# Patterns of Crime in Canadian Cities :  A Multivariate Statistical Analysis

## 4. Crime Patterns of Individual Cities

Besides factor loadings of the 4 crime components, the factor analysis also produced 4 factor scores (1 for each component) for each of the 600 cities (see Appendix 2 for detailed factor scores for all cities). These 4 factor scores provide information on whether a city has high crime rates for offences contained in each of the 4 components and also on how those crime rates compare to other cities in Canada. As a result, the factor scores can function as 4 crime indices and are a reasonable substitute for the 25 crime rates in describing the crime pattern of individual cities.

The factor scores are distributed normally (in a bell-shaped curve with a mean of 0 and a standard deviation of 1) and commonly range from ‑4 to +4. However, they can occasionally be outside this range. A factor score of 0 means that the crime level (as represented by a specific crime component) for a particular city is about the average of that component for all Canadian cities. In general, +1 (one standard deviation above the mean) means that the crime level is higher than 84% of all Canadian cities; +2 means that the crime level is higher than 97% of all Canadian cities; +3 means that the crime level is higher than 99% of all Canadian cities. Conversely, a factor score of 1 means that the city has a crime level lower than 84% of all Canadian cities.

For example, Waterloo Region, Ontario has the following factor scores for the 4 crime components:

Crime Pattern of Waterloo Region, ON (factor scores)
Component Factor Score
Component 1 – Minor Crimes -0.17
Component 2 – Violent Crimes -0.60
Component 3 – Major Property Crimes 0.23
Component 4 – Moral Offences 0.35

These factor scores indicate that Waterloo Region has slightly below average minor crime rates, much lower than average violent crime rates, slightly higher than average major property crime rates, and higher than average moral offence rates.

A more easily understandable way of presenting these same factor scores is to represent the scores by percentiles (see Appendix 3 for detailed scores for all cities). These percentiles will show the exact positions relative to all Canadi an cities. The percentiles range from a low of 0 to a high of 99. A percentile of 45 for a city (such as component 1 here) means that 45% of other Canadian cities have lower crime rates than this particular city, or conversely, 55% of other Canadian cities have higher crime rates than this particular city. In other words, higher thepercentile, higher the crime level. Again, for Waterloo Region, the percentiles for the 4 crime components are:

Crime Pattern of Waterloo Region, ON (percentiles)
Component Percentile
Component 1 – Minor Crimes 45
Component 2 – Violent Crimes 11
Component 3 – Major Property Crimes 70
Component 4 – Moral Offences 79

These percentile values show that Waterloo Region is higher than the average crime rates of Canadian cities (with values higher than 50) for components 3 and 4 and is lower than the average crime rates of Canadian cities for components 1 and 2. In terms of violent crimes (component 2), Waterloo Region is higher than 11% of other Canadian cities (in other words, lower than 89% of other Canadian cities). In terms of moral offences (component 4), Waterloo Region is higher than 79% of other Canadian cities.

The results show that factor scores and the percentiles are successful in representing the crime pattern of individual cities, both in terms of the level and the position relative to all cities in Canada.

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