Has UK employment gone down? Maybe. And maybe not.

David Smith, Economics editor of the Sunday Times, wrote an article headlined Fall in jobs casts a cloud over consumer spending on December 17th (excerpt available here) in which he highlighted the “ fall in employment announced by the Office for National Statistics (ONS), 56,000 in the August-October period compared with the previous three months”, saying “it may signal the start of a significantly weaker trend”.

This may very well be true, but two points are missing from his story. First, not only was employment reported to have fallen, the number of unemployed was reported to have gone down as well — this may seem bizarre, but simply means there are more economically inactive people falling into neither group.

The main omission, though, was any mention of the uncertainty around this 56,000 reduction in employed.

The figure is based on the latest labour market statistics from the ONS, and diligently digging down into their website reveals a spreadsheet, a portion of which is shown below.

Part of spreadsheet showing sampling variabilities (95% confidence intervals) for survey-based UK employment statistics

So this 56,000 reduction has a surprisingly large margin of error of ……. +/- 146,000! This means that the 95% confidence interval for the true change in the number employed runs from a 202,000 decline, to a 90,000 increase. So maybe we should not be too confident that employment has dropped at all.

Using the estimate and the sampling variability, we can draw a Normal probability distribution that expresses our uncertainty about the true reduction in employment, as shown in the Figure below (this is strictly speaking a Bayesian approach**). On the balance of probabilities employment has gone down, but there is still a 35% probability (shown shaded) that employment has actually increased over the last quarter.

Probability distribution representing uncertainty about change in UK employment between May-Jul 2017 and Aug-Oct 2017. This distribution has a mean off -56,000, and 95% of the probability lies between -202,000 and +90,000. The probability that employment actually increased is 35%.

The estimated employment rate declined from 75.28% to 75.07% from May-Jul 2017 to Aug-Oct 2017, a fall of 0.21%, with a margin of error of +/- 0.3%. And there’s a nice visual way of looking at this, with the trend in employment rate over the last five years shown below. The reduction highlighted in the Sunday Times article is the drop between the last-but-three point, and the last point (but note the little blip upwards in the last month).

Employment rate in UK, ages 16–64, seasonally adjusted.

ONS’s spreadsheet shows the sampling variability around these percentages is 0.4%, and we can add this uncertainty to the plot in the form of a density strip, which simply uses density of ink to represent the probability distribution around the central estimate:

Employment in UK, ages 16–64, seasonally adjusted, with uncertainty represented as a density strip

This may make you feel as if you need to see an optician, but possibly putting on someone else’s glasses and squinting at the trend plot would give a far more accurate impression of what we really know about changes in employment rate, and might stop us over-interpreting small changes in the central estimates.

Many people might be surprised at the size of margins of error on these figures, and ONS do not make them exactly easy to find. But in the Sunday Times article the changes in employment are treated as known facts, whereas they are fairly uncertain estimates. Acknowledging this uncertainty would make the weakness of the underlying evidence rather clearer, and it might make it more difficult to write a good story — but it would allow readers to make a much better judgement about the matter in point.

** In Bayesian statistics, probability densities can be used to represent our uncertainty about an existing but unknown quantity — so-called epistemic uncertainty.


The Winton Centre for Risk and Evidence Communication is hosted within the Department of Pure Mathematics and Mathematical Statistics in the University of Cambridge. Transparent evidence designed to inform, not to persuade.

Thanks to Alex Freeman

David Spiegelhalter

Written by

Statistician, communicator about evidence, risk, probability, chance, uncertainty, etc. Chair, Winton Centre for Risk and Evidence Communication, Cambridge.


The Winton Centre for Risk and Evidence Communication is hosted within the Department of Pure Mathematics and Mathematical Statistics in the University of Cambridge. Transparent evidence designed to inform, not to persuade.

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