Technical Guide on Demographic Estimates at Statistics Canada
Chapter 13
Quality of Population Estimates

The quality of population estimates is regularly assessed. The Demographic Estimates Program uses two main indicators for this: the precocity error and the error of closure. This chapter describes how these two indicators are calculated.

Precocity error

The precocity error is used to evaluate the quality of preliminary postcensal population estimates and preliminary components of population growth. It measures the trade-off between data accuracy and timeliness, with preference given to the latter.

The precocity error for a given region is calculated by subtracting the final postcensal population estimates from the preliminary postcensal estimates, then dividing the result by the final population estimates.

This calculation can also be used for the components of population growth. It involves subtracting the final estimates of a component from the preliminary estimates and dividing the result by the final postcensal population estimates.

The precocity error is calculated as follows. The example below calculates the error for births:

$$PE(t-1,t)=\frac{(B_{(t-1,t)}^{preliminary}-B_{(t-1,t)}^{final})}{P_{(t-1)}^{postcensal}}x1000$$

where:

The error can be positive (when the preliminary estimate is higher than the final estimate) or negative (when the final estimate is higher than the preliminary estimate). It is usually expressed per thousand. A small error (i.e., close to zero per thousand) indicates a high level of coherence between the preliminary and final estimates.

Annual precocity errors by province and territory and by component are presented in Table 17-10-0163-01.

For most years and jurisdictions, smaller precocity errors are associated with components that have similar sources and methods to calculate preliminary and final estimates, such as births, deaths, and immigration. Conversely, components with more different sources or methods, such as total emigration, net non-permanent residents and interprovincial migration, generally have larger precocity errors.

Error of closure

The error of closure is the main quality indicator for population estimates. It is used to assess the accuracy of postcensal estimates from the previous cycle, before they become intercensal estimates.

The error of closure is defined as the difference between the final postcensal estimate on Census Day and the census population estimate adjusted for coverage errors (base population). The relative error of closure is equal to the error of closure divided by the adjusted census count, expressed as a percentage. Mathematically, the equations are as follows:

$$EC=P_{DEP}-P_{AC}$$

$$EC(\%)=\frac{P_{DEP}-P_{AC}}{P_{AC}}x100$$

where:

The error can be positive (when the postcensal population estimates overestimated the population) or negative (when the postcensal population estimates underestimated the population).

The error of closure comes from three sources: errors primarily due to sampling when measuring start-of-period census coverage, errors primarily due to sampling when measuring end-of-period census coverage, and errors in the components of population growth over the intercensal period. For each five-year intercensal period, the error of closure can only be calculated once census data and CNU estimates have been released.

Table 13.1 presents the postcensal population estimates as of May 11, 2021, the adjusted census counts and the errors of closure for Canada, the provinces and territories for the 2001 to 2021 censuses. At the national level, the error of closure was estimated at -41,269 (-0.11%) in 2021. This is down from 2016 (+0.33%).

The population estimates underestimated the population of six provinces, one territory and the country as a whole. Five regions had errors of closure greater than 1% or less than -1%. Of these regions, only the estimated population of the Northwest Territories differed from the adjusted census count by more than +/-2% (+2.57%). In 2016, five provinces and one territory had errors of closure greater than 1% or less than -1%.

By considering CNU variance, statistically significant errors of closure can be identified.

The error of closure is statistically significant for five provinces and one territory, meaning that the population estimates significantly overestimated or underestimated the population of these regions. As mentioned above, these results are due to both the variability in measuring coverage error and the errors measuring the components of population growth. The components most associated with the error of closure are generally interprovincial migration, non-permanent residents and emigration.