Gender Pay Gap Misreporting: Beware Simpson’s Paradox

It has not taken long for “gender pay is not equal pay” to become an employers’ (and an employment lawyers’) mantra.

The Equality Act 2010 (Gender Pay Gap Information) Regulations 2017 (SI 2017/172) require employers with 250 or more staff to publish, by no later than 4 April 2018, six key pieces of information including their mean pay gap, their median pay gap, their mean bonus gap and their median bonus gap, based on “snapshot” payroll data as at 5 April 2017. Many employers are already finding that their headline numbers paint a difficult picture: a significant pay gap, often widening to a chasm on bonuses.

“But we pay everyone in a fair and non-discriminatory fashion, we don’t have an equal pay problem!” goes the cry. They may well be right. Which is where a statistical quirk called Simpson’s Paradox comes in.

The paradox is named after a former statistician and civil servant called Edward Simpson. It holds that relationships that appear to exist in data at the broad level may disappear or completely reverse when the data is sensibly grouped. It goes a long way towards explaining why so many large employers have such “bad” headline figures.

Take the following example of a technology company with a (very common) mean gender pay gap of 20%. Then take a look at the underlying data that got it there.

Gender Pay Gap Simpson’s Paradox in Figures

Gender Headcount Mean hourly pay
Male 500 £20.00
  • Management
200 £25.00
  • R&D / engineering
100 £20.00
  • Sales
100 £20.00
  • Support (marketing, HR etc)
100 £10.00
Female 500 £16.00
  • Management
120 £25.00
  • R&D / engineering
60 £20.00
  • Sales
60 £20.00
  • Support (marketing, HR etc)
260 £10.00

We can see that, in each of the four sub-groups which produced an overall gender pay gap of 20%, there is actually a 0% pay gap. Men and women, in the aggregate, are being paid identically. The cause of the company’s gender pay gap is clearly a demographic one. They have fewer women in management positions and other roles which tend to command a premium (such as research and development and software engineering) and fewer men in support roles (such as marketing and HR).

This sort of pattern is very normal in UK plc. It also goes a long way towards explaining why nationwide gender pay gap statistics are as they are. While there may be all sorts of valid questions about why women are under-represented in particular sections of the workforce (such as those requiring STEM degrees) and what obstacles still need to be overcome to see more women in senior management positions, it does mean that the size of the country’s (and any given company’s) equal pay problem may not be as great as gender pay figures would tend to imply.

For employers grappling with the new reporting requirements, Simpson’s Paradox demonstrates the importance of the “narrative” which accompanies the headline figures (the narrative is optional, but highly recommended). Employers may find that when they compare apples with apples rather than with oranges (for example, analysing everyone within the same job grade or level or band) the gender pay gap either vanishes or shrinks to a statistically insignificant level. Employers’ greatest concerns with the new regulations are the potential for adverse publicity, particularly for an organisation unfavourably compared with its competitors, and for an uptick in complaints, grievances and even litigation from employees confusing a gender pay issue for an equal pay problem. Positive data from more meaningful like-for-like comparisons may let employers tackle such issues head on.

If the figures are still bad, this may at least point employers towards the parts of their organisation where the problems are greatest, and where they should focus their energies on steps to improve. In this case, the narrative may be better focused on a range of initiatives aimed at attracting and retaining female talent and encouraging progression to the highest levels of the organisation. This could include targeted recruitment campaigns, overhauls of appraisal and pay-setting processes, sponsorship and mentoring schemes and training for managers to address unconscious biases.

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