# Coverage Technical Report, Census of Population, 2016 9. Estimation

Estimation for the DCS, the RRC and the COS is covered in Section 6.2, Section 7.4 and Section 8.5, respectively. This section describes how the results of census coverage studies are combined to produce estimates of population undercoverage ($U$), population overcoverage ($O$) and population net undercoverage ($N$) in different domains. The impact of sampling errors on the quality of the estimates is also measured by an estimated standard error for each estimate. Reverse Record Check (RRC) results and census data are used to produce undercoverage estimates, while the Census Overcoverage Survey (COS) results estimate overcoverage. Net undercoverage is the difference between undercoverage and overcoverage. This section expands on how these estimates and the associated standard errors are calculated.

The following definitions are used:

$C$
=
published census count of the number of persons in the target population
$\stackrel{^}{U}$
=
undercoverage estimate
This is an empty cell
=
estimated number of persons not included in $C$ who should have been included
$\stackrel{^}{O}$
=
overcoverage estimate
This is an empty cell
=
estimated number of enumerations included in $C$ that should not have been included
$\stackrel{^}{N}$
=
net undercoverage estimate
This is an empty cell
=
estimated number of enumerations not included in $C$ that should have been included, less the number of enumerations included in $C$ who should not have been included
This is an empty cell
=
$\stackrel{^}{U}-\stackrel{^}{O}$
$\stackrel{^}{T}$
=
estimated number of persons in the census target population based on census enumerations and the estimate of population net undercoverage
This is an empty cell
=
$C+\stackrel{^}{N}$
${\stackrel{^}{R}}_{U}$
=
estimated undercoverage rate
This is an empty cell
=
$100*\frac{\stackrel{^}{U}}{\stackrel{^}{T}}=100*\frac{\stackrel{^}{U}}{C+\stackrel{^}{N}}$
${\stackrel{^}{R}}_{O}$
=
estimated overcoverage rate
This is an empty cell
=
$100*\frac{\stackrel{^}{O}}{\stackrel{^}{T}}=100*\frac{\stackrel{^}{O}}{C+\stackrel{^}{N}}$
${\stackrel{^}{R}}_{N}$
=
estimate of net undercoverage rate
This is an empty cell
=
$100*\frac{\stackrel{^}{N}}{\stackrel{^}{T}}=100*\frac{\stackrel{^}{U}-\stackrel{^}{O}}{C+\stackrel{^}{N}}$

$\stackrel{^}{U}$ is calculated using RRC results and census data, and $\stackrel{^}{O}$ is produced from the COS, as shown below:

Table 9.1
Components of the population coverage error estimates for Canada
Table summary
This table displays the results of Components of the population coverage error estimates for Canada. The information is grouped by Components (appearing as row headers), Number of
ComponentsTable 9.1 Note 1 Number of persons
Estimate of U 1,557,061
Estimate of O 707,335
Estimate of N 849,726
C 35,151,728
C + estimate of N 36,001,454

The estimated standard errors are defined as follows:

By definition, we have $v\left(\stackrel{^}{U}\right)=v\left(\stackrel{^}{M}\right)$ (refer to Section 7.4.7).

$v\left(\stackrel{^}{M}\right)$
=
estimated variance of $\stackrel{^}{M}$ based on the RRC design
$v\left(\stackrel{^}{O}\right)$
=
estimated variance of $\stackrel{^}{O}$ based on the COS design

Therefore:

$se\left(\stackrel{^}{U}\right)=\sqrt[]{v\left(\stackrel{^}{M}\right)}$

$se\left({\stackrel{^}{R}}_{U}\right)=\sqrt{\left(\frac{{\stackrel{^}{U}}^{2}+{\stackrel{^}{T}}^{2}-2\stackrel{^}{U}\stackrel{^}{T}}{{\stackrel{^}{T}}^{4}}\right)v\left(\stackrel{^}{M}\right)+\frac{{\stackrel{^}{U}}^{2}}{{\stackrel{^}{T}}^{4}}v\left(\stackrel{^}{O}\right)}$

$se\left(\stackrel{^}{O}\right)=\sqrt[]{v\left(\stackrel{^}{O}\right)}$

$se\left({\stackrel{^}{R}}_{O}\right)=\sqrt{\left(\frac{{\stackrel{^}{O}}^{2}}{{\stackrel{^}{T}}^{4}}\right)v\left(\stackrel{^}{M}\right)+\left(\frac{{\stackrel{^}{U}}^{2}+{\stackrel{^}{T}}^{2}-2\stackrel{^}{O}\stackrel{^}{T}}{{\stackrel{^}{T}}^{4}}\right)v\left(\stackrel{^}{O}\right)}$

$se\left(\stackrel{^}{N}\right)=\sqrt[]{v\left(\stackrel{^}{M}\right)+v\left(\stackrel{^}{O}\right)}$

$se\left({\stackrel{^}{R}}_{N}\right)=\sqrt{\left(\frac{{\left(\stackrel{^}{U}-\stackrel{^}{O}\right)}^{2}+{\stackrel{^}{T}}^{2}-2\left(\stackrel{^}{U}-\stackrel{^}{O}\right){\stackrel{^}{T}}^{2}}{{\stackrel{^}{T}}^{4}}\right)\left[v\left(\stackrel{^}{M}\right)+v\left(\stackrel{^}{O}\right)\right]}$

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