several points in the ability range. For example IQs 70, 80, 90, 100,110, 120, 130. I could not find any results plotted out in that way.

They say: We begin by examining bivariate relationships between three variables: family background, low cognitive skills in early childhood and labour market success in adulthood. These simple statistics provide estimates of the raw correlations between family income or parental social class and children’s early cognitive test scores, the relationship between these test scores and position in the wage distribution at age 42 and the relationship between family background and position in the age 42 wage distribution.

However, they do not give those correlations. Worse, they do not give the overall plots of the data, which would allow us to judge whether the bivariate division made any sense. On the matter of making a composite score of the cognitive tests the author says she follows the work of Parsons (2014) but that turns out to be an unpublished “data note”. There is another Parsons working paper which I eventually found. It makes one general reference to composite scores, but I could not find the Principal Components Analysis referred to in the report.

The first finding is: In the raw data we find that, on average, children from lower income families or those with less advantaged social class backgrounds do not perform as well in a series of cognitive tests taken at age 5 as children from higher income families or those from advantaged social class backgrounds.


Figure 1 is a projective test. You and I know that there are two likely causes: different genetics and different circumstances. The depicted results could be due to parents’ intelligence (passed on in their genes) allowing their children to get better paid jobs; or unfairly obtained money and power allowing parents to buy their children educational toys and other advantages. The report makes zero references to “genetic” or “genetics” or “heredity”. However, there is one use of the word “inherited”:

It has been suggested that the reason success runs in families is that ability is inherited: the only reason that poorer children don’t succeed is because they are not as bright or don’t work as hard, or are not academic. This is simply not the case.

The authors go on to quote the work of Feinstein (2003). I had long and friendly exchanges with Feinstein at the time of this publication, saying that a genetic explanation for his results was equally plausible, but he reiterated that he thought it was due to the way in which middle class parents encouraged and taught their children. We could not resolve the issue since no measures of parental ability were collected, but his surmise about environmental effects was widely accepted as a basis for government policy.

McKnight sees Feinstein as supportive evidence, whereas I see it as having obvious genetic confounding. McKnight does quote concerns about measurement error and regression to the mean. She says that having a variety of cognitive measures and taking a common factor reduces such error.

We attempt to minimise the impact of ‘regression to the mean’ in three ways. (1) In our research we define ability groups based on cognitive test scores at age 5 and define family background at a different age (age 10). (2) We use the results from five separate cognitive skill tests taken at age 5 to create a composite measure of attainment. This minimises the chance that the score from one test, driven by good luck or bad, results in a child being allocated to a high or low attaining group in error. (3) We avoid looking at the extremes of the ‘ability’ distribution.

Method 1 merely introduces another source of error, in that social status at age 10 may be different from social status at age 5. Method 2 is better, so long as we can see the loadings of each test. It might have been even better to use the Peabody Picture Vocabulary Test which is the best of the bunch, or that and the Goodenough Draw A Man test. We need to see the data on that, and it is not available in the internal reports mentioned. Method 3 loses data, and assumes that measurement error will be more evident at the extremes, whereas it will be present in every test score.

A very large number of the references in this report are to “working papers”, not peer-reviewed papers published in journals. Reeves and Howard (2013) is given significant mentions 4 times in the text, but not shown in the reference list. I have found a paper “The Parenting Gap” of theirs that year, but on examination the main finding is work done by Waldfogel and Washbrook in 2011 saying that parenting is the major source of income related gaps in children’s cognitive outcomes. It is probably another paper “The Glass Floor” which is more substantive, and seems to have provided many of the catch-phrases and data analytic techniques.

The unpublished work of Joshi is mentioned 8 times, the published paper of Sophie Stumm (with Ian Deary and others) 6 times, the very many published papers on the genetics of academic achievement by Robert Plomin 0 times. People are right to disparage social sciences because too many of them cluster into confirmatory tribes, averting their gaze from contrary findings. We are all tempted to into this self-serving research apartheid, but must learn to avoid it. If we cannot achieve linkage between research projects such that educationalists use twin studies where possible, and if findings in any research area do not make other researchers review their methods and interpretations, we will never progress from a cottage industry of pamphleteers. Genetic research is driving a coach and horses into the territory of old explanations. Telescopes supplant naked-eye astronomy.

I expected that the report would show the basic data, that is to say, the means and standard deviations of each of the cognitive tests taken at each age, and then a figure showing those scores (or a composite) plotted out by social class of origin. Plots of early cognitive ability against achievements in adulthood for each social class would also be interesting. In this way the reader could be oriented properly into the basics of the data set. There is no link to supplementary tables. There is a footnote saying: “The tables containing the complete sets of regression results can be downloaded from the Social Mobility and Child Poverty Commission website” but I cannot find them on that site. I would like to see the correlations between all the cognitive measures and academic measures taken at all stages. It is very hard to judge the end results without being able to look at those important details.

The report, having given its conclusions, then sets out its method: the two lower quintiles of cognitive ability at age 5 will be measured against the upper two quintiles in binary comparisons. This is a massive data loss. Why not plot the all children against the social mobility measures so that we can see the shape of the relationship?

I want to see through the glass clearly, not be confused by frosted glass, and have prepared assumptions forced on me.

Talking about high and low attaining children the author says: There remains an unexplained additional advantage associated with high income or advantaged social class background. High attaining children from disadvantaged family backgrounds appear to be less successful at or less able to convert early high attainment into later labour market success.

This might be a genetic advantage, or middle class encouragement, or both. How does the report go about investigating this?

Quintiles, quintiles quintiles. No data plots or correlation coefficients. Time and space are wasted. The report plods through the findings that middle class people do better, but says of these effects that they are “reinforcing patterns of advantage”. Well, yes, or sustained evidence that bright and diligent families get ahead because of some genetic advantage.

