The odd ones out: Local Moran's I, explained simply
The Clusters map finds busy and quiet stretches of a city, but not the exceptions inside them. One switch adds two verdicts - Busy among quiet and Quiet among busy - for a hex genuinely unlike the hexes around it. That is Local Moran's I, worked through with London's pubs.
The busy hex in a quiet street, and the quiet one in a busy center
The Clusters map finds the stretches of London where there are genuinely more pubs, or genuinely fewer, than chance would explain. It cannot see the exceptions inside them: a hex (one hexagon on the map, about 350 m across) packed with pubs in a quiet suburb, or a hex with almost none in the middle of the busiest part of town. One switch, Also show the odd ones out, adds exactly those two: Busy among quiet and Quiet among busy. For London's pubs it finds 31 of the first and 36 of the second.
Each is a hex genuinely unlike the hexes around it - not just a bit different, but different by more than random scatter would produce. The field calls the test behind it Local Moran's I.
Also show the odd ones outthe field's term: Local Moran's I
Pubs in London, with the odd ones out switched on. Orange is genuinely busy, as before. The light-blue hexes inside central London are Quiet among busy; the pink hexes dotted across outer London are Busy among quiet.
The idea, in one sentence
The cluster test reads a hex together with its neighbors; the odd ones out read a hex against them. That one change of preposition is the whole feature.
Busy among quiet
Genuinely more here than in the hexes around it. A hex full of pubs whose surroundings have few or none.
Quiet among busy
Genuinely less here than in the hexes around it. A hex with few pubs or none, surrounded by busy ones.
Why can't the Clusters test see these on its own? Because it judges each hex by its surroundings. A quiet hex inside a busy center reads Genuinely busy - true of its neighborhood, and exactly the hole you might want to find. A lone busy hex in a quiet suburb gets averaged in with its quiet neighbors and reads Nothing unusual. The Clusters post shows that test on the same pubs.
Where to click
The switch lives on the Clusters panel and nowhere else, under the measure and its Count as row. Turn it on and the map redraws with five verdicts instead of three.
Where to click
Map type
Clusters
Pub
Also show the odd ones out
The switch, on, with its one-line promise: 'A hex genuinely busier or quieter than the hexes around it.' The counts below update to five verdicts.The whole panel. Of the 12,646 hexes measured, 1,597 are genuinely busy, 10,982 are nothing unusual - and 67 are odd ones out, 31 busy among quiet and 36 quiet among busy. London has no genuinely quiet stretch for pubs.
Reading the map
The two new verdicts take paler versions of the colors they sit beside: pink next to orange for the busy side, light blue next to blue for the quiet side.
Five rows, busy side on top. The note under them still applies: hexes at the edge of the data aren't judged, because their surroundings are incomplete.
Genuinely busy
More around here than chance would explain - the cluster test's verdict, unchanged.
Busy among quiet
Genuinely more here than in the hexes around it.
Quiet among busy
Genuinely less here than in the hexes around it.
Hover an odd one out and the card says so in words: “Busy among quiet: genuinely more here than in the hexes around it”, or “Quiet among busy: genuinely less here than in the hexes around it”. Every other hex keeps the words it had with the switch off.
A hex near Lewisham with one pub, still Genuinely busy with the switch on. It sits in a busy neighborhood, and whatever difference it has from the hexes around it is not big enough to beat chance.
That last point is the test doing its job. Plenty of hexes are a little quieter or a little busier than their neighbors; only the ones where the difference is too big to be luck become odd ones out.
The math, honestly
For each hex, measure how far its own count sits from the London average, in standard steps. Do the same for each of its neighbors and add those up. Multiply the two. If the hex is above average and its neighbors below - or the other way round - the product is negative: the hex is unlike its surroundings. The numbers below are illustrative.
A pub-heavy hex in a quiet suburb
This hex, against the London averagefar above average, in standard steps
+4.5
Its neighbors, against the average, added upall of them a little below average
−6.0
Local Moran's I
4.5 × −6.0 = −27
Negative means unlike its neighbors. The app then compares it with what shuffling London's own values would normally give, and only a hex far enough out - after the correction below - becomes an odd one out. This one is above the average, so it is Busy among quiet.
Same neighbors, same correction. It uses the cluster test's own neighbors (with the hex itself left out - it is compared against them, not with them) and the same false-discovery correction (Benjamini-Hochberg), so the hexes that would look odd by luck alone are removed.
Only “unlike” counts. A strongly positive value means a hex is like its neighbors - busy among busy - and that is already the cluster test's to call. Only a strongly negative value is relabeled.
Which of the two? The hex's own value decides: above the London average, Busy among quiet; below it, Quiet among busy.
One hex at a time. An odd one out replaces the cluster verdict for that hex alone. Every other hex keeps exactly the verdict it had with the switch off.
In the field, the statistic is Local Moran's I, from Luc Anselin's LISA family (1995). As on the Clusters map, the number itself never appears on the map - only the verdict it supports.
Why the two belong together
Clusters answers “where are the busy and quiet parts of town?”; the odd ones out answer “what breaks the pattern inside them?”. A Quiet among busy hex in central London is a gap in a strong neighborhood; a Busy among quiet hex in an outer borough is a lone strong point with little around it. Often there is a plain reason on the ground - a park, a railway yard, a single busy junction - but the map only says the difference is real, not why.
What the switch cannot tell you
An odd one out is a statement about difference, not quality: a Quiet among busy hex is not a recommendation to open a pub there, and a Busy among quiet one is not proof it is thriving. The places come from Overture Maps (release 2026-08-19), and a pub missing from the data is missing from the test. The switch exists only on the Clusters map, because only there is there a test for it to sit beside. Read it as decision support, not a forecast.
Also show the odd ones out is a switch on the Clusters map that adds two verdicts.
Busy among quiet: genuinely more than the hexes around it. Quiet among busy: genuinely less.
Clusters reads a hex with its neighbors; the odd ones out read it against them. That is Local Moran's I.
Same neighbors, same correction as the cluster test; only a difference too big to be luck counts.
For London's pubs: 31 Busy among quiet, 36 Quiet among busy, and every other hex keeps its cluster verdict.
Hover an odd one out for its verdict in words.
New to the cluster test itself? Start with the Clusters post.
Quick questions
What does 'Also show the odd ones out' do?
It is a switch on the Clusters map that adds two verdicts: Busy among quiet, a hex with genuinely more than the hexes around it, and Quiet among busy, a hex with genuinely less.
What statistic is behind it?
Local Moran's I, from Luc Anselin's LISA family. It compares each hex with its neighbors and keeps only the hexes that are unlike them by more than chance would explain.
Why can't the Clusters test find these on its own?
The Clusters test reads a hex together with its neighbors, so a quiet hex in a busy center reads Genuinely busy and a lone busy hex in a quiet suburb reads Nothing unusual. The odd ones out read a hex against its neighbors instead.
Does switching it on change the other verdicts?
No. An odd one out replaces the cluster verdict for that hex alone; every other hex keeps exactly the verdict it had with the switch off.
How many odd ones out are there for pubs in London?
31 hexes are Busy among quiet and 36 are Quiet among busy, out of 12,646 hexes measured.
See it on a real map
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Builds MapBees's location-intelligence pipeline end to end — census and Overture Maps ingestion, H3 hex scoring, and the map interface — and writes the methodology behind every number on the site.
