Magic Statistics

“I accept no responsibility for statistics, which are a form of magic beyond my comprehension.” — Robertson Davies

January 14th, 2006 at 9:37 pm

A primer on crime statistics

Dueling crime statistics (how's that for irony?) has emerged as a theme in the Canadian election campaign. David Frum's piece in the National Post of 3 January serves as a flashpoint. Mr Frum's column is chock-full of statistics, but we'll focus on this one as it typifies the thrust of his argument: "Canada's overall crime rate is now 50% higher than the crime rate in the United States".

Needless to say, Frum's claim was highly controversial. Relapsed Catholic Kathy Shaidle posted two items with correspondence from David Frum and an unnamed Relapsed Catholic reader. In this post, Frum specified his data sources. His Canadian data came from this Statistics Canada report based on the 2004 General Social Survey (GSS), while his US data were found in this pdf document from the US Department of Justice reporting findings from the 2004 National Crime Victimization Survey (NCVS). The GSS is a survey conducted in Canada by Statistics Canada, while the NCVS is an American survey conducted by the US Department of Justice, Bureau of Justice Statistics.

Kathy Shaidle's unnamed correspondent found problems with Frum's calculations. Frum presented his conclusion in the form of an overall crime rate, but both source reports present separate calculations for violent crime and property crime. For one thing, Frum does not appear to have aggregated the violent and property crime rates properly. For another, the Canadian violent crime rate is 106 incidents per 1000 residents aged 15 and over, while the US violent crime rate is 22.9 per 1000 residents aged 12 and over. A simple comparison of the two survey results indicates that Canadians report being victims of violent crime at a rate well over four times that of Americans. This does not seem credible. Unless proof of comparability were provided, I would have to think that the questionnaires, methodologies, definitions, and analytical protocols used in the two surveys are so different that their results cannot be directly compared.

Chris Selley at Tart Cider took a closer look at the two source reports and was also highly critical of Mr Frum's contention. Besides the dubious result of a simple direct comparison of the two violent crime rates, the household property crime rates cannot be directly compared either because the Canadian rate includes vandalism while the American does not. Another wrinkle that Selley did not notice is that the Statistics Canada report includes a third category of crime called "theft of personal property". This is not a criticism of Mr Selley; I didn't notice it myself until I tried to figure out the table styled "Self-reported victimization incidents reported to the police, 2004" at the very bottom of the report. It is not clear how to combine the household property theft rate with the personal property theft rate since the former is expressed as a rate per 1000 households while the latter is expressed as a rate per 1000 individuals. To say the least, this Statistics Canada report is not up to the agency’s usual high standards of lucidity.

Mr Selley, I think, goes too far, however, when he rejects outright the use of victimisation surveys to measure crime:

Frum isn't actually talking about the "crime rate" but about the "crime victimization rate", which relies on citizens self-reporting whether they were victims of crime in the preceding year. (That's just what it sounds like - the crime, if indeed there was one, needn't even have been reported to police to qualify.)

Does Mr Selley think that unreported crime is ipso facto unimportant, if not imaginary? Is he assuming that very few, if any, serious crimes go unreported? Even sexual assaults? His reference to "the crime, if indeed there was one" implies that he believes survey respondents systematically fabricate incidents when asked about their personal experiences with crime. At the very least, he seems to think that society need concern itself only with those crimes that are actually reported to the police.

Obviously, Statistics Canada and the US Department of Justice take a different view; else they wouldn't bother arranging and financing victimisation surveys. So also statistical and justice agencies in virtually every developed country. This page, the main crime statistics portal at the UK Home Office, gives access to both police-recorded crime figures and data from the British Crime Survey. The latter is described as "the most reliable indicator of long-term crime trends".

There are fundamentally two sources of crime statistics: police-reported crime and victim-reported crime. The former generates estimates from administrative records of incidents reported to or detected by the police, while the latter is based on questionnaire data collected from samples of randomly selected residents. The Statistics Canada report (in pdf format), "An Overview of the Differences Between Police-Reported and Victim-Reported Crime, 1997" describes the rationales, advantages, and disadvantages of the two approaches to crime statistics.

