Coverage Technical Report, Census of Population, 2021
12. Special topics

12.1 Collection undercoverage

Up to this point, this report focused on undercoverage in the census population counts. This section deals with the concept of Census 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, represents only part 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 (occupied dwelling misclassified as vacant) and was not covered by non-response follow-up.

Also discussed in Section 3.3, an estimate of the actual number of persons in the census target population 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^{Note 1} (enumerations)

$\widehat{O}$ = an estimate of the number of excess enumerations^{Note 2}

$\left(I+\widehat{U}\right)$ = 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 census collection undercoverage is given by:

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

The corresponding estimate of the Census of Population collection undercoverage rate is:

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

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

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

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 or not they were taken into account in the census through imputations. Table 12.1 shows the 2021 Census of Population collection undercoverage estimates $\widehat{L}$ and ${\widehat{R}}_L$ and the population undercoverage estimates $\widehat{U}$ and ${\widehat{R}}_U$ (also see Table 1.3). It also shows their estimated standard errors. The results are shown by province or territory and for Canada, and by age group and gender. At the national level, the 2021 Census collection enumerated 92.58% of the target population ($100-{\widehat{R}}_L$), whereas the official published 2021 Census count represented 95.02% of the persons who should have been included in this figure ($100-{\widehat{R}}_U$). The difference between these two rates is simply attributable to the inclusion of the imputations in ${\widehat{R}}_L$. The 2016 Census enumerated 93.63% of the target population, when 95.68% of the persons who should have been included in the official 2016 Census counts were included. Therefore, the 2021 Census collection enumerated a slightly lower percentage of the target population than the previous census, and there were more imputations than in 2016.

12.2 Participation of reserves and settlements

12.2.1 Introduction

In 2021, there were 1,026 reserves and settlements, 63 of which were considered incompletely enumerated. For the 63 incompletely enumerated reserves and settlements, dwelling enumeration either was not permitted or was interrupted before it could be completed. There were no 2021 data for the incompletely enumerated reserves and settlements and, as a result, they were not included in any calculations. In the 2016 Census, 14 reserves and settlements were declared incompletely enumerated and, of these, 1 took part in the 2021 Census. In 2011, there were 31 incompletely enumerated reserves and settlements. The large increase in the number of incompletely enumerated reserves and settlements for the 2021 Census relative to the 2016 Census was mainly because of health and safety measures related to the COVID-19 pandemic.

Further information can be found here: Incompletely enumerated reserves and settlements.

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

12.2.2 Incompletely enumerated reserves and settlements

For 63 incompletely enumerated reserves and settlements, the 2021 Census was not able to produce population counts, and the coverage studies could not directly estimate net population undercoverage. This was because of a lack of 2021 Census data. The counts and net undercoverage were estimated using alternative methods.

To estimate census population counts, a model-based methodology was used for these incompletely enumerated reserves and settlements. For the estimation model, linear regression without intercept was chosen. The model parameter was estimated based on reserves that were completely enumerated in both the 2016 and the 2021 censuses. The model assumed that the 2021 Census count was a linear function of the 2016 Census count for all provinces, with separate estimates for the slope for each province. In particular, incompletely enumerated reserves and settlements were assumed to follow the same growth pattern as completely enumerated reserves and settlements. The model was evaluated for the basic regression assumptions: independence of errors, homogeneity of variances and normality of errors. For each of the 63 incompletely enumerated reserves and settlements, the input variable for the regression model was either the actual census count in 2016 or the estimated census count from the 2016 model. The output of the model was the estimated census count in 2021 for these 63 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.

In the 2016 Census, 14 reserves, with approximately 28,000 persons, were classified as incompletely enumerated. Among the 63 reserves and settlements for which model-based estimates were produced for the 2021 Census, 50 were considered to have been completely enumerated in the 2016 Census, while the other 13 were classified as incompletely enumerated. The total population for the 63 incompletely enumerated reserves and settlements was estimated at 58,480—more than double from 2016.

The model-estimated population counts for the 63 incompletely enumerated reserves and settlements are subject to coverage errors, just like the census population counts for the rest of the country. Net undercoverage for these 63 areas was estimated by calculating the net undercoverage rate for all completely enumerated reserves in the country. That rate was then applied to the estimated census counts of all the incompletely enumerated reserves and settlements. The estimated total population of 58,480 for incompletely enumerated reserves and settlements in 2021 includes this adjustment for coverage errors.

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

The population estimates for incompletely enumerated reserves and settlements are included in demographic estimates. The estimates, broken down by province and territory, can be found in Table 1 of the “Data quality concepts and methodology” section in the following demographic estimates publication: Annual Demographic Estimates: Canada, Provinces and Territories (Total Population only), 2023, Statistics Canada Catalogue no. 91-215-X.