The Redditch projectA decision tree you can read, on 273 output areas
Grow trees of different sizes, test them on areas they have not seen, and see whether the readable one loses.
Three Census 2021 tables come down from the Nomis API, covering each of Redditch's output areas: kind of home, number of cars or vans, and age. The question is whether at least half of an area's households live in detached houses, which is true for 62 of the 273 areas. The clues are all taken from the other two tables, so the answer cannot leak in: the share of households with no car or van, the share with two or more, and the shares of residents under 15, aged 20 to 39 and aged 65 or over. Because only 62 areas are mostly detached, a lazy model that always says "no" is already right 77.3% of the time, and every tree has to beat that.
A decision tree learns by asking the single yes-or-no question that most cleanly splits the two kinds of area, then repeating inside each branch. Its depth is the number of questions allowed in a row. The learner tests trees from one question up to no limit at all, using 5-fold cross-validation repeated 20 times: each tree is trained on four fifths of the areas and judged on the fifth it never saw.
Decision trees of different depths, tested on unseen output areas, 20 repeats of 5-fold cross-validation, our Python run, 29 September 2026| Tree | End points | Accuracy on training areas | Accuracy on unseen areas |
|---|
| Always "not mostly detached" | 1 | 77.3% | 77.3% |
| One question | 2 | 88.8% | 86.7% |
| Two questions deep | 4 | 91.0% | 86.6% |
| Three questions deep | 8 | 93.1% | 85.9% |
| Four questions deep | 13 | 95.4% | 85.0% |
| No limit | 26 | 100.0% | 83.3% |
The one-question tree is the winner. Grown on every area, its whole reasoning fits in a sentence: if more than 59% of households have two or more cars or vans, predict mostly detached. That rule scores 86.7% on unseen areas. Letting the tree grow makes it look better and work worse: with no limit it memorises every training area, scoring 100.0%, but drops to 83.3% on areas it has not met, and its false alarms rise from 16.5 to 24.0 per test run. Here the model a person can read is also the most accurate one.
Accuracy alone still hides something. The one-question tree finds 42.2 of the 62 mostly-detached areas on average, a recall of 68.1%, and when it says "mostly detached" it is right 71.9% of the time, its precision. Those two numbers matter more than 86.7% when the thing you are looking for is the rarer case. The tree also shows its limits honestly: it says nothing about why car ownership and detached homes go together in Redditch, only that they do, and this project does not claim a cause.
Ages 8 to 11
Sort a pile of animal cards with as few yes-or-no questions as possible, then sketch those questions as branches.
Ages 11 to 15
Compute each area's car shares in Python, then apply the one-question rule and count the hits.
Ages 15 and up
Grow trees with scikit-learn, cross-validate them and report recall and precision.
ONS counts, our trees
The counts for every output area are Census 2021 figures from the Office for National Statistics, read through Nomis. The labels, the trees, the cross-validation and every percentage are our own work.