Some would argue that crime trends are best revealed by official police-reported statistics. Others contend that reporting behaviour is erratic and the police often exercise discretion in deciding what is and is not a crime. Furthermore, in some cases, police officers may decide to divert an offender instead of laying charges. Out of these concerns have emerged attempts to develop alternative ways of measuring crime. The most significant of these is the victimization survey approach.

Another informed perspective is provided by this paper, posted at the US Bureau of Justice Statistics (pdf format).

One of the questions raised in the media as a result of the UCR [police-reported] and NCVS [victimization survey] releases was, "Which is the better measure of crime?" This question misstates the issue and is based on a misunderstanding of the relationship between the two programs. Both are the better measure for what they are intended to measure. The UCR provides information on the amount of crime reaching law enforcement, and can help inform police departments on their manpower needs. The NCVS provides a national picture of what people are experiencing, what proportion of crime does not reach police, the characteristics associated with offenses, and the consequences and costs of crime. Crime, like other phenomena, must be examined from a number of perspectives in order to fully understand it.

Another important aspect to keep in mind is that, because of the many differences, large and small, in the ways national police agencies classify crimes, it is not simple or easy to compare crime rates internationally using police-reported crime statistics. Thus, John Lott's oft-cited article posted at National Review Online last August is completely erroneous. He compares FBI statistics on violent crime in the United States with Statistics Canada data on violent crime in Canada, and concludes that Canada's violent crime rate is twice as high as that of the US. But the FBI does not include simple (level 1) assault in its violent crime figures, while Statistics Canada does. Given that simple assault accounts for probably 50%, if not more, of Canada's police-reported violent crime, Dr Lott's simplistic comparison isn't even close. (Note, however, that, as discussed above, this was not the source of David Frum’s statistic.)

It is possible to compare crime rates internationally using police-reported data—but only if definitions and classifications of crime are carefully studied and appropriate distinctions are made. This Statistics Canada discussion of crime in the US and Canada used only crimes that are comparably defined in the two countries. It concluded that, for the particular violent crimes that could be included, prevalence was lower in Canada but, for the property crimes considered, prevalence was higher in Canada.

Another example of international comparison of crime using police-reported data is this report (pdf format) by the UK Home Office, which details changes in reported levels of crime in EU member nations and other countries. In the first section, based on police reports, only absolute numbers of crimes and changes over time are given; no crime rates are reported.

Over the period 1995-1999, recorded crime fell by 1% in the EU Member States with falls in 8 countries, the largest being in Ireland (21%), England & Wales (10%) Scotland (8%) and Denmark (8%). There were falls in other countries too (in the USA (16%) and in Canada (11%)).

Later sections of the report look at victimisation rates, sentencing, and prison population statistics.

This New Zealand report on police-reported violent crime arises from another careful analysis. The section comparing violent crime in New Zealand and Canada reports that New Zealand's violent crime rate is 44% lower than Canada's, but as much text is devoted to warnings about misinterpreting the data as to actual presentation of results.

In 2004, the US Bureau of Justice Statistics issued a massive report (pdf format), Cross-National Studies in Crime and Justice, that focused on six serious crimes that are defined similarly in eight countries: England (and Wales), United States, Australia, Canada, Netherlands, Scotland, Sweden, and Switzerland, using a combination of police-reported and victim-reported crime. Even though only small subset of total crime was analysed, direct international comparisons were kept to a minimum. Virtually the entire document was devoted to eight individual country-by-country studies. The report contains a wealth of information on crime in the subject countries, but very little in the way of direct comparison of crime rates.

The alternative to police-reported crime statistics is statistics arising from victim surveys. However, as already seen in considering the crime victimisation surveys in Canada and the US, simply comparing survey findings from different countries does not automatically guarantee reliable results. One must be sure that the surveys use the same methodology, definitions, and analytical principles.

