Annual Demographic Estimates: Subprovincial Areas, July 1, 2023
Quality of demographic data

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.

Coverage errors occur when individuals are missed, enumerated more than once, or enumerated while not being part of the census universe (this last aspect is not estimated because it is deemed negligible). 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. The Centre for Demography 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 gender.

When creating base populations, the Demographic Estimates Program (DEP) 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 DEP 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 gender 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, gender 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 reserves and settlements 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 gender within a province or a territory as well as by province or 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, 2011, and 2016 Census Technical Report on Coverage. The technical report on coverage for the 2021 Census will be available on October 23, 2024.

Components

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

Immigration, Refugees and Citizenship Canada (IRCC) administers data files that allow the measurement of the numbers of immigrants, asylum claimants as well as work, study and temporary resident permit holders in Canada. As immigration is controlled by law, data on immigrants and NPRs are collected upon and after arrival in Canada. These data include only regular immigrants and are considered to be of very high quality.

Differences may exist for the province or territory of destination: the one envisaged by the immigrant at the time of arrival may differ from the one where they will actually reside. NPR estimates are more error-prone than immigrant data, notably because the province or territory of residence of certain groups of permit holders is missing, the number of family members living with permit holders needs to be modeled, and finally, data sources on NPR exiting Canada are limited.

C. Emigration, returning emigration

Of all the demographic components that are used in the DEP, emigration and returning 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 two components have historically been of a lower quality than other components.

Estimates of the number of long-term emigrants and long-term returning emigrants are both derived using Canada Child Benefit (CCB) data provided by Canada Revenue Agency (CRA). Data are adjusted to consider 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 short-term emigrants and short-term returning emigrants does not exist, estimates are based on the Census Undercoverage Study (CUS) and the census. For short-term emigrants, estimates for the intercensal period are based on the CUS and are distributed according to long-term emigration data. For short-term returning emigrants, mobility data from the last census is subtracted from estimates of the number of long-term returning emigrants over the entire last intercensal period. Assumptions were made to distribute the data by province and territory, and annual data by quarter and by subprovincial and subterritorial region. Assumptions must also be made to establish the variation for the postcensal period. Any geographical or quarterly variation may introduce error in the estimation of these components.

D. Interprovincial migration and intraprovincial migration

Preliminary interprovincial and intraprovincial migration estimates are based on data from the Canada Revenue Agency (CRA). Canada child benefit (CCB) data is used for children while T1FF data from the prior year is used for adults as that data is not yet available for the most recent year when preliminary estimates are produced.

Final estimates are obtained by comparing addresses indicated on personal income tax returns over two consecutive tax years, by making use of the latest T1FF files (with the exception of Quebec’s subprovincial areasNote 1). An adjustment is also required to consider migrants who do not file income tax returns.

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 gender. 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 regarding the distribution of other components (non-permanent residents, emigrants, returning emigrants, and interprovincial and intraprovincial migrants). Finally, the size of error due to the age and gender distribution may vary by period and errors in some components may have a greater impact on a given age group or gender.

Geographical changes

Subprovincial geographical boundaries may change from one census to another. To facilitate chronological studies, population estimates for CDs, CAs, CMAs and ERs were produced for the 2001 to 2023 period according to the Standard Geographical Classification (SGC) 2021.

To clarify the demographic significance of geographical boundary changes, the 2016 population Census counts are converted in SGC 2021. Afterward, we compare the converted counts with the population counts of the 2016 Census in SGC 2016. Data presented here apply to population enumerated in the 2016 Census without adjustment for census net undercoverage.

Census metropolitan areas (CMAs)

With the adoption of the SGC 2021, six census agglomerations under SGC 2016 became census metropolitan areas: Fredericton (N.B.), Drummondville (Que.), Red Deer (Alb.), Kamloops (B.C.), Chilliwack (B.C.), and Nanaimo (B.C.). Among the 35 CMAs defined by the SGC 2016, 11 have undergone boundary changes under SGC 2021.

Census Agglomerations (CAs)

With the transition from SGC 2016 to the SGC 2021, five new CAs have been created: Saint-Agathe-des-Monts (Que.), Amos (Que.), Essa (Ont.), Trail (B.C.), and Ladysmith (B.C.). The CAs of Bay Roberts (Nfld.) and Cold Lake (Alb.) were removed because their population dropped below 10,000 in 2021. As well, the CAs of Arnprior (Ont.) and Carleton Place (Ont.) were absorbed into the CMA of Ottawa-Gatineau (Ont.), while the Leamington (Ont.) AR became part of the CMA of Windsor (Ont.)

