The Bebington projectGetis-Ord Gi*: finding hot spots, then doubting them
One measure, 1,080 areas, three neighbourhood sizes and a shuffle.
The measure is deliberately plain: the share of households in each Census output area that live in a purpose-built block of flats. Wirral has 1,080 output areas and 143,257 households, of which 16,988 are in such flats. The share is very uneven, and 402 areas have no purpose-built flats at all. Using the ONS centre point of every area, the program finds each area's closest neighbours and computes Gi* for the area and those neighbours together. The usual convention calls a score above 1.96 a hot spot and a score below minus 1.96 a cold spot. The learner runs it with 4, 8 and 16 neighbours.
Hot and cold spots for the share of households in purpose-built flats, by neighbourhood size (our Python run on Census 2021 data)| Neighbours used | Hot spots in Wirral | Cold spots in Wirral | Of those, in the Bebington built-up area |
|---|
| 4 | 94 | 0 | 3 hot, 0 cold |
| 8 | 114 | 0 | 0 hot, 0 cold |
| 16 | 115 | 98 | 1 hot, 13 cold |
With eight neighbours there are 114 hot spots: 78 in the Birkenhead built-up area, 24 in Wallasey, 8 in West Kirby, 3 in Hoylake and 1 in Heswall. None of Bebington's 195 areas is among them. Yet with four neighbours Bebington has three, and with 16 it has 13 cold spots that did not exist a moment earlier. The reason for the missing cold spots is a floor. A share cannot fall below zero, and with a borough average of about 11%, nine areas of zero are not far enough below it to cross the line; seventeen can be. Anyone shown only the middle row would come away with a different picture of Bebington from anyone shown the row beneath it.
Then comes the check that matters most. The learner shuffles the 1,080 shares among the areas at random, which destroys any real geography, and runs the eight-neighbour test again, 200 times. On average 43.2 areas still come out "hot", and in one shuffle 80 do. So the 1.96 rule, which assumes bell-shaped data, overstates badly on a lopsided measure like this one. The real map's 114 is well beyond what shuffling produces, so the clustering is genuine, but not every one of the 114 is. Raise the bar to allow for making 1,080 tests at once and 22 remain. And 24 of the 114 are areas whose own share is below average, five of them with no flats at all: they are hot because of their neighbours.
Ages 8 to 11
Colour a grid of numbers, circle where big numbers bunch together, then shuffle the numbers and look again.
Ages 11 to 15
In Python, total each square with its neighbours and rank the totals to find the hottest patch.
Ages 15 and up
Compute Gi* for 1,080 real areas, vary the neighbour count and build the shuffle test.
Data and licence
Household counts are from the Office for National Statistics Census 2021 (table TS044) via Nomis, and centre points and lookups are from the ONS Open Geography Portal, under the Open Government Licence. The statistic, the shuffles and the counts of hot spots are our own working. We describe where flats are concentrated and make no claim about why.
