The Braintree projectDasymetric mapping: guessing small-area populations three ways
Take seven published middle-sized totals, spread each over its small areas, and mark every guess against the census.
The census reports people for several sizes of area. Around Braintree, seven middle-layer areas hold between 7,451 and 10,611 residents each, and inside them sit 196 output areas, the smallest units the census publishes, holding 132 to 608 people. The learner pretends to know only the seven big totals and tries to recover the 196 small ones. Method one shares each total in proportion to land area, using the official boundaries: the areas range from 1.0 hectare to 1,094.2 hectares. Method two shares it by the number of postcodes in each area, 1,589 postcode points from the Ordnance Survey's open list. Method three ignores the map altogether and gives every small area an equal share.
Average error per output area, and share of the 196 areas estimated within 20% of the census count (our Python run)| Method | Average error (people) | Within 20% |
|---|
| Share by land area | 307.5 | 28 of 196 |
| Share by postcodes | 152.4 | 55 of 196 |
| Equal share, no map at all | 60.2 | 119 of 196 |
Land area failed worst, as expected: one rural output area of 539.5 hectares, home to 291 people, was handed 5,257. Postcodes did better, because postcodes follow addresses, but not by much: their count per area matched population only loosely, with a correlation of 0.37, and one large area with 47 postcodes, which can include business addresses, was given 1,821 people instead of 451. The winner was the method with no information at all. Restricting the test to the 135 output areas inside the town changed nothing: equal shares still came out ahead, 56.2 people out on average, against 146.8 by postcodes and 213.5 by area.
The reason is in how output areas are drawn. The ONS builds them to hold similar numbers of people and households, within set minimum and maximum sizes, so knowing nothing but "these are output areas" already tells you each holds roughly the same number. Dasymetric mapping is powerful when zones are arbitrary, such as grid squares or areas drawn for some other purpose; here, the zones were designed around the very thing being estimated. One more lesson hides in the totals: the published counts for small areas do not add exactly to the published middle-layer figures, because the census adds small adjustments to protect privacy, so the methods spread the published totals rather than any sum of parts.
Ages 8 to 11
Share 100 counters among six rooms three ways, by floor size, by number of beds, and equally, and see which matches a real list.
Ages 11 to 15
Load the Braintree tables in Python, compute each estimate, and measure the average error for every method.
Ages 15 and up
Match postcode points to boundaries with a point-in-polygon test, then investigate why the worst estimates went wrong.
Sources and limits
Population counts are Census 2021 table TS001 via Nomis, and boundaries and the area lookup come from the ONS Open Geography Portal, all under the Open Government Licence. Postcode points are from OS Code-Point Open, which contains Ordnance Survey data (Crown copyright and database right). Postcodes include business addresses, which is one reason they track residents loosely. The estimates and error figures are our own.
