ARCHIVED – A description of the ethnic segregation/mixing within major Canadian metropolitan areas project

Representing the numbers: Interpretation of indices

a) Location quotients:

Meaningful comparisons of the relative spatial concentration and dispersion of many different immigrant and visible minority groups within the same city, as well as between cities, is a major challenge for this type of mapping project. One option is to map a specific immigrant or visible minority group as a proportion of the total population within a census tract or as a proportion of that particular group’s total metropolitan population found in each census tract. Such maps have the great advantage of being relatively easy to interpret as the mapped values are simple percentages. Often it is difficult, however, to compare maps based on percentage values for different groups because usually there are significant differences in the degree of concentration of groups across a metropolitan area, hence different class intervals are required to represent adequately the distribution. As a consequence, maps for different groups can be made to look quite similar because the same colour scheme and number of classes is used. Such maps suggest comparability, but in fact they can be based on very different class intervals and are not directly comparable.

To facilitate meaningful comparisons, the maps for this project are based on location quotient values for each individual immigrant and visible minority group. Location quotients compare the relative concentration of an immigrant or visible minority group in a small geographic area (i.e., a census tract) to the relative concentration of that same group in a much larger area (i.e., the entire metropolitan area). The quotient is a ratio of the group’s representation as a percentage of a tract’s total population relative to its percentage of the metropolitan area population. Location quotient values indicate the degree to which a tract departs from the overall proportion that a group constitutes of the metropolitan area. For example, if British immigrants constituted 6 percent of the total population of census tract “004.00”, but only 3 percent of the total population in the metropolitan area, the location quotient for census tract “004.00” is 2.

In terms of interpretation, if the location quotient for a census tract is 1, this means that the tract has exactly the same relative frequency for the immigrant or visible minority group being considered as is found in the entire metropolitan area. A location quotient of greater than 1 indicates that the group is over-represented in the census tract and that there is a relative concentration of the group in the tract. For example, a location quotient value of 2 indicates that the group’s share of the population in that tract is double its share of the population at the metropolitan area. By the same token, a location quotient of less than 1 indicates an under-representation or a low concentration in the census tract relative to the metropolitan average. [note 8]

For this project, the following class categories for mapping location quotients will be used:

  • 0 – 0.49
  • 0.5 – 1.49
  • 1.5 – 2.99
  • 3.0 – 7.99
  • 8.0 and greater

These classes were selected because they are relatively easy to interpret, especially in terms of identifying locations of significant under- and over-representation. The intent is not to over exaggerate the degree of concentration experienced by some groups; consequently range of values less than and greater than ‘one’ indicate geographic areas that fairly closely match a group’s representation in the metropolitan area. It is important to bear in mind that the absolute size of the group must be remembered in interpreting any map representing areas of under- or over-representation. Simply put, a map showing a few areas of significant over-representation for a group that is small in number (e.g., a couple of thousand people) points to a different social phenomenon and set of considerations relative to a map representing tens of thousands of people.

b) Diversity (Entropy) index:

As explained above, maps are produced for each city that indicate the degree of ethnocultural diversity that exists in each city at the census tract level. These maps draw on visible minority data and are based on Diversity or Entropy values for individual census tracts in the metropolitan area (Allen, 2005; Sandoval et al., 2002; White, 1986). Instead of measuring the degree to which a particular group is concentrated in a small area, the diversity index assesses how diverse an area is with respect to the total number of ethnocultural groups found in the metropolitan area overall. The diversity scores range from 0 to 100, where 0 is complete homogeneity (i.e., the area is dominated exclusively by one group) and 100 is complete heterogeneity (i.e., all the groups are equally represented in the area). In short, the higher the number, the more equal the representation of all of the groups, and the lower the number, the more one immigrant or ethnocultural group dominates. A low value does not necessarily mean that an area is completely homogeneous, just that the proportional distribution among the groups is not equal and that only a couple of groups occupy the area in any substantial way. The calculation of the index is:

Mathematical equation


Hi = Diversity index for tract i

P(i) = Proportion of the tract population in visible minority group k

K = The total number of visible minority group categories

There is little agreement in the literature about the breakpoints for diversity versus homogeneity using this index. Allen (2005) considers scores over 84 to be indicative of high diversity, whereas Sandoval et al. (2002) suggest that a score of over 75 indicates strong diversity. The maps created for this project are based on the following class intervals for:

  • 71 – 100 (high)
  • 56 – 70
  • 41 – 55 (modest)
  • 21 – 40
  • 0 – 20 (low)

The threshold value for the highest class was set at ‘71 and over’ for this project to facilitate comparison between cities. In Toronto, Vancouver, and Montréal, a fairly large number of census tracts would fall into the highest class even if the threshold value were 75 or 84. In other Canadian cities that are significantly less diverse, only few tracts, if any, would make it into the highest class interval if the threshold were set higher than 71.

Diversity maps are presented for both places of residence and work. For place of residence, the maps are based on the 13 categories that comprise the visible minority variable as defined by the Canadian government for employment equity purposes. For place of work maps, however, the number of categories has been reduced through the amalgamation of some groups into larger regional groupings to minimize the problem of data suppression due to small numbers (Table 3). Given that the place of work data are based only on the population that is active in the labour force and that has a fixed place of employment, and that many immigrant and visible minority groups have a relatively small proportion of their population active in the labour force, it was necessary to amalgamate some groups in order to conduct analyses that do not suffer from excessive data suppression problems.

Table 3: Visible Minority Groups Used in Calculation of Diversity Index Scores for Place of Residence and Work
Place of Residence Place of Work
  • Chinese
  • East Asian (Chinese, Korean, Japanese)
  • South Asian
  • South Asian
  • Black
  • Black
  • Filipino
  • Southeast Asian (Southeast Asian, Filipino)
  • Latin American
  • Arab
  • Southeast Asian
  • Others (Latin American, West Asian, Visible Minority n.i.e., Multiple Visible Minority
  • Arab
  • All others (European-origin or ‘white’ population)
  • West Asian
  • Korean
  • Japanese
  • Visible Minority, n.i.e. (not identified elsewhere)
  • Multiple visible minorities
  • All others (European-origin or ‘white’ population)


[8] One of the conceptual limitations of location quotient is that values of “under-representation” are constrained to values between 0 and 1, whereas those of “over-representation” are measured on an unlimited scale. As a consequence, it is somewhat problematic to evaluate the degree of under- or over-representation using a location quotient simply because of scale differences in relation to unity.

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