Quality of demographic data

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Notes related to the quality of demographic estimates

In this case, the adjustment for the census net undercoverage (CNU) also includes the incompletely enumerated Indian reserves.
Unless otherwise noted, the term preliminary include both preliminary and updated estimates.

The estimates contain certain inaccuracies stemming from two types of errors:

  • errors in the Census data;
  • imperfections in other data sources and the method used to estimate the components.

Census Data

Coverage, response and imputation errors

The errors attributable to census data can be divided into two groups: Response and processing errors, and coverage errors. The first group implies non-response error, misinterpretation by respondents, incorrect coding and non-response imputation. Errors in the second group primarily result from census undercoverage and, to a lesser extent, overcoverage. It should be noted that both types of errors are intrinsic to any survey data.

The coverage errors occur when dwellings and/or individuals are missed, incorrectly included (except for the 2006 and the 2011 Censuses, where peoples incorrectly included where not considered in the Census Overcoverage Study) or counted more than once. Following each census, Statistics Canada undertakes coverage studies to measure these errors. The main studies are the Reverse Record Check Survey (RRC) and the Census Overcoverage Study (COS). Based on these studies, estimates of undercoverage and overcoverage are produced for each province and territory. Demography Division adjusts the population enumerated in the census by province and territory using these estimates. At the subprovincial level these rates are applied to all geographic regions in the province or territory by age and sex.

When creating base populations, the Estimates Program corrects the census populations only for coverage errors. This correction, which is based on the findings of coverage studies, is primarily subject to sampling errors, and to a lesser extent, processing errors. Statistical tests indicate that coverage adjustments improve the quality of census data. The Estimates Program uses the estimates from coverage studies for the provinces and territories. However, given the size of the samples in these studies, estimates by age and sex are modeled. Furthermore, it is assumed that the coverage rates estimated for a province or territory apply to the regions within that geographic area. With respect to the coverage studies, statistical analysis concluded that the adjustment, although not without errors itself, improved the quality of census data (Royce, 1993). They were deemed to be consistent over time and across geographical areas, and to provide logical results. Users should also be aware that when calculating census net undercoverage (CNU) rates for small areas, it is likely that the underlying assumptions may be violated. If this is true, the resulting CNU rate would be misleading. Errors associated with these assumptions are, however, very difficult to quantify.

The corrections to the census data due to CNU improved, in general, the quality of the estimates by compensating for the differential undercoverage by age, sex and by province/territory across censuses.

The adjustment also incorporates the results of a study on the estimates of the number of people living on incompletely enumerated Indian reserves to complete the corrections for coverage errors in the census. The results of the coverage studies contain mainly sampling errors.

These adjustments have a direct impact on:

  • The error of closure and its distribution by age and sex within a province or a territory as well as by province/territory as the CNU and its distribution vary from one census to another;
  • within-cohort consistency of population estimates. If for example, the male cohort in age group 0 to 4 in 1981 was tracked up to the 2001 Census (unadjusted for CNU) the age group 20 to 24 would be noticeably smaller in 2001 than the age group 15 to 19 in 1996. Since Canada receives many immigrants within these age groups, the opposite would be expected. However, only after adjustment for CNU, the cohort size increases from 1996 to 2001.

For further information regarding the main coverage studies, please see the following document on Statistics Canada's web site: 1996, 2001, 2006, and 2011 Census Technical Report on Coverage.


Errors due to estimation methodologies and data sources other than the census can also be significant.

A. Births and deaths

Since the law requires the recording of vital statistics, the final estimates for births and deaths data meet very high quality standards. Nevertheless, since preliminary estimates are derived, they can be slightly different from final estimates.

B. Immigration and non-permanent residents

With respect to immigrants and non-permanent residents (NPRs), Citizenship and Immigration Canada (CIC) administers special data files on both of these components. Since immigration is controlled by law, data on immigrants and NPRs are compiled upon arrival in Canada. These data represent only "legal" immigration and exclude illegal immigrants. Thus, for the "legal" part of international movement into Canada, the data are considered to be of high quality. However, some biases such as the difference between the stated province of intended residence at the time of arrival and the actual province of residence, may persist. Finally, since information provided by the Visitor Data System (VDS) from CIC is not complete (age and sex of dependents, province of residence for certain groups of permit holders), estimates of NPRs are more prone to error than data on immigrants.

