Why statistics are tricky: the case of average public sector pay.

Every month the CSO publishes a Earnings & Labour Costs report (example here). That report includes a nice graph similar to the one above, and nice figures saying what the average salary in the public sector and the average salary in the private sector are.

avg public sector vs avg private sector pay

However these figures cannot be used to compare salaries between the public sector and the private sector. Seems odd, but the CSO themselves point this out on the same page as the graph:

It should be noted that estimated averages do not reflect differences in characteristics of the job or the employees. As EHECS collects aggregate data from each enterprise it is not possible to correct for such differences using EHECS data. For a more detailed analysis of the difference in public and private sector pay please refer to supplementary analysis of the National Employment Surveys 2007.

To explain why this is, here is a story about statistics:

Once there was a boy who asked his parents to double his pocket money to €40 a month. When his parents laughed, he got angry. “The average people in my class get every month is ten times that”, he said. His parents were gobsmacked, but they weren’t taking his word for it. They asked their friends and all of their kids were getting €20 a month too. When they quizzed their son further he owned up that he had included the teacher’s after tax salary in his average of €503 [€15,000+(30x€20) divided by 31].

This highlights the difference between the average (or mean) and other measures. If the son had reported the mode (most common figure) or the median (the figure at which half the set got more & half got less), both of those would have been €20. But the mean can get skewed by a small number of more highly paid individuals.

It also, incidentally, shows that pay can be fair and yet averages vary between groups. Imagine that there were another class with an identically paid teacher and only ten pupils. Instead of an average of €503 [15,000+(30x€20) divided by 31] the average for that class would be €1,381 [€15,000+(10x€20) divided by 11]. Both teachers are paid the same, all students are paid the same, but the average for one class (€1,381) is almost three times the other (€503).

This is what the CSO is getting at when talking about “characteristics of the job”. The mix of employment in each means average public sector pay and average private sector pay will always be different. There are more doctors in the public sector; more retail staff in the private. You might argue retail staff should be paid more, you might argue public sector workers are paid more here than in other countries – those are separate questions. While the mix is different the raw averages can’t be usefully compared, any more than the two class averages above can, and that is why every month the CSO warn not to directly compare these figures.

Comparisons can be done (and a blog on this will be appearing on factsaresacred soon), but it is a little more complex than pulling the figures from the CSO Earnings & Labour Costs report and saying “well, they’re the CSO figures”.