Archived Content

Information identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please contact us to request a format other than those available.

9. Estimation

Estimation for the DCS, the RRC and the COS is covered in Section 6.2, Section 7.4 and Section 8.6 respectively. This section provides a description of how the results of the census coverage studies were combined to produce estimates of population undercoverage ( $U$ ), population overcoverage ( $O$ ) and population net undercoverage ( $N$ ) for various domains. The impact of sampling error on the quality of the estimates is also determined by calculating an estimated standard error for each estimate. Reverse Record Check (RRC) results and census data are used to construct estimates of undercoverage, while the Census Overcoverage Survey (COS) results provide estimates of overcoverage. Net undercoverage is the difference between undercoverage and overcoverage. This section contains details about the calculation of these estimates and the associated standard errors.

Let

C

published census count of the number of persons in the target population

\hat{U}

estimate of undercoverage

estimate of the number of persons not included in

C

who should have been

\hat{O}

estimate of overcoverage

estimate of the number of enumerations included in

C

that should not have been

\hat{N}

estimate of net undercoverage

estimate of the number of persons not included in

C

who should have been less the number of enumerations included in

C

that should not have been

\hat{U} - \hat{O}

\hat{T}

estimate of the number of persons in the census target population based on census enumerations and the estimate of population net undercoverage

C + \hat{N}

{\hat{R}}_{U}

estimate of the undercoverage rate

100 * \frac{\hat{U}}{\hat{T}} = 100 * \frac{\hat{U}}{C + \hat{N}}

{\hat{R}}_{O}

estimate of the overcoverage rate

100 * \frac{\hat{O}}{\hat{T}} = 100 * \frac{\hat{O}}{C + \hat{N}}

{\hat{R}}_{N}

estimate of the net undercoverage rate

100 * \frac{\hat{N}}{\hat{T}} = 100 * \frac{\hat{U} - \hat{O}}{C + \hat{N}}

$\hat{U}$ is obtained from RRC results and census data and $\hat{O}$ is obtained from COS as shown below:

Top of Page

Table 9.1
Components of the estimate of population coverage error for Canada

The estimated standard errors are defined as shown below:

By definition, we have $v (\hat{U}) = v (\hat{M})$

$v (\hat{M})$ = estimated variance of $\hat{M}$ based on the RRC design

$v (\hat{O})$ = estimated variance of $\hat{O}$ based on the COS design

Then

$s e (\hat{U}) = \sqrt[]{v (\hat{M})}$
$s e ({\hat{R}}_{U}) = \sqrt{(\frac{{\hat{U}}^{2} + {\hat{T}}^{2} - 2 \hat{U} \hat{T}}{{\hat{T}}^{4}}) v (\hat{M}) + \frac{{\hat{U}}^{2}}{{\hat{T}}^{4}} v (\hat{O})}$
$s e (\hat{O}) = \sqrt[]{v (\hat{O})}$
$s e ({\hat{R}}_{O}) = \sqrt{(\frac{{\hat{O}}^{2}}{{\hat{T}}^{4}}) v (\hat{M}) + (\frac{{\hat{U}}^{2} + {\hat{T}}^{2} - 2 \hat{O} \hat{T}}{{\hat{T}}^{4}}) v (\hat{O})}$
$s e (\hat{N}) = \sqrt[]{v (\hat{M}) + v (\hat{O})}$
$s e ({\hat{R}}_{N}) = \sqrt{(\frac{{(\hat{U} - \hat{O})}^{2} + {\hat{T}}^{2} - 2 (\hat{U} - \hat{O}) {\hat{T}}^{2}}{{\hat{T}}^{4}}) [v (\hat{M}) + v (\hat{O})]}$

Date modified:: 2016-01-04

Language selection

Search and menus

Search

Archived Content

9. Estimation