The Halifax projectCan a classifier place Calderdale from its ages?
Build a nearest-centroid model on 296 districts, then test it the honest way.
The data comes from the Nomis API as Census 2021 table TS007A, for every English local authority district as it stood in April 2023, fetched in nine requests, one per region. Each district becomes a list of 18 numbers: the share of its residents in each five-year age band. As a first check, the learner confirms that the 18 bands add up exactly to the published total for all 296 districts, which they do. For each of the nine regions the program then works out a centroid, the average age profile of its member districts. To classify a district, it measures the straight-line distance from that district's profile to each centroid and picks the closest one.
How often the classifier names the right region, 296 English districts, our Python run, 28 September 2026| Method | Correct | Accuracy |
|---|
| Always guess South East, the most common region | 64 of 296 | 21.6% |
| Nearest centroid, each district included in its own centroid | 98 of 296 | 33.1% |
| Nearest centroid, leave-one-out | 86 of 296 | 29.1% |
| Leave-one-out with centroids weighted by population | 77 of 296 | 26.0% |
The first score, 33.1%, flatters the model, because each district helped build the very centroid it is then compared against. Leave-one-out testing fixes that: every district is removed in turn, the centroids are rebuilt without it, and only then is it classified. Accuracy drops to 29.1%. That beats the lazy baseline of always answering South East, 21.6%, but not by much. Weighting each district by its population sounds more correct and does worse, 26.0%. In a weighted average the largest districts carry most of the weight, and finding out why that hurts here makes a good follow-up task.
Leave-one-out results by true region (the diagonal of the confusion matrix)| True region | Named correctly |
|---|
| London | 27 of 33 |
| South West | 16 of 27 |
| South East | 16 of 64 |
| East | 9 of 45 |
| North West | 7 of 35 |
| East Midlands | 5 of 35 |
| North East | 3 of 12 |
| Yorkshire and The Humber | 2 of 15 |
| West Midlands | 1 of 30 |
A confusion matrix records, for each true region, which region the model named. Its diagonal shows that the overall score hides very uneven results. London districts are recognised 27 times out of 33; the West Midlands is recognised once in 30. Only two Yorkshire districts, Hull and Sheffield, are placed in Yorkshire. Calderdale is not one of them: its profile sits nearest the South East centroid, with the Yorkshire centroid only seventh of nine. Leeds is sent to London, and Bradford, Kirklees and Wakefield to the North West. These are mistakes by the model, not descriptions of the places.
Calderdale's distance to each leave-one-out centroid, multiplied by 1,000 (smaller is closer)| Region centroid | Distance |
|---|
| South East | 12.73 |
| North West | 13.32 |
| East | 13.63 |
| West Midlands | 13.89 |
| East Midlands | 16.45 |
| North East | 17.69 |
| Yorkshire and The Humber | 18.40 |
| South West | 26.99 |
| London | 68.92 |
Looking inside the centroid shows part of the reason. In the 20 to 24 age band York has 10.04% of its residents, Sheffield 9.14% and Leeds 8.68%, against 4.90% in Calderdale, and the plain Yorkshire average across its 15 districts comes to 6.08%. Members that far from the rest can drag an average away from districts like Calderdale. Small groups are also unstable: removing a single district can move the Yorkshire centroid by up to 3.59 thousandths, about twice the largest shift seen in the 64-district South East. The project measures these shares but does not test why they differ.
Ages 8 to 11
Sort picture cards into groups, find the middle of each group, and place a new card by the nearest middle.
Ages 11 to 15
Turn census counts into shares in Python and classify a few districts by hand-checked distances.
Ages 15 and up
Code leave-one-out testing, compare against a baseline and read the confusion matrix.
ONS counts, our model
The age counts are Census 2021 figures from the Office for National Statistics, read through Nomis. The classifier, the distances, the accuracy figures and the tables built from them are our own calculations.
