Adjusting the census for under- and over-count

Despite an intended 100% population coverage, every census misses some people (undercount) and accidentally captures some people twice (over count). In the UK census data are adjusted, prior to publication, to take account of the best statistical estimate of this under/over count. Current solutions suffer from a number of limitations, which we are seeking to address by treating census adjustment as a survey calibration problem.

Following the census, the Office for National Statistics conducts a ‘post-enumeration survey’ to check the quality of the census data that they have captured. This post-enumeration survey permits accurate estimation of a few key aspects of local population distributions that take account of census under- and over-count. Our solution is to calibrate the collected census data to fit these local area distributions, using innovative techniques to provide a solution with integer weights that is guaranteed to be ‘globally optimal’. We have converted our solution into a survey calibration tool, ‘GO’, which can be used for any kind of survey calibration, not just for census adjustment, and can be accessed via

Espuny-Pujol, F., Morrissey, K., & Williamson, P. (2018). A global optimisation approach to range-restricted survey calibration. STATISTICS AND COMPUTING, 28(2), 427-439. doi:10.1007/s11222-017-9739-5