Crime stats messed up

Changes in the number of
reported crimes and changes
in the crime rate don’t reconcile
On Thursday Police Minister Nathi Mthethwa presented
the SAPS 2012/2013 national crime statistics. In his
statement he listed the increases or decreases of various
categories of crime in terms, not in absolute numbers,
but in the rate or ratio per 100 000 of the population.
Thus he stated, for instance, that total sexual offences
decreased by 0.4% and robbery in non-residential
premises by 0.6%. He added that there had been an
increase of 1.2% in aggravated robbery, 3.3% in
residential burglary, 0.6% in commercial crime, and 3.6%
in residential robberies.Mthethwa also stated that "we
have witnessed a slight increase of 0.6%" in the murder
In absolute terms however there were 16 259 murders in
2012/2013, 620 up from the 15 609 recorded in
2011/2012. This is a 4.2% increase. How then can the
differential between a 0.6% increase in the murder rate
be reconciled with this 4.2% increase in the total number
of murders?
The short answer is, it can’t.
One possible explanation is that the population of South
Africa grew by 3.3% between 2011 and 2012. However,
Statistics South Africa estimates that the population of
South Africa only grew by 1.34% between 2011 and 2012
(see here.)
In fact, what seems to have happened is the following:
The 2011/2012 crime statistics’ ratios per 100,000 of the
population were calculated using Stats SA’s 2011 mid-
year population estimate of 50 586 757. For the
2012/2013 crime statistics the SAPS worked out the ratios
using the Stats SA estimate of a population of 52 274 945
in 2012. It then worked out the change in the ratios per
100 000 of the population between the two.
However, the differential between the 2011 StatsSA
estimate used by the SAPS and the 2012 one is 1 688 188,
an implausibly large 3.34% gap. This doesn’t reflect a
real change in the population, but rather an adjustment
upwards in StatsSA’s estimate of the population
(presumably post-Census 2011). According to these
adjusted estimates the population in 2011 was 51 579 548
– only 695 397 (or 1.35%) fewer than in 2012.
If one uses the updated population figures of StatsSA for
2012 and 2011 then the murder rate actually increased by
2.78% (not 0.6%). There was a 1.53% increase in the rate
of sexual offences (not a decrease of 0.4%) and an
increase of 1.30% in non-residential robberies (not a
decrease of 0.6%). The rate of aggravated robbery was up
3.24% (not 1.2%), that of residential burglary by 5.33%
(not 3.3%), commercial crime by 2.61% (not 0.6%), and
residential robbery by 5.65% (not 3.6%).
The table below sets out the change in the number of
crimes committed, in various categories, between
2011/12 and 2012/2013 – and then the change in the ratio
per 100 000 of the population using the old Stats SA
population estimates for 2011 versus the new ones.


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