Tyranny of the Average

Where to start? The use of ‘the average’ is possibly the thing that annoys me most in social and policy analysis. Essentially, taking complex distributions and reducing them to a single figure makes any subsequent analysis ridiculous. Political comments about ‘glass ceilings’ and the problem of leave for childcare are based on beliefs that cannot be inferred from a simple average.

I’m sure this problem will come up elsewhere (so many examples of this to debunk) but on this occasion I’ll use the annual figures about the gender pay gap. Latest figures suggest that the average woman earns 13% less per hour than the average man ( http://www.statistics.gov.uk/cci/nugget.asp?id=167). Here the ‘average’ is the median, and the difference in the means is slightly higher.

I’m so glad that at least government statisticians are numerate. They use the median and not the mean because of the skewing effect of the very highest earners (http://www.womenandequalityunit.gov.uk/pay/pay_facts.htm), hurrah! Once you get to the media, however, all accuracy is lost as everything is just reported as an average (http://news.bbc.co.uk/1/hi/business/3765535.stm) and the debate just ends up as an argument about whose figures are accurate without thinking about what they mean.

This all begs a further question, though. If high earners cause skewing, are there any other peculiarities in the distribution that might be worth investigating.

The distributions below (Microsoft chose pink and blue, not me) are hypothetical, but are designed to fit my feeling that there may be two populations in the workplace. One population is in professional career jobs, and the other in non-career jobs, which may be white collar e.g. secretarial, but are unlikely to lead to the operational and managerial roles that graduates take. I’ve also taken the liberty of imagining that there isn’t any cross-over in these wages between the two groups: everyone earning £25 or over is a professional, and all those earning less are not.

 

In this distribution, the mean and the median of female earnings is considerably less than that of men.

However, this difference can be entirely due to differences in the pay of the non-professional jobs.

If the non-professional women are in low paying jobs that tend to have flexibility (caring, cleaning etc.) and the non-professional men are in higher paying jobs that require 8am-5pm (trades, engineering and so on) then their pay distributions pull the averages to different places. For these women, childcare and other caring / household requirements do affect their earnings.

At the top of the income scale there is absolute equality. Women are just as likely as men to be in the professional jobs, and have the same chances of progressing: there is no glass ceiling in this model, and no effect of childbirth for the professional classes.

The implications of this model, which fits with the averages usually given, are that all efforts to promote workplace equality should be aimed at the bottom of the income scale, whereas when you read the newspapers it seems to be all about career women. Using averages, without examining the whole distribution first, tells us little about what should be done.

Advertisement

The graduate premium

This takes me back. It’s not just about simplicity, but a case of bad science…

Once upon a time a Labour government wanted to convince us that students should pay for their degrees. But this can only really be justified if having a degree is a private good as opposed to a public good (this sort of goes against every government’s own arguments for higher education in that it’s good for the economy as a whole, but that’s another argument). Anyway, the best argument for education being a private good is that graduates earn more than non-graduates and so they personally gain financially.

So Margaret Hodge made a claim that graduates in the UK earn on average £400,000 more than non-graduates over their lifetime (http://education.guardian.co.uk/specialreports/tuitionfees/story/0,,840939,00.html).

Of course this story is a bit more complicated. First, this average figure hides differences between male and female graduates (female graduates taking time out for childcare), black and white graduates, rich and poor graduates. Indeed, some graduates (doing social sciences at less prestigious universities) would end up earning less than if they hadn’t gone to university at all.

On top of this simplification, there’s another story about where the figure came from anyway. I looked into this and found that it was a projection from the earnings profile of those in Margaret Hodge’s generation. For these people university was for a very small minority, as compared to almost a majority now. How one can extrapolate from the earnings of the top 5% (by education) to the planned 50% with degrees I’ll never know. As I said here (http://education.guardian.co.uk/egweekly/story/0,,856726,00.html), it seems unlikely that this 50% of current young people will all be in the top 5% of jobs.

In the beginning…

By far the easiest way to make a political point stick seems to be to use numbers, how much money or how many people being the most effective. What gets lost in these numbers is the vast amount of background and process that determines how these numbers relate to the reality they are meant to describe. The point of all statistics and figures is that they summarise, that is they take a lot of information and make it smaller. How one summarises is the important thing.

This is pretty much where I began my journey into being a researcher.  I loved to see stories about my generation (X, supposedly) saying we were all doing really well, making money, having fun. The class system was dead, opportunities were everywhere etc. etc. And not only that, everyone was making money out of a rocketing house market. However, it didn’t add up… How could everyone be getting well paid jobs? Surely some people had to have the bad jobs, not everyone could be making money. I started digging, thinking and writing.