Crime rates – the butler did it. But statistics were an accessory

Crime rates – the butler did it. But statistics were an accessory

Birth rates, death rates, crime rates, home ownership rates, you get the idea, rates are everywhere! In this blog I explore the calculation of crime rates … and the impact of the revisions of the official population count on these …


The Australian Bureau of Statistics (ABS) has now released the final rebased and revised estimated resident population (ERP) data for 1991-2011 (catalogue numbers 3218.0 and 3235.0). Previous .id blogs have explained the need for this one-off revision (Re-re-re-revisions), and the changes to the official population count the national and state level (What’s happening with population growth in Australia?) This blog explores the impact of these new population data on the calculation of crime rates.

What do rates tell us about our communities?

Birth rates, death rates, crime rates, home ownership rates, cancer rates… you get the idea, rates are everywhere!

Rates describe a phenomenon by scaling the number of observations to the size of that population. Rates can be preferable to the number of occurrences (depending on what you are looking at), as they remove the effect of a varying population size. You would usually expect an area with a larger population to have a higher number of occurrences.

For example Yarra Police Service Area (PSA) recorded 824 assaults, while Whittlesea PSA recorded 1218, as you would expect for an area with a larger population. Although Whittlesea PSA had a higher number of assaults, the rate of assault for Whittlesea in that year was lower than the rate for Yarra. Whittlesea had a rate of 759.5 assaults per 100,000 people in their population, while Yarra had 1042.8. This tells us that the residents of Yarra PSA had a higher chance of being assaulted than the residents of Whittlesea.

Conversely, Geelong and Greater Shepparton recorded similar rates of motor vehicle theft , with 274.5, and 257.5 per 100,000 of population, respectively. However the number of motor vehicle thefts varied, with 159 cars stolen in Shepparton Police Service Area, and 599 stolen in Geelong. Because the population of Geelong area is around the same proportion higher than Shepparton (3.5 times higher), as the proportion of cars stolen in the two areas (3.7 times higher) the rates per 100,000 of population are comparable. This example tells us that there is only a slightly higher chance of having your car stolen in Geelong compared with Greater Shepparton.

I accessed the Victoria Police’s ‘My Place’ webpage to review crime statistics for the areas above. These examples really shows the value of calculating a rate in order to properly understand how a phenomenon is experienced by a community.

Calculating rates

To calculate a crime rate, the number of crimes is the numerator, it is divided by the number of people in a particular area (the denominator), which is then multiplied by 100,000, resulting in the rate per 100,000 population.

Using an example from above, to calculate the rate of assault in Yarra PSA in the year ending 30 June 2012 we divide the number of assaults (824) by the total population (79,015), (Victoria Police use the population at the start of the period ie. 30 June 2011), resulting in the per person rate (0.010428), which is then multiplied by 100,000 to result in a rate of assault for Yarra of 1042.8 per 100,000 population.

Please note that in the examples above I have used the provisional 2011 estimated resident population (ERP) data for consistency with the Victoria Police ‘My Place’ tables, the ERP data has since been recast and finalised, so there is a good chance that the rates of crime are now different. There are a number of common pitfalls in calculating rates, there can be problems with both the numerator and the denominator…

Common problems with rates per 100,000 of population

Problems with the numerator

Changes in how data is classified, or what is considered ‘in scope’ when counting occurrences, can lead to variation in how data is reported. This can also be an issue when attempting to compare data from different states, territories and especially comparing other countries.

Sometimes a rate appears to change dramatically between years, leading to a conclusion that there has been a change in society, this is not always the case, it’s always worth reading footnotes and explanatory notes to be sure.

The ABS’ National Crime Statistics Unit’s report on Differences in Recorded Crime Statstics (2005) found that recorded crime victim data for assault and sexual assault are not currently comparable across all states and territories because of the different bases on which these offences are recorded, they also found that “some jurisdictions almost always record a reported criminal incident on their crime recording system, whereas other jurisdictions apply a form of threshold test prior to a record being made (e.g. whether the victim wishes to proceed against the offender, or the seriousness of the incident). These thresholds vary across jurisdictions and are not currently guided by national standards.”

Problems with the denominator

The denominator can be a problem in situations where the size of the population doesn’t reflect the number of people who are present in that area for example inner city areas with a high volume of commuters and visitors. In this situation the resident population count which is used as the denominator might result in a rate which is inflated due to the higher number of offences due at least in part to the higher number of people present in the area, but not counted in the resident population count. Victoria Police put it this way on their Explanatory Notes webpage, “It should be noted that crime rates in areas with large transient populations (e.g. tourists or commuters) should be interpreted with caution. Rates are calculated using the estimated resident population, and so areas that experience a large transient population, such as Melbourne CBD, are likely to have high crime rates.”

Revisions to the estimated resident population data

The estimated resident population (ERP) data, used as a denominator in many calculations, is subject to revisions, which in some cases result in changes to the estimated number of people in a particular area, this in turn can change the result of a rate calculation. If there are 100 offences in an area with a population of 100,000, you have a rate of 100 per 100,000, if the population is revised to 104,000 the rate becomes 96.1 per 100,000 people, i.e. when the denominator increases and the number of observations stays the same, then the rate goes down, and vice versa.

As noted above, the crime rates for police service areas (PSAs) are calculated on the data that was available at the time of publication, the provisional rebased ERP for 2011-12, this has since been superseded by the final rebased, recast, ERP.

Geelong PSA, for example, comprises two Local Government Areas (LGAs), Greater Geelong, and Queenscliffe. When the My Place statistics were compiled, the most recent ERP data available was the provisional rebased ERP, the table below shows the difference in rate calculation using the different ERP as a denominator in selected Police Service Areas. While the differences are fairly minor what is interesting is the lack of uniformity in the difference, the impact of this is that both the rate of crime changes and also the relativities between various areas change.

Total Crime Rates for Selected Police Service Areas, Comparison of Difference Between Rates Derived with Preliminary/Final Rebased ERP
Police Service Area Crime No. of Offences Recorded for 1 July 2011-30 June 20123 ERP at 30 June 2011 Total Crime Rate per 100,000 of Population Difference Between Rates Derived with ERP1 and ERP2
Ballarat Total Crime 9,874 101,7341 9705.7 -0.21%
101,9442 9685.7
Geelong Total Crime 15,310 218,2051 7016.3 -0.32%
218,8982 6994.1
Melbourne Total Crime 28,186 100,6111 28,014.8 0.004%
100,2402 28,118.5
Wangaratta Total Crime 3,879 67,6481 5734.1 -0.06%
67,6862 5730.9

1 Source: Australian Bureau of Statistics, 2011-base Estimated Resident Population (preliminary, rebased), published on 30 April

2013.2 Source: Australian Bureau of Statistics, 2011-base Estimated Resident Population (final, rebased, recast), published on 30 August

2013.3 Source: Police Victoria, My Place, Crime Statistics in Your Area, accessed 8 October 2013.

Do you calculate rates as part of your role in the community? How have the recent revisions affected how you understand your community? Please leave a comment below.

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Esther - Team Forecast

Esther joined .id after working in the demography teams at both Statistics New Zealand and the Australian Bureau of Statistics producing national and regional statistics. Esther produces the top-down model for .id’s SAFi (Small Area Forecast information). This involves synthesising overseas, interstate and regional migration patterns to quantify regional change. Esther loves the way statistics assist in understanding our communities and can dispell urban myths or stereotypes.

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