Area weighting (apportioning)

Why figures need apportioning

Census figures are published for fixed areas: mesh blocks, SA1s, SA2s, councils, suburbs and postcodes. A trade area, a catchment around a site, a sales territory or an earlier edition's boundaries will cut across some of those areas, and the part that falls inside has to be estimated. Apportioning gives the new area a share of each overlapping area's counts.

Three ways to weight

• Area weighting. The share is the fraction of the published area's land that falls inside. If 30% of an SA1's land is inside a catchment, 30% of its counts are allocated to it. This assumes the figure is spread evenly across the land.
• Population weighting. The share is the fraction of the published area's residents who live inside, measured from a finer layer such as mesh block populations or population modelled to residential addresses. The ABS's standard correspondences are weighted this way.
• Dwelling weighting. The share is the fraction of dwellings inside. The ABS's 2012 paper on converting data found mesh block dwelling weights converted address counts closely.

When the assumption fails

Area weighting fails wherever people are unevenly spread, which happens wherever an area includes parkland, industrial land, farmland or water in it. The ABS's example is two SA2s, one with nursing homes and one an industrial estate, where weighting by population gives the nursing-home SA2 the whole population and the industrial estate none, while weighting by area would split the residents between them. In the ABS's tests, deaths data converted by area weighting was markedly less accurate than the same data weighted by people aged 65 and over. The ABS recommends area weighting for data that tends to be uniform, such as agricultural or environmental data.

Population weighting removes that problem and keeps a narrower one, because it assumes a characteristic such as renting, high income or a language is spread across a published area in line with its residents. Where a catchment boundary cuts through an SA1 with a block of units on one side and detached houses on the other, the estimate takes the SA1's average mix for both. The error is smaller when the pieces being apportioned are small, and the ABS notes that converting smaller units into larger ones generally gives more accurate results than converting between areas of similar size. Building from SA1s or mesh blocks keeps the apportioned slivers at the edge of a catchment small.

How the ABS builds its own areas

The ABS builds its Non ABS Structures, such as councils, suburbs and postal areas, from whole mesh blocks without splitting any, each designed where possible to hold 30 to 60 dwellings. Each mesh block is generally allocated to the council where the largest proportion of its population is located, and to the postal area and suburb with the largest population contribution. The results are approximations, and the ABS states that its mesh block approximations of council boundaries do not match official council boundaries, and some official suburbs and postcodes don't appear because their mesh blocks went to neighbours.

Medians and percentages

Apportioning works on counts, so a median for a piece of an area can't be taken as the area's median times a share, and a set of medians can't be averaged into a median for a catchment. Apportion the counts in each range, add them across the pieces, and find the range where the middle value falls. Percentages are rebuilt the same way, from an apportioned numerator and denominator.

Area weighting and Censible

Censible builds every custom area, whether a drawn shape, a circle around a point or a drive or walk time, from 2026 SA1s. Each SA1 is weighted by the share of its residents whose mesh blocks fall inside the area, using dwellings, then the number of mesh blocks, where an SA1 has no residents, and the same weight applies to every figure.

Counts are added up before anything else is calculated, so a percentage is the added-up numerator over the added-up denominator and a median is read from the added-up ranges. Medians built from SA1s run slightly above the ABS's own national figures (household income by 0.9%), which appears to come from the ABS's small-count adjustments accumulating across thousands of SA1s, so figures for Australia and the states are added up from councils instead.

Sources: ABS, Information Paper: Converting Data to the ASGS, 2012 (Geographic Correspondences); ABS, ASGS Edition 3, Non ABS Structures; Do, Thomas-Agnan and Vanhems, Accuracy of areal interpolation methods for count data.