Economic Regions (ERs)

There were no changes in Economic Region boundaries between SGC 2016 and SGC 2021.

Census divisions (CDs)

There were no changes to Census divisions boundaries between SGC 2016 and SGC 2021.

Quality assessment

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:

P E ( t 1 , t ) = ( N ( t 1 , t ) p r e l i m i n a r y N ( t 1 , t ) f i n a l ) P ( t 1 ) p o s t c e n s a l x 1,000 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaadw eadaWgaaqcbawaaiaacIcacaWG0bGaeyOeI0ccbiqcbaKaa8xmaKqa GjaacYcacaWG0bGaaiykaaqabaGccaaMf8Uaeyypa0JaaGzbVpaala aabaWaaeWaaeaacaWGobWaa0baaKqaGfaacaGGOaGaamiDaiabgkHi TKqaajaa=fdajeaycaGGSaGaamiDaiaacMcaaeaacaWFWbGaa8NCai aa=vgacaWFSbGaa8xAaiaa=1gacaWFPbGaa8NBaiaa=fgacaWFYbGa a8xEaaaakiaaywW7cqGHsislcaaMf8UaamOtamaaDaaajeaybaGaai ikaiaadshacqGHsisljeaqcaWFXaqcbaMaaiilaiaadshacaGGPaaa baGaamOzaiaadMgacaWGUbGaamyyaiaadYgaaaaakiaawIcacaGLPa aaaeaacaWGqbWaa0baaKqaGfaacaGGOaGaamiDaiabgkHiTKqaajaa =fdajeaycaGGPaaabaGaamiCaiaad+gacaWGZbGaamiDaiaadogaca WGLbGaamOBaiaadohacaWGHbGaamiBaaaaaaGccaaMf8UaaeiEaiaa ywW7caqGXaGaaeilaiaabcdacaqGWaGaaeimaaaa@7D51@

where:

P E ( t 1 , t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbGaamyra8aadaWgaaWcbaWdbmaabmaapaqaa8qacaWG0bGa eyOeI0IaaGymaiaacYcacaWG0baacaGLOaGaayzkaaaapaqabaaaaa@3DB3@
the precocity error for the period from t-1 to t
N ( t 1 , t ) p r e l i m i n a r y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGobWdamaaDaaaleaapeWaaeWaa8aabaWdbiaadshacqGHsisl caaIXaGaaiilaiaadshaaiaawIcacaGLPaaaa8aabaWdbiaadchaca WGYbGaamyzaiaadYgacaWGPbGaamyBaiaadMgacaWGUbGaamyyaiaa dkhacaWG5baaaaaa@475B@
the preliminary estimate of a component of demographic change
N ( t 1 , t ) f i n a l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4HqaqFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaDa aajeaybaGaaiikaiaadshacqGHsislieGajeaqcaWFXaqcbaMaaiil aiaadshacaGGPaaabaGaamOzaiaadMgacaWGUbGaamyyaiaadYgaaa aaaa@4202@
the final estimate of a component of demographic change
P (t 1) p o s t c e n s a l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaDaaaleaapeGaamiDaiabgkHiTiaaigdaa8aabaWd biaadchacaWGVbGaam4CaiaadshacaWGJbGaamyzaiaad6gacaWGZb GaamyyaiaadYgaaaaaaa@4366@
postcensal estimates of population for the relevant geographical area at time t-1

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, 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 and 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 timelier preliminary estimates. In the case of births and deaths, small precocity errors can be explained using short-term projections for preliminary estimates.

According to the analysis of the most recent precocity errors and if 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 gender.

By dividing the error of closure by the census population adjusted for CNU the differences are relatively small at the national level (0.16% for 2001, 0.12% for 2006, 0.46% for 2011, 0.33% for 2016, and -0.11% for 2021). 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 and 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) and census agglomerations (CAs), population estimates overestimated the total  population (0.1%), while population was underestimated by -0.1% for Economic Regions.

Population estimates overestimated the population of 128 of the 293 census divisions (CDs). For 123 of the CDs, the absolute difference between population estimates and adjusted census counts was less than 1%. The error of closure of 256 CDs, that is 87% of all CDs, was comprised between -3% and 3%.


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