Guide to the Census of Population, 2016
Appendix 1.9 – Standard errors of estimates from 2016 Census long form sample

This note analyzes the standard errors for different levels of geography for estimates of totals and averages for some variables common to 2016, 2011 and 2006. It provides context for the measure of variability released for the 2016 Census long form, which is the standard error (SE). The note starts with some highlights of the SEs for the 2016 Census long form, 2011 National Household Survey (NHS) and the 2006 Census long form for Canada, the provinces and territories and four Census subdivisions (CSDs). Following these highlights, an analysis of the SEs for 2006, 2011 and 2016 is provided. Finally, in the tables, some 2016 SEs are compared with the corresponding 2011 and 2006 SEs for eight 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 2006 Census long form, 2011 NHS and 2016 Census long form standard errors

Standard errors are provided for eight different characteristics of the 2006 Census long form, 2011 NHS and the 2016 Census long form. Levels of geography provided are national, provincial and territorial and census subdivision (CSD). Results for only four CSDs are presented. These CSDs are the same as those shown in a previous note disseminated in 2013 about the precision of the 2011 NHS estimates. The same four CSDs were chosen for consistency purposes. These four geographic areas were initially selected to feature CSDs of varying regions and population sizes.

It should be noted that the SEs for Nunavut were nil in 2006, but greater than nil in 2011 and 2016. Since all households were included in the sample, there was no sampling variance in this territory. However, there was a small non-response variance, which was not measured in 2006 but was in 2011 and 2016. The following analysis will therefore not include Nunavut for 2006.

For the characteristics and geographic areas presented in the tables, the 2016 SEs are almost always lower than the corresponding 2006 and 2011 SEs. It is also observed that the 2016 SEs are lower for more characteristics when compared to 2011 than when compared to 2006.

There are two types of estimates in the tables: estimates of counts (i.e. people) and estimates of averages (i.e. income). One would expect to see, as the population size increases, the SE to increase for the estimates of counts and to decrease for estimates of averages. As expected, it can be observed that, at the Canada level, the SEs are higher for estimates of counts and lower for estimates of averages, than for estimates at the CSD level, due to the larger population size. Despite the fact that the estimates of counts at the Canada level have a higher SE, it does not mean that the quality of these estimates is lower than that of estimates at the CSD level.

For the five estimates of counts, the SEs in 2016 are roughly half of those for 2011 and 2006 for almost all of the geographic areas, which is a considerable reduction. Two exceptions to this reduction are the territory of Nunavut and the CSD of Joliette (Ville). In both geographic areas, when accounting for population size increases over time, the SEs of the five estimates of counts in 2016 are generally smaller or at least comparable to 2011 and 2006. For the three estimates of average, the 2016 SEs are similar to 2011 and 2006 in large geographic areas (e.g. Canada, Ontario and Quebec) and either smaller or larger than those of 2011 and 2006 in smaller geographic areas.

About half of the geographic areas in the tables have lower SEs in 2016 compared to 2006 and 2011 for all characteristics. The other geographical areas have some characteristics with higher SEs for 2016 compared to 2006 and 2011. At the Canada level, in Prince Edward Island, New Brunswick, Ontario, Saskatchewan, British Columbia, Niagara Falls (City) and Port Coquitlam (City) the SEs are lower in 2016 than in either 2006 or 2011 for all characteristics. For estimates of counts, only three characteristics (non-immigrants, immigrants and visible minority) have SEs lower in either 2006 or 2011 than in 2016. This only occurs in Northwest Territories, Nunavut, Charlottetown (City) and Joliette (Ville). For estimates of averages, the 2006 and 2011 SEs are at times lower than the 2016 SEs estimates in Newfoundland and Labrador, Nova Scotia, Quebec, Manitoba, Alberta, Yukon, Northwest Territories, Charlottetown (City) and Joliette (Ville).

It was expected that the SEs would be, in general, lower for 2016 than for 2011 due to the simpler sample design, higher response rate and improved calibration procedures. However, they were also much lower than for 2006, especially for estimates of counts. Factors that may explain why the 2016 SEs are considerably smaller than those for 2006 include a larger number of responses due to a higher sampling fraction (i.e. 25% in 2016 versus 20% in 2006) and changes in weight calibration.

Calibration may either reduce or increase the variability of the estimates. On the one hand, variability may be reduced by calibration for long form sample variables that are correlated to calibration variables. On the other hand, when a very large number of calibration totals are used, the variability of the estimates may increase. The fact that, overall, considerably more calibration was performed in 2006 than in 2016 could, to some extent, explain why SEs were usually larger in 2006.

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