The Bexhill projectA funnel plot of home working across 154 Bexhill output areas
Take one census question, compare every small area with the district, and let Python decide which gaps are bigger than chance.
The 2021 census asked people in work how they usually got there, and one answer was "work mainly at or from home". Across Rother, the published count is 12,306 of 37,932 working residents, or 32.44%; across England it is 31.51%. The learner downloads the same table for the 154 output areas that the ONS assigns to the Bexhill-on-Sea built-up area. Each holds between 6 and 287 working residents, 107 in the middle one. The raw home-working share runs from 7.1% to 54.5%, and 104 of the areas sit below the Rother figure while 50 sit above it.
Where the funnel limits sit around the Rother share of 32.44%, by number of working residents (exact binomial, our Python run)| Working residents in the area | 95% limits | 99.8% limits |
|---|
| 30 | 16.7% to 50.0% | 10.0% to 60.0% |
| 107 | 23.4% to 41.1% | 18.7% to 46.7% |
| 287 | 27.2% to 38.0% | 24.0% to 41.1% |
Plot every area as a dot, with its number of working residents along the bottom and its home-working share up the side, then draw those limits as curves. They form a funnel, wide on the left where areas are small and narrow on the right. Now look at the ten areas with the highest raw shares. Their middle size is 67.5 working residents against 107 for all areas, so small places crowd the top of the list, just as the lead predicted. Seven of the ten fall outside the 95% funnel, but only one, where 43 of 81 people worked mainly from home, clears the 99.8% line. The very highest raw share, 24 of 44 or 54.5%, is inside the 99.8% funnel.
The wider picture is more surprising. If every Bexhill area truly shared the Rother rate, chance would put about five of them outside the 95% limits: across 500 simulated censuses the count averaged 5.9 and never passed 13. The real count is 56, mostly on the low side: 46 below the funnel and 10 above it, with 21 below even the 99.8% line. So the areas really do differ from the district, and more strongly than a simple coin-flip model allows. Statisticians call that overdispersion, and it is a warning that the funnel's limits, not only the dots, rest on an assumption. The funnel shows where to look; it cannot say why an area differs.
Ages 8 to 11
Flip coins in sets of 10 and of 100, write down the share of heads, and see which sets give odd results.
Ages 11 to 15
Load the Bexhill table in Python, compute each share, and plot the dots against size with matplotlib.
Ages 15 and up
Compute exact binomial limits, simulate censuses, and test whether the spread is more than chance allows.
Sources and limits
Counts are Census 2021 table TS061 from Nomis, published by the Office for National Statistics under the Open Government Licence. Census counts are adjusted slightly to protect privacy, and small areas are affected most. The centre line is the published Rother figure, not a Bexhill total we made by adding areas. The limits, the simulations and every percentage for a single area are our own calculations.
