Data quality, concepts and methodology

Quality of estimates

Post-2001 postcensal population estimates

The postcensal estimates contain certain inaccuracies stemming from:

1. errors in the 2001 Census data (the base population on which these estimates were constructed) and
2. imperfections in other data sources and the method used to estimate the components.

Errors in census data

Census data for total population by province or territory are affected by coverage errors. These errors occur when dwellings and/or individuals are missed, incorrectly included or counted more than once. Following each census, Statistics Canada undertakes coverage studies to measure these errors. The main study are the Reverse Record Check Survey (RRC) and the Census Overcoverage Study (COS). Based on these studies, estimates of net undercoverage (which is equal to the difference between undercoverage and overcoverage) are produced. Demography Division adjusts the population enumerated in the census by province and territory using these estimates.

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

Errors coming from methodology and other data sources

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

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

With respect to immigrants and non-permanent residents, Citizenship and Immigration Canada administers special data files on both of these components. Since immigration is controlled by law (the Immigration Act), data on immigrants and non-permanent residents 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 from Citizenship and Immigration Canada is not complete (age and sex of dependents, province of residence for certain groups of permit holders), estimates of nonpermanent residents are more prone to error than data on immigrants.

Estimates of the number of emigrants and returning emigrants are both derived using Child Tax Benefit (CTB) data provided by Canada Revenue Agency (CRA). Data are adjusted to take into account the incomplete coverage of the CTB 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. Provincial/territorial distributions are obtained from RRC. Moreover, assumptions were made to allow for the distribution of annual to a quarterly level. Any geographical or quarterly variation may introduce error in the estimation of these components.

While preliminary estimates of interprovincial migration are produced using data from the Child Tax Benefit (CTB) program, final estimates are calculated from the annual taxfile received from Canada Revenue Agency (CRA). Since the two estimates of interprovincial migration are produced from different sources of information, they are more subject to error.

Quality assessment

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

Precocity errors

The quality of preliminary estimates of components is analysed using precocity errors. Precocity error, which is calculated on a quarterly basis, 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.

Precocity error allows for useful comparisons between components, as well as between provinces and territories or geographical areas of different population size. Note that when compared to the total population for an area, the differences between preliminary and final estimates of the components are quite small. There are, however, differences in the amount of impact on the population estimates between components and between provinces and territories.

Generally speaking, net interprovincial migration yields the greatest precocity errors. This is likely the result of the use of different data sources for preliminary and final estimates of interprovincial migration. 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 support 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.

Errors of closure

The error of closure measures the exactness level of the final postcensal estimates. It can be defined as the difference between the enumerated population of the most recent census (after adjustments for net undercoverage) and the most current postcensal population estimates as of census day.

The error of closure comes from two sources: differences in the amount of net undercoverage and errors in the components of population change over the intercensal period. This can be calculated for population estimates and for age, sex and marital status. With each 5-year intercensal period, the error of closure can only be calculated with the release of census data and estimates of net undercoverage.

By dividing the error of closure by the adjusted census population rates are relatively small at the national level (0.38% for 1996 and 0.15% for 2001). At the provincial and territorial level, differences are understandably larger, since the estimates are also affected by errors in estimating interprovincial migration. Nevertheless, the provincial/territorial final postcensal estimates generally fall within 1% of the adjusted census population.