C. Emigration, returning emigration and net temporary emigration

Of all the demographic components that are used in the population estimates program, emigration, returning emigration and net temporary emigration are the most difficult to estimate with precision. Canada does not have a complete border registration system. While immigration and non permanent residents (NPRs) are well documented by the federal government, Statistics Canada has always used indirect techniques for the estimation of the number of persons leaving the country. For this reason, available statistics regarding these three components have historically been of a lower quality than other components.

Estimates of the number of emigrants and returning emigrants are both derived using Canada Child Tax Benefit (CCTB) data provided by Canada Revenue Agency (CRA). Data are adjusted to take into account the incomplete coverage of the program and to derive the emigration and returning emigration of adults.

These adjustments and the delay in obtaining the data are the two main sources of errors.
As current information on the number of persons living temporarily abroad does not exist, estimates are based on the Reverse Record Check (RRC) and the census. Estimates for the intercensal period, distributed equally among the five years, are maintained constant for the postcensal period. Moreover, assumptions were made to allow for the distribution of provincial/territorial data by subprovincial regions. Any geographical or quarterly variation may introduce error in the estimation of these components.

D. Interprovincial migration and intraprovincial migration

Since July 1993, preliminary interprovincial migration estimates have been based on Canada Child Tax Benefit (CCTB) files. Under this program, only 76% of children aged 0-17 at the Canada level were entitled to benefits on July 1, 2001. Consequently, preliminary CCTB based estimates are subject to larger error than final estimates derived from Canada Revenue Agency (CRA) tax files.

Moreover, as no preliminary data is available for intraprovincial migration, we assume the same level of migration as the previous year. The last two years are therefore identical for this component. Nevertheless, it is possible for data of the last two years to be different, because of some adjustments that are performed to correct negative populations.

E. Level of detail of components

As a more detailed breakdown of the data introduces a greater risk of inaccuracy into the estimates, the possibility of error in the components is augmented by the method used to distribute the estimates by age and sex. It seems that, in general, the initial errors should be minimal where the distribution of annual estimates of births, deaths and immigrants is concerned, and more significant with regard to the distribution of other components (non-permanent residents, emigrants, returning emigrants, net temporary emigrants and interprovincial and intraprovincial migrants). Finally, the size of error due to the age and sex distribution may vary by period and errors in some components may have a greater impact on a given age group or sex.

Geographical changes

Subprovincial geographical boundaries may change from one census to another. In order to facilitate chronological studies, population estimates for CDs, CMAs and ERs were produced for the 2001 to 2013 period according to the Standard Geographical Classification (SGC) 2011.

In order to clarify the demographic significance of geographical boundary changes, the 2006 population Census counts are converted in SCG 2011. Afterward, we compare the converted counts with the population counts of the 2006 Census in SGC 2006. Data presented here apply to population enumerated in the 2006 Census without adjustment for census net undercoverage.

Census metropolitan areas (CMAs)

Among the 34 CMAs as defined in the SGC 2006, 7 have undergone geographical boundary changes in the SGC 2011. Had the latter been applied in 2006, population in all 34 CMAs would have reached 21,509,000 instead of 21,534,000 representing a slight increase of 25,000 persons or 0.1%.

In most CMAs, the demographic repercussion of boundary changes was relatively small, that is under 5% for Saguenay, Québec, Sherbrooke, Trois-Rivières, Montréal and Ottawa-Gatineau. The CMA of Guelph has the highest proportion with 5.3%.

Economic Regions (ERs)

Four ERs out of the 76 have undergone geographical boundary changes between the 2006 and the 2011 Census. As ERs cover the entire country and because their number did not change, changes are rather simple. In New Brunswick, there were boundary changes for Campbellton-Miramichi and Fredericton-Oromocto. In British Columbia, the ER of North Coast received part of the Nechako ER. The differences are around 1%.

Census divisions (CDs)

Boundary changes affected 22 of the 293 CDs in Canada and population in six CDs was only slightly affected with relative gains/losses not exceeding 0.1%.

