12. Special topics

12.1 Collection undercoverage

Up to now, we have been concerned with undercoverage in the census population count. This section introduces the concept of population collection undercoverage. It is useful to expand the concept of undercoverage to include persons not enumerated for any reason. Undercoverage is defined as the number of persons not included in the census counts. As discussed in Section 3.3, the census counts C are composed of two elements: $C=E+I$,

where $E$ = the number of enumerations and $I$ = the number of persons imputed.

Undercoverage, therefore, is a secondary series of all persons who were not listed on a census form but should have been. It does not include persons who were not enumerated either because no census form was returned for the dwelling (non-response dwelling) or because the dwelling was erroneously classified as unoccupied (misclassified occupied dwelling) and was not covered by non-response follow-up.

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

$\widehat{T}=C+\widehat{N}=C+\widehat{U}-\widehat{O}$

If we combine these two equations, we get:

$\widehat{T}=C+\widehat{N}=C+\widehat{U}-\widehat{O}=E+\left(I+\widehat{U}\right)-\widehat{O}$

This formulation of $\widehat{T}$ has three components:

$E$ = the number of persons listed on a census form^Footnote1 (enumerations)

$\widehat{O}$ = an estimate of the number of excess enumerations^Footnote2

$\left(I+\widehat{U}\right)$ = an estimate of the number of persons who were not listed on a census form but should have been.

The last component, $\left(I+\widehat{U}\right)$, is an estimate of the number of persons missed in the census for any reason. The Census of Population collection undercoverage (L) refers to persons not enumerated for any reason. The estimate of population collection undercoverage is given by:

$\widehat{L}=\left(I+\widehat{U}\right)$,

and the corresponding estimate of the census of population collection undercoverage rate is:

${\widehat{R}}_L=100*\frac{\widehat{L}}{\widehat{T}}=100*\left(\frac{I+\widehat{U}}{C+\widehat{N}}\right)$.

Census of population net collection undercoverage can be calculated by subtracting overcoverage $\widehat{O}$ from $\widehat{L}$.

Thus we have:

$\widehat{T}=C+\widehat{N}=E+\left(I+\widehat{U}\right)-\widehat{O}=E+\widehat{L}-\widehat{O}$

Although net collection undercoverage cannot be applied to census data to adjust for coverage error, $\widehat{L}$ and ${\widehat{R}}_L$ provide a broader picture of how well the census was able to enumerate the target population. In fact, they include persons not enumerated, whether they were taken into account in the census through imputations or not. Table 12.1 shows the 2011 Census population collection undercoverage estimates $\widehat{L}$ and ${\widehat{R}}_L$, and the population undercoverage estimates $\widehat{U}$ and ${\widehat{R}}_U$ (see also Table 1.3) and their estimated standard errors for provinces and territories and for Canada, by age group and sex. At the national level, the 2011 Census enumerated 93.65% of the target population ($100-{\widehat{R}}_L$), compared with 95.93% of the 33,476,688 persons included in the official 2011 Census count ($100-{\widehat{R}}_U$). The difference between these two rates is simply the inclusion of the imputations in ${\widehat{R}}_L$. The 2006 Census enumerated 92.87% of the target population, compared with 95.74% of the 31,612,867 persons in the official 2006 Census figure. Hence, the 2011 Census enumerated a larger percentage of the population, and there were fewer imputations than in 2006.

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12.2 Participation of Indian reserves and Indian settlements

Introduction

Users should also be aware of the extent to which Indian reserves and Indian settlements participated in the 2011 Census. In some cases, enumeration was not permitted or was interrupted even before it started. In other cases, the quality of the enumeration was considered inadequate. These geographic areas, 31 in all, are referred to as incompletely enumerated Indian reserves and Indian settlements. There are no 2011 data for the incompletely enumerated Indian reserves and Indian settlements, and they are not included in any calculations. Similar problems have occurred in previous censuses. In the 2006 Census, 22 Indian reserves and Indian settlements were declared incompletely enumerated (30 in 2001). Fourteen of them took part in the 2011 Census.

The estimates for incompletely enumerated Indian reserves and Indian settlements are based on a model. Since no reliable source is available to verify the assumptions used in the models, these estimates must be used with caution.

Incompletely enumerated Indian reserves and Indian settlements

For 31 incompletely enumerated Indian reserves and settlements, the 2011 Census was not in a position to produce population counts and the coverage studies could not directly estimate net population undercoverage both due to limited 2011 Census data. The counts and net undercoverage were estimated using approximations.

To estimate census population counts, a model-based methodology was used for 18 of the incompletely enumerated Indian reserves and settlements. The estimation model is as follows; the linear regression was constructed using all Indian reserves that were completely enumerated in both the 2006 and the 2011 Census. The model assumes that the 2011 Census count is a linear function of the 2006 Census count 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 of the 18 incompletely enumerated reserves for which the model based methodology was used, the input variable for the regression model was either the actual census count in 2006 or the best predicted census count from the 2006 model. The output of the model was the estimated census count in 2011 for these 18 communities. 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 model based estimates depends on the extent to which the model assumptions capture the true underlying situation.

For the remaining 13 incompletely enumerated Indian reserves and settlements that were affected by forest fires in Northern Ontario, a special National Household Survey data collection was done in the fall of 2011. The population counts were estimated from this collected data and released separately for these 13 incompletely enumerated Indian reserves and settlements. Refer to the following link for the Profile for the NHS Special Collection for 13 Indian reserves and Indian settlements in Northern Ontario, 2011:

http://www12.statcan.gc.ca/nhs-enm/2011/ref/no13reserves/index.cfm?Lang=E

In the 2006 Census, 22 reserves, with approximately 40,000 persons, were classified as 'incompletely enumerated.' Among the 18 reserves and settlements used in the model-based estimates in the 2011 Census, five were considered to have had complete enumerations in the 2006 Census, while the other 13 were 'incompletely enumerated' or 'refusal.' The total population for the 18 incompletely enumerated Indian reserves and settlements for which model-based estimates were produced and the 13 incompletely enumerated Indian reserves and settlements that were affected by forest fires in Northern Ontario was estimated at 37,392, a decrease from 2006.

The estimated population counts for the 31 incompletely enumerated Indian reserves and settlements are subject to coverage errors in the same way as are the census population counts for the rest of the country. Net undercoverage for these 31 areas 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 and settlements in the province.

Further information and results can be found at:

http://www12.statcan.gc.ca/census-recensement/2011/ref/aboriginal-autochtones-eng.cfm

The estimates for incompletely enumerated Indian reserves and Indian settlements are not included in the estimates of undercoverage, collection undercoverage, overcoverage and net undercoverage presented in this report because they are based on a model and not on census coverage studies. In addition, they do not provide the same level of detail (for example, estimates by mother tongue or marital status) as the other estimates.