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12. Special topics

12.1 Persons not enumerated

12.2 Aboriginal peoples

12.2.1 Introduction

12.2.2 Participating reserves

12.2.3 Incompletely enumerated Indian reserves and settlements

12.1 Persons not enumerated

This section introduces the concept of census population collection undercoverage. Although this new measure does not specify the error in census data from coverage error, it provides a picture of how well the census was able to enumerate its target population. Also, collection undercoverage removes the issue of bias between the true number of persons living in occupied non-response dwellings, the estimate of this number resulting from imputation, and the RRC estimate.

It is instructive to expand the concept of undercoverage to include persons not enumerated for any reason. Undercoverage is defined to be the number of persons not included in the census count. As discussed in Section 3.3, the census count C is composed of two elements:  An equation showing that C is equal to E plus I where E = the number of enumerations, and I = the number of imputed persons. Undercoverage, therefore, is a subset of all persons who were not listed on a census form but should have been. It does not include those who were not enumerated either because no completed census form was returned for the dwelling (non-response dwelling) or the dwelling was not subject to non-response follow-up because they were erroneously classified as unoccupied (misclassified occupied dwelling).

Also from Section 3.3, an estimate of the true number of persons in the census target population T is given by

Two equations showing that T is equal to C plus N, and that T is also equal to C plus U minus O

Combining these two equations:

Three equations showing the calculation of T hat

This formulation of T hat has three components:

  1. E = the number of persons who were listed on a census form1;
  2. O hat = an estimate of the number of excess enumerations2; and
  3. I plus U hat = an estimate of the number of persons who were not listed on a census form who should have been.

The last component, I plus U hat, estimates the number of persons missed in the census for any reason. Let us define census population collection undercoverage, denoted by L, as persons not enumerated for any reason. Then, the estimate of census population collection undercoverage is

An equation showing that L hat is equal to I plus U hat and the corresponding estimate of the rate of census population collection undercoverage rate is:

Two equations showing the calculation of R hat subscript L

Net census collection undercoverage can be defined by subtracting overcoverage O hat from L hat.

Then:

Three equations showing the calculation of T hat

Although net collection undercoverage cannot be applied to census counts to adjust for coverage error, L hat and R hat subscript L provide a broader picture of how well the census was able to enumerate its target population. Also, collection undercoverage removes the issue of bias between the true number of persons living in occupied non-response dwellings, the estimate of this number resulting from imputation, and the RRC estimate.

Table 12.1 gives the estimated 2006 Census population collection undercoverage L hat and R hat subscript L, and population undercoverage U hat and R hat subscript U (also in Table 1.3) and their estimated standard errors for provinces and territories and for national age and sex groups. At the national level, the 2006 Census achieved an enumeration for 92.87% of its target population 100 minus R hat subscript L. This compares to 95.74% of the target population included in the 2006 Census count of 31,612,897 persons 100 minus R hat subscript U. The difference between these two rates is simply the inclusion of the imputations in R hat subscript L. The 2001 Census achieved an enumeration for 94.17% of its target population compared to 97.57% of the target population included in the 2001 Census count of 30,007,094 persons. The decrease in these two rates from 2001 to 2006 is from an increase in undercoverage and an increase in imputations.

12.2 Aboriginal peoples

12.2.1 Introduction

Users should also be aware of the extent to which Indian reserves and Indian settlements participated in the 2006 Census. In some cases enumeration was not permitted or was interrupted before it could be completed. In other cases the quality of the enumeration was considered inadequate. These geographic areas, a total of 22, are called incompletely enumerated Indian reserves and Indian settlements. Data for 2006 are therefore not available for the incompletely enumerated reserves and settlements, and are not included in tabulations. Similar problems have occurred in previous censuses. In the 2001 Census there were 30 Indian reserves and Indian settlements that were declared incompletely enumerated. Among these, 14 became participating reserves in the 2006 Census.

This section presents estimates of 2006 Census net population undercoverage for participating reserves. For incompletely enumerated Indian reserves and Indian settlements, model‑based estimates are presented. Since no reliable source exists to verify the assumptions used in the models, these estimates must be used with caution.

