# Coverage Technical Report, Census of Population, 2016 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 $T$ is given by:

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

If we combine these two equations, we get:

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

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

$E=$ the number of persons listed on a census formNote 1 (enumerations)

$\stackrel{^}{O}=$ an estimate of the number of excess enumerationsNote 2

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

The last component, $\left(I+\stackrel{^}{U}\right)$, 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:

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

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

${\stackrel{^}{R}}_{L}=100*\frac{\stackrel{^}{L}}{\stackrel{^}{T}}=100*\left(\frac{I+\stackrel{^}{U}}{C+\stackrel{^}{N}}\right)$

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

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

Although net collection undercoverage cannot be applied to census data to adjust for coverage error, $\stackrel{^}{L}$  and ${\stackrel{^}{R}}_{L}$ 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 2016 Census of Population collection undercoverage estimates $\stackrel{^}{L}$  and ${\stackrel{^}{R}}_{L}$, and the population undercoverage estimates $\stackrel{^}{U}$  and ${\stackrel{^}{R}}_{U}$ (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 sex. At the national level, the 2016 Census collection enumerated 93.63% of the target population ($100-{\stackrel{^}{R}}_{L}$), whereas the official published 2016 Census count represented 95.68% of the persons who should have been included in this figure ($100-{\stackrel{^}{R}}_{U}$). The difference between these two rates is simply attributable to the inclusion of the imputations in ${\stackrel{^}{R}}_{L}$. The 2011 Census enumerated 93.65% of the target population, when 95.93% of the persons who should have been included in the official 2011 Census counts were included. Therefore, the 2016 Census collection enumerated the same percentage of the target population as the previous census, and there were fewer imputations than in 2011.

Table 12.1
Estimated population collection undercoverage, population undercoverage and standard errors for various characteristics, 2016 Census
Table summary
This table displays the results of Estimated population collection undercoverage. The information is grouped by Characteristics (appearing as row headers), Population collection undercoverage and Population undercoverage (appearing as column headers).
Characteristics Population collection undercoverage Population undercoverage
Estimated
number
Standard
error
Estimated
rate (%)
Standard
error (%)
Estimated
number
Standard
error
Estimated
rate (%)
Standard
error (%)
Canada 2,294,997 41,050 6.37 0.11 1,557,061 41,050 4.32 0.11
Provinces and territories
Newfoundland and Labrador 31,562 1,982 5.96 0.35 20,848 1,982 3.94 0.36
Prince Edward Island 8,676 864 5.93 0.56 5,875 864 4.01 0.57
Nova Scotia 53,714 2,965 5.71 0.30 34,872 2,965 3.70 0.30
New Brunswick 47,699 2,701 6.25 0.33 32,382 2,701 4.24 0.34
Quebec 359,668 18,074 4.39 0.21 211,077 18,074 2.57 0.21
Ontario 895,268 31,508 6.47 0.21 640,831 31,508 4.63 0.22
Manitoba 79,409 4,772 6.06 0.34 51,742 4,772 3.95 0.35
Saskatchewan 84,444 4,375 7.45 0.36 56,494 4,375 4.99 0.37
Alberta 283,307 13,293 6.77 0.30 188,706 13,293 4.51 0.30
British Columbia 436,767 16,215 9.01 0.30 305,948 16,215 6.31 0.31
Yukon 4,440 188 11.61 0.44 3,219 188 8.42 0.45
Northwest Territories 5,948 255 13.30 0.49 3,500 255 7.83 0.53
Nunavut 4,093 228 11.10 0.55 1,565 228 4.25 0.59
Sex and age group
Both sexes, all ages 2,294,997 41,050 6.37 0.11 1,557,061 41,050 4.32 0.11
0 to 4 years 105,966 10,269 5.47 0.50 73,537 10,269 3.79 0.51
5 to 14 years 180,455 15,125 4.60 0.37 115,279 15,125 2.94 0.37
15 to 17 years 72,117 9,823 5.99 0.77 52,294 9,823 4.35 0.78
18 to 19 years 82,426 11,878 9.42 1.23 67,506 11,878 7.71 1.25
20 to 24 years 275,310 15,422 11.52 0.57 230,347 15,422 9.64 0.58
25 to 34 years 528,131 22,742 10.71 0.41 424,019 22,742 8.60 0.42
35 to 44 years 331,357 20,305 7.01 0.40 239,817 20,305 5.07 0.41
45 to 54 years 306,879 21,216 5.93 0.39 199,652 21,216 3.86 0.39
55 to 64 years 224,065 21,011 4.53 0.41 109,145 21,011 2.21 0.42
65 years and older 188,291 17,172 3.20 0.28 45,465 17,172 0.77 0.29
Males, all ages 1,303,844 34,853 7.30 0.18 941,799 34,853 5.27 0.18
0 to 4 years 58,617 7,140 5.86 0.67 42,169 7,140 4.22 0.68
5 to 14 years 80,292 10,944 4.02 0.53 46,881 10,944 2.35 0.54
15 to 17 years 38,094 7,153 6.21 1.09 27,918 7,153 4.55 1.11
18 to 19 years 40,736 8,857 9.05 1.79 33,232 8,857 7.38 1.82
20 to 24 years 165,697 12,392 13.29 0.86 142,866 12,392 11.46 0.88
25 to 34 years 313,678 17,559 12.57 0.62 260,481 17,559 10.44 0.63
35 to 44 years 192,359 15,790 8.22 0.62 145,997 15,790 6.24 0.63
45 to 54 years 186,765 16,114 7.24 0.58 133,156 16,114 5.16 0.59
55 to 64 years 131,573 16,959 5.38 0.66 76,049 16,959 3.11 0.67
65 years and older 96,033 11,254 3.57 0.40 33,050 11,254 1.23 0.41
Females, all ages 991,153 33,151 5.46 0.17 615,262 33,151 3.39 0.18
0 to 4 years 47,349 8,465 5.04 0.86 31,368 8,465 3.34 0.87
5 to 14 years 100,163 11,173 5.21 0.55 68,398 11,173 3.56 0.56
15 to 17 years 34,023 6,540 5.77 1.04 24,376 6,540 4.13 1.06
18 to 19 years 41,690 8,159 9.81 1.73 34,274 8,159 8.07 1.77
20 to 24 years 109,612 9,473 9.59 0.75 87,480 9,473 7.66 0.77
25 to 34 years 214,454 14,560 8.81 0.55 163,539 14,560 6.71 0.56
35 to 44 years 138,998 13,180 5.82 0.52 93,820 13,180 3.93 0.53
45 to 54 years 120,114 14,635 4.62 0.54 66,496 14,635 2.56 0.55
55 to 64 years 92,492 12,585 3.70 0.48 33,096 12,585 1.32 0.50
65 years and older 92,258 13,484 2.88 0.41 12,415 13,484 0.39 0.42