In the Northwest Territories, CDs have been restructured and their number went from two to six. Therefore, the population of the former Fort Smith CD, now called Region 6, decreased by 40.5%. In British Columbia, a new CD was created from Comox-Strathcona. The two CDs are now called Strathcona and Comox Valley. Stikine CD, which lost 43.0% of its population to the Kitimat-Stikine CD, was the only other CD experiencing a major boundary change.

Quality assessment

In order to assess the quality of our estimates, two evaluation measures are used: precocity errors and errors of closure.

A. Precocity errors

The quality of preliminary estimates of components is evaluated using precocity errors. Precocity error is defined as the difference between preliminary and final estimate of a particular component in terms of its relative proportion of the total population for the relevant geographical area. It can be calculated for both population and component estimates. The precocity error measures the impact of the trade-off of accuracy in favour of timeliness on the estimated population. The precocity error is calculated as:

The precocity error of a component gives us information on the size of the error between the preliminary and the final population estimate. Analysis of precocity errors allows for useful comparisons between components, as well as between geographical areas of different population size. Precocity error can either be positive or negative. A positive precocity error denotes that the preliminary estimate is larger than the final estimate while a negative precocity error indicates the opposite. Note that when compared to the total population for an area, the differences between preliminary and final estimates of the components are quite small. However, this type of error has a different impact on each component and geographical area.

Generally speaking for subprovincial estimates, net interprovincial and intraprovincial migration yields the greatest precocity errors. This is likely the result of the use of different data sources for preliminary and final estimates. In most years and for most provinces/territories, births, deaths and immigration estimates yielded the smallest precocity errors. For immigration estimates, this reflects the completeness of the data source and the availability of data for the more timely preliminary estimates. In the case of births and deaths, small precocity errors can be explained by the use of short-term projections for preliminary estimates.

According to the analysis of the most recent precocity errors and assuming that the quality of the basic data remains constant, the present postcensal estimates should have an acceptable degree of reliability.

B. Errors of closure

The error of closure measures the exactness of the final postcensal estimates. It is defined as the difference between the final postcensal population estimates on Census Day and the enumerated population of the most recent census adjusted for census net undercoverage (CNU). A positive error of closure means that the postcensal population estimates have overestimated the population.

The error of closure comes from two sources: errors primarily due to sampling when measuring census coverage and errors related to the components of population growth over the intercensal period. For each five-year intercensal period, the error of closure can only be calculated following the release of census data and estimates of CNU. The error of closure can be calculated for the total population of each province and territory as well as by age and sex.

By dividing the error of closure by the census population adjusted for CNU the differences are relatively small at the national level (0.2 % for 2001, 0.1 % for 2006 and 0.5 % for 2011). At the provincial and territorial level, as at the subprovincial level differences are understandably larger, since the estimates are also affected by errors in estimating interprovincial and intraprovincial migration. Nevertheless, the provincial/territorial final postcensal estimates generally fall within 1% of the adjusted census population, except for the territories and a few other exceptions.

For census metropolitan areas (CMAs), population estimates overestimated the total CMA population (0.9%) and the population of 24 out of 34 CMAs. The difference between population estimates and adjusted census counts was higher than 2% for 4 CMAs: Winnipeg (3.0%), Victoria (2.4%), St. John’s (-2.1%) and Halifax (2.0%).

Population estimates overestimated the population of 33 out of 76 economic regions (ERs). The difference between population estimates and adjusted census counts was higher than 3% for 4 ERs: Nechako, B.C. (-4.4%), Yorkton – Melville, Sask. (-3.3%), Northern, Sask. (-3.2%) and Montréal, Que. (3.1%).

Population estimates overestimated the population of 124 out of 293 census divisions (CDs). For 99 of the CDs, the difference between population estimates and adjusted census counts was less than 1%. The error of closure of 267 CDs, that is 91% of all CDs, was comprised between -3% and 3%. The most important errors of closure were observed in Division No. 11 of Newfoundland and Labrador (8.8%), in Region 4 of Northwest Territories (6.4%) and in Division No. 19 of Manitoba (6.0%). The population was less than 4,000 people in the first two CDs.

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