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.

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Filed under Gender, Statistics and simplicity

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