Guide to the Census of Population, 2021
Appendix 1.8 – Variability of estimates from the 2021 Census long-form sample

This note provides a broad comparison of the quality of long-form estimates between the 2016 and 2021 censuses. This comparison is based on an analysis of the precision of estimates of totals and averages for some variables common to the two censuses. The analysis is performed for Canada and the provinces and territories. The variance-based quality indicator provided in most data tables with long-form estimates is the confidence interval. Confidence intervals are ideal for performing statistical inferences. However, the coefficient of variation (CV) was chosen as the variance-based quality indicator for this analysis because it is well suited for comparing the precision of estimates whose sizes differ from one another. The CV of a survey estimate is the ratio of the standard error of the estimate to the estimate itself. It is expressed as a percentage.

The note first presents some highlights of the CVs for the 2016 and 2021 Census long-form estimates for Canada, the provinces and territories. Following these highlights, an analysis of the CVs for 2016 and 2021 is provided. Both the highlights and the analysis are based on the tables, which show 2016 and 2021 estimates together with their CVs and confidence intervals for nine characteristics.

Highlights

The following observations apply only to the variables and geographic areas presented in the tables, i.e., the results do not necessarily extend to other variables and geographic areas.

Analysis of the 2016 and 2021 Census long-form coefficients of variation

CVs are provided for nine different characteristics of the 2016 and 2021 Census long-form estimates. Confidence intervals are also shown. The levels of geography provided are national, provincial and territorial.

For the characteristics and geographic areas presented in the tables, the differences between the 2016 and 2021 CVs are generally quite small. In 11 out of the 14 geographic areas, the differences are less than 0.1% for the majority of the characteristics. It was expected that the CVs would be generally similar for 2016 and 2021, since there were no significant changes between the two censuses to the sample design or to the methods used to produce survey weights and estimates.

The relatively large increases in CVs for Yukon, the Northwest Territories and Nunavut can be explained by the lower long-form questionnaire response rates in 2021, compared with 2016, for these areas. On average, response rates to the census long-form questionnaire were slightly lower in 2021 than in 2016. For Canada and the provinces and territories, the largest decreases in response rates between the two censuses occurred in Yukon, the Northwest Territories and Nunavut. Non‑response contributes to the variability of estimates, and therefore lower response rates generally lead to larger CVs.

Even for those geographic areas in the tables where the increases in CVs between the 2016 and 2021 censuses are largest, the differences are still quite small. For areas other than those presented in the tables, it is possible for the differences in variability of estimates between the two censuses to be large if the geographic area is small, particularly if there was a large difference in the response rate for the area. To evaluate the quality of estimates in specific use cases, it is recommended that data users examine the entire suite of available data quality indicators. More information on quality indicators is provided in the 2021 Census Data Quality Guidelines, Statistics Canada Catalogue no. 98‑26‑0006.

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