Essentially, all I can find after reading the entire report several times is that it finds “unexplained additional advantage” for higher social classes. Determining why this is the case is left for another day. The results would be consistent with higher class children being somewhat slower to mature, and rising slowly to better achievements, as befits a slow lifestyle. By the way, any difference is described as an instance of things being “unequal”. If you have read this far, while others haven’t, that is an instance of unequal chances.

Here are the report’s conclusions:

Why should parental education contribute to children’s chances of career success? Parents’ education can indirectly affect this likelihood through the extent to which education equips parents to: help their children develop cognitive and non-cognitive skills, choose the best primary and secondary schools for their children, assist them with their homework, help them with exam preparation, help guide them through the process of making further and higher education choices, assist them with career choices and interviews. It is natural for parents to want to do the best they can to help their children do well and this should not be discouraged. If parental education is directly related to children’s skills, affecting social mobility, then policy should be directed at trying to redress educational inequality among adults in the UK. Many attempts have been made and they have been largely unsuccessful but this does not mean that a solution should not be sought.

Notice there is no mention of the possibility that brighter and more diligent parents have children who eventually mature into brighter and more diligent adults for reasons which are partly genetic.

Some of the correlation between parental education and children’s career success could be driven by unmeritocratic factors. If highly educated parents are using their connections to help their children find good jobs. This amounts to opportunity hoarding and results in fewer opportunities available for equally able but less connected children.

Apart from innuendo, the report has no data on these “un-meritocratic” factors.

Parents’ education could also be giving children an unfair advantage in the selection of primary and secondary schools. Focusing on increasing choice can simply result in parents who are in a better position to make informed choices and able to exercise that choice sending their children to the best performing schools, thereby hoarding these school places at the expense of less-advantaged children. Could reducing choice actually increase outcomes if instead these parents are limited to working with schools to drive up standards? The question remains unanswered.

We find a clear advantage for children who attend a Grammar or a private secondary school.

There is an obvious artefact here: we need to know whether the cognitive abilities of children sent to private schools are any different from those sent to state schools. Simple statistics are the royal road to understanding data sets.

I cannot substantiate the newspaper headlines with anything in this report. The report does not plot out all the data in a way I can understand. It does not use a multiple regression model or SEM approach on all the available data. Instead it goes for binary categories, and then plods through the quintiles until most readers will have lost the will to live. Finally, without giving us the proper comparison, it jumps to innuendo to account for residuals. You read it, and tell me if I have missed the crucial (non-existent) page where they give me a simple Chi square of adult outcomes by class versus age 5 ability.

The report gives some of the data, explains some of the approaches, and is supported by some of the literature. It is not a proper paper, and does not let the reader into the fundamentals of the data. It is written to be read by policy makers, which is not always a bad thing, because it makes the writing clear. The downside is that the methods are not as clear as they should be. The report does not give anything like the full picture, and does not substantiate the conclusions that have been drawn from it. Authors cannot be held responsible for occasional misreporting, but if the BBC and all the press cover it in the same mistaken way then the authors and their university publicity departments have something to explain.

I repeat: if you can find the killer result, showing that bright working class children are being held back by less bright middle class children, in a proper, balanced, like-for-like comparison, direct me to the page and paragraph in the report.

A more world-weary view is that the report has probably achieved its purpose, which is to imply that middle class people cheat. Their wish to educate their children and make them productive is “opportunity hoarding”. Hoarding is mentioned 65 times. They base this conclusion on an imperfect model which in their view means that outcomes must have been manipulated. Yet the alternate hypothesis, which is that the behaviour of parent and child are half driven by the same genetics, carrying similar genes for ability and effort, has had no chance to be evaluated. The report casts middle class helping as unfair, but working class lack of helping is judged to be entirely due to lack of material resources, not lack of interest.

In the same week that this report was given such glowing coverage Robert Plomin has published a paper in Nature looking at the genetics of GCSE achievement. I will try to post about that shortly, but it appears to confirm that academic success has genetic elements over and above those which account for general intelligence.

I shouldn’t get the least bit agitated about this report and its credulous reception, but I do feel a stirring of dismay, so I am writing my despairing words in this little blog, and will then watch the wild West wind blowing rain through the garden.


  1. "children from lower income families or those with less advantaged social class backgrounds do not perform as well in a series of cognitive tests taken at age 5 as children from higher income families or those from advantaged social class backgrounds."

    I've always been amused that The Left views cognitive tests as the work of the devil - except when they can twist the results to suit their ends. Still, incentives work, don't they? You pay for braindead cant, you get braindead cant.

  2. "Method 3 loses data, and assumes that measurement error will be more evident at the extremes, whereas it will be present in every test score. "

    Measurement error is larger in the extremes. That's the reason regression towards the mean happens. With no measurement error, no regression towards the mean.


    Their choice to analyze the results in discrete groups introduces error however. I don't know why they do that.


    "Essentially, all I can find after reading the entire report several times is that it finds “unexplained additional advantage” for higher social classes. Determining why this is the case is left for another day."

    A favorite of people arguing for gender discrimination in wages. First they fit some model to the data, then calculate R^2. Then 1 - R^2. The remaining value is usually not exactly 0 (measurement error being generally impossible to eliminate completely). The unexplained variance is then assumed to be due to discrimination. In effect, this sets up a reverse burden of proof. Instead of having to prove discrimination, they argue that the model can't explain all the variation and the rest is due to discrimination.

  3. On your second point about unexplained variance, we are in agreement. Now to the issue about "avoiding extremes". I think that error variance must be considered possibly present every time a person takes any test. We do not know that an extreme score has more error than a common score. The test taker may simply be very bad at that task. Errors runs through every measurement.