Statistical crimes [UPDATED]

09/03/2012 § 8 Comments

Time for the Dominion Post to refresh their statistics capabilities. The headline is Capital burglaries most likely in day. The reporting is based on ‘figures from AA Insurance’.

Exhibit A:

Wellingtonians were far less likely to be burgled than their Auckland counterparts, with 31 per cent of all burglaries taking place in the Auckland region, compared with just under 9 per cent in Wellington.

Let’s consider the probabilities. At the 2006 Census, Auckland had 1.3 million of the 4.0 New Zealanders, or 32.4 per cent of the population. Wellington had 0.45 million, or 11.1 per cent. That gives us 32.4:11.1 versus 31:9. Wellingtonians are a bit less likely to be burgled, but (a) it isn’t ‘far less likely’, and (b) there’s no basis for the assessment without the base population figures.

Exhibit B:

Security alarms had proven effective for preventing burglaries, with 60 per cent of claims between 2009-11 coming from homes without alarm systems.

This is meaningless by itself. How many houses have alarm systems? I don’t know. How many readers do know? What we’d need to know is the proportion of burglaries versus the proportion of house with alarms. That second bit of data is crucial.

This reminds me of an old Dilbert comic. They wind up the pointed-haired manager by telling him that 40 per cent of absences happen on a Monday or Friday.

Base probabilities — they aren’t just a good idea, they’re Bayes’s law.

UPDATE: Eric Crampton nominated this story and blog post for the University of Auckland Department of Statistics’ Stats ChatStat of the Week‘ competition. We won! Very cool. Thanks, Rachel and the others at Stats Chat, and thanks to Eric, too. I highly recommend the Stats Chat blog for thinking about how stats are used and misused.

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