Gender pay gap reporting and Simpson’s Paradox

For many employers, dealing with the impact of these regulations will be their biggest challenge over the coming years – both in relation to the drafting of the reports themselves and the public or employee relations impact of any fallout.

The regulations will require employers to publish details of some very broad headline pay and bonus gap figures, calculated by looking at all male and female employees in the business.

However, it is entirely possible for employers to report statistics that lead to completely misleading conclusions. A statistical quirk called “Simpson’s Paradox” may come into play.

Named after former statistician and civil servant Edward Simpson (rather than nuclear power station worker Homer Simpson), the paradox states that relationships that appear to exist in data at the broad level may disappear or completely reverse when the data is sensibly grouped.

The following examples explain how this might crop up in practice.

Example 1: Springfield Nuclear Power Plant’s mean pay gap statistic hides systemic discrimination

Springfield Nuclear Power Plant (UK) Limited has 1000 employees. Half are women and half are men, with mean pay being identical.

The mean gender pay gap at the power plant is therefore (quite obviously) 0% - both gender groups earn the same. On the face of this statistic, it looks like the sort of egalitarian paradise that Ned Flanders would surely rave about.

Yet when we break the data into individual groups, a completely different picture appears.

For white collar workers, there is a mean gender pay gap of 48.7% (£52.00 less £26.67, divided by £52.00 and all multiplied by 100%), whilst for blue collar workers there is a mean gender pay gap of 16.7%. The story of the egalitarian paradise that the data initially showed has disappeared and instead we seem to have evidence of systemic pay discrimination more suited to a business run by Mr Burns. His power plant now looks like it has a real gender pay issue.

The converse can also happen. A company with complete pay equality at every level could easily have terrible statistics when assessed at the broad level that the regulations require.

Example 2: Krusty Burger’s mean pay gap statistic hides pay equality

Here is the data for the Krusty Burger fast food chain.

Krusty Burger would have to report a mean gender pay gap of 20%.  However, we can see that at both the blue and white collar levels there is actually a 0% pay gap, as both men and women appear to be paid identically.

The cause of Krusty Burger’s gender pay gap is clearly a demographic one - they have a lot fewer women performing the higher paying roles. Although this may suggest other types of discrimination, it seems that there is no pay discrimination going on.

Conclusion

When it comes to complying with these new obligations, employers need to be mindful of statistical quirks like Simpson’s Paradox and how these might be impacting upon their reportable figures. Where appropriate, these quirks should be drawn out in the narrative that accompanies reports.

Data can tell all sorts of stories. It is important for employers to know what those stories are and separate the fiction from the non-fiction. In many cases, employers will want to do more analysis than the bare bones that the regulations require, and use this extra information to tell a different story.

Find out more about how Lewis Silkin can assist with gender pay gap reporting, or email genderpaygap@lewissilkin.com.