## 12.2 Participation of Indian reserves and Indian settlements

### 12.2.1 Introduction

In 2016, there were 984 Indian reserves and Indian settlements, 14 of which were considered incompletely enumerated. For the 14 incompletely enumerated reserves and settlements, dwelling enumeration either was not permitted or was interrupted before it could be completed. There were no 2016 data for the incompletely enumerated Indian reserves and Indian settlements and, as a result, they were not included in any calculations. In the 2011 Census, 31 Indian reserves and Indian settlements were declared incompletely enumerated and, of these, 22 took part in the 2016 Census. In 2006, there were 22 incompletely enumerated Indian reserves and Indian settlements.

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

The estimates for incompletely enumerated Indian reserves and Indian settlements were 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.

### 12.2.2 Incompletely enumerated Indian reserves and Indian settlements

For 14 incompletely enumerated Indian reserves and settlements, the 2016 Census was not able to produce population counts, and the coverage studies could not directly estimate net population undercoverage. This was because of limited 2016 Census data. The counts and net undercoverage were estimated using approximations.

To estimate census population counts, a model-based methodology was used for these incompletely enumerated Indian reserves and settlements. For the estimation model, the linear regression was constructed using all Indian reserves that were completely enumerated in both the 2011 and the 2016 censuses. The model assumed that the 2016 Census count was a linear function of the 2011 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: independence of errors, homogeneity of variances and normality of errors. For each of the 14 incompletely enumerated reserves, the input variable for the regression model was either the actual census count in 2011 or the best predicted census count from the 2011 model. The output of the model was the estimated census count in 2016 for these 14 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 2011 Census, 31 reserves, with approximately 37,000 persons, were classified as “incompletely enumerated”. Among the 14 reserves and settlements used in the model-based estimates in the 2016 Census, 4 were considered to have been completely enumerated in the 2011 Census, while the other 10 were classified as “incompletely enumerated” or “refusal”. The total population for the 14 incompletely enumerated Indian reserves and settlements for which model-based estimates were produced was estimated at 27,790—a decrease from 2011.

The estimated population counts for the 14 incompletely enumerated Indian reserves and settlements are subject to coverage errors, just like the census population counts for the rest of the country. Net undercoverage for these 14 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.

The demographic estimates for incompletely enumerated Indian reserves and Indian 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 demographic estimates for incompletely enumerated Indian reserves and Indian settlements 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, 2018 (Total Population only), catalogue number 91-215-X.

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