12.2.2 Participating reserves

The following table gives estimates of 2006 Census net undercoverage for all persons living on participating reserves including those without Aboriginal identity for Canada, for the eastern region: Newfoundland and Labrador, Prince Edward Island, Nova Scotia, New Brunswick, Quebec and Ontario, and for the western and northern region:  Manitoba, Saskatchewan, Alberta, British Columbia, the Yukon Territory and the Northwest Territories: Census population net undercoverage 'on reserve,' for Canada.

Limitations of the coverage studies do not permit the production of estimates by Aboriginal identity. The rate of census net undercoverage indicates what proportion of the entire population that should have been enumerated is, on a net basis, not included in 2006 Census tabulations. Users are advised to consult the standard error of an estimate to determine its suitability for use.

The estimate of net undercoverage is the estimate of population undercoverage less the estimate of population overcoverage. One limitation of the estimate of overcoverage is that for a particular geography such as participating reserves, the estimate includes persons who appear on questionnaires for two dwellings where at least one of the dwellings is on reserve. The other dwelling may be on the same reserve, on a different reserve, or not on a reserve. Since the COS does not determine at which dwelling an individual should have been listed at, the assumption is made that it is equally likely that the individual should have been listed at the first dwelling as at the second dwelling. Therefore, in order to produce estimates of overcoverage, half of the weight for the person is assigned to each dwelling. This concept is important for small domains such as the 'on reserve' population. About half of the overcoverage cases involving a dwelling on reserve also involved a dwelling off reserve.

12.2.3 Incompletely enumerated Indian reserves and settlements

Neither the 2006 Census nor the Reverse Record Check is in a position to produce an estimate of the population living in the 22 incompletely enumerated Indian reserves and settlements. In order to produce official estimates of population, a model-based methodology was used to prepare estimates of population for these geographical areas. The resulting estimates should be used with caution as they are based entirely on a model whose assumptions cannot be verified. The validity of these estimates depends on the extent to which the model assumptions capture the true underlying situation.

The national model results can be found at: Model estimates for incompletely enumerated Indian reserves and settlements for Canada.

In the 2001 Census, 30 reserves, with approximately 34,500 persons, were classified as 'incompletely enumerated.' Among the 22 reserves and settlements considered as incompletely enumerated in the 2006 Census, six were considered to have had complete enumerations in the 2001 Census while the other 16 were 'incompletely enumerated' or 'refusal.' The population for the 22 incompletely enumerated reserves and settlement was estimated at approximately 40,000, an increase from 2001.

The estimation model is as follows. A two step model was developed to estimate the population. The first step uses a simple linear regression to predict the Census count in 2006. The linear regression was constructed using all Indian reserves that were completely enumerated in both the 2001 and the 2006 Census. The model assumes a linear growth from 2001 to 2006 for all provinces with separate estimates, for the intercept and the regression parameters for each province. The model was evaluated for the basic regression assumptions of independence of errors, homogeneity of variances and normality of errors.

For each incompletely enumerated reserve, the input variable for the regression model was either the actual census count in 2001 or the best predicted census count from the 2001 model. The output of the model was the estimated census count in 2006.

The second step is done to produce consistency with the results of the census coverage studies. An adjustment was made to the estimated 'census' count to account for net undercoverage of all subjected census counts. Net undercoverage for the incompletely enumerated reserves was estimated by calculating the net undercoverage rate for all completely enumerated reserves in each province and then applying that rate to the estimated 'census' count of all the incompletely enumerated Indian reserves in the province. The estimated 'census' count and the 'estimated net missed persons' in each reserve were then summed to create an 'estimated' population for the incompletely enumerated Indian reserves.

For provincial estimates please refer to: Incompletely enumerated Indian reserves and Indian settlements.

Note:

  1. It is possible that some of the persons listed on the form may not appear in the final census database. So, in the strictest sense, 'persons listed on the form' is used in this section to represent persons in the final census database.
  2. Most cases of overcoverage involve duplicate enumerations where the same person appears twice on the database. In a small number of cases, however, the same person appears more than twice. O hat estimates the number of excess enumerations rather than the number of persons involved in multiple enumerations.

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