The best solution would be for some international agency to devise a comprehensive crime victimisation survey to be administered simultaneously in many countries. Well, that's already been done. UNICRI, the United Nations Interregional Crime and Justice Research Institute, has overseen the International Crime Victims Survey (ICVS) through several iterations, mostly recently in 2005. Results of the most recent survey are expected later this year. Meanwhile, reports covering major findings from the earlier surveys are available here, and an outline of the methodology is posted here. You can even download the data files in SPSS format and do some analysis yourself.

Due to various constraints, however, not even the ICVS covered the whole gamut of crime, but focused on selected types of property crime—car-related crime (vandalism and theft of or from a car), motorcycle theft, bicycle theft, burglary (in Canada, this is usually known as "break and enter")—and violent crime (what the ICVS called "contact crime")—robbery, sexual assault, offensive sexual behaviour, assault, and threat of assault. (Many other crime-related issues were surveyed as well: reporting crimes to police, attitudes toward police, fear of crime, home security, etc.)

The 2000 ICVS asked respondents about experience with crime in 1999. The results for all aggressive contact crimes (robbery, sexual assault, and assault with force), found on page 11 of this pdf document and shown in the above chart, show that, among the 17 developed countries surveyed, the US ranked thirteenth in percentage of residents victimised at least once during 1999, while Canada tied with Scotland for third. The overall percentage in all 17 countries was 2.4%; Canada stood at 3.4%; the United States at 1.9%. Australia was first with 4.1%; England & Wales was second with 3.6%. The results indicate that Canada's victimisation rate for aggressive contact crimes is significantly higher than that of the United States.

The above chart, found on page 16, summarises the results for all crimes covered in the 2000 ICVS. The bars on the left side, marked "incidence", count the number of incidents per 100 residents during 1999. The bars on the right, marked "prevalence", show the percentage of individuals victimised once or more during the year. Canada ranks fifth in prevalence and seventh in incidence, while the US ties for ninth in prevalence but ties for fifth in incidence. This indicates that, compared to Canada, relatively more individuals in the US are victims of multiple crimes. For both prevalence and incidence, there is really not much difference between the US and Canada. The differences between the two countries that show up in this chart are not large enough to be statistically significant.

Both police-reported crime statistics and victim-reported crime statistics have advantages and disadvantages. Nevertheless, all things considered, I think that, for purposes of estimating prevalence of particular crimes, findings based on victimization surveys are generally superior. So, for comparing crime in Canada and the US, the ICVS is, on the whole, the best source available.

Alas, the General Social Survey, source of Canadian crime victimisation statistics, is not conducted in Yukon or Canada's other two northern territories. All we have to go on here is police-reported crime statistics. This document (pdf format) contains a comprehensive analysis of Yukon crime statistics for 1995-2003. Yukon crime rates for 1995-2002 are compared with those of other provinces and territories on pages 121-128. The Yukon has a much higher rate of police-reported violent crime than do the provinces, but the other two territories are even higher. And folks in Ontario think they have a violent crime problem!

UPDATE (17 Jan.): I got some feedback that it wasn't easy to tell which piece of text referred to the chart, so I added a second chart showing the aggressive contact crime victimisation statistics from the ICVS.

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January 14th, 2006 at 12:16 pm

Martian polar ice caps shrinking

More evidence of global warming on Mars from the January 2006 issue of Astronomy:

Mesas of dry ice at the martian south pole have been retreated by about 10 feet (3m) per Mars year since Mars Global Surveyor arrived in 1999. These images compare the same region in 1999 and 2005. Mars seems to be in a warm spell. Dry ice turns to gas on the mesas's sides, but no new ice is being deposited. Over time, the polar pits will merge into plains, mesas will shrink into buttes, and buttes will vanish forever.

If only Kyoto had been agreed to earlier.

via Clayton Cramer.

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