The accuracy of areal interpolation techniques: standardising 19th and 20th century census data to allow long-term comparisons

The census has been collected in Britain since 1801 and has published detailed attribute data at district-level about the population since 1851. Comparing censuses over the long-term is, however, highly problematic due to the problem of boundary changes. The only traditional response to this has been to aggregate data; however, this is highly unsatisfactory. The Great Britain Historical Geographical Information Systems (GIS) allows census data to be linked to the boundaries that were used to publish them, and areal interpolation techniques allow data from many dates to be standardised onto a single administrative geography to allow long-term comparison. Areal interpolation, however, inevitably introduces error and quantifying this error with real-world data is usually impossible. In this paper the accuracy of several areal interpolation techniques suitable for use with historical data are compared using “synthetic” districts and parishes created from Enumeration District-level data from the 1991 census. The errors introduced are analysed for several different variables and show that the effectiveness of the technique depends on the variable to be interpolated and the choice of target geography. While this paper is mainly applied to historical data, these results have relevance to any areal interpolation problem.