# Sampling and Weighting Technical Report, Census of Population, 2016 7. Conclusion

The reintroduction of the mandatory long form allowed for several desirable characteristics in terms of sampling and weighting. Mainly, the sampling design was greatly simplified compared with that of the 2011 National Household Survey (NHS) (see Statistics Canada, 2015 for more details on the 2011 NHS sample design). As a direct result, the weighting procedure was also simplified, and the final weights were less variable than those of the 2011 NHS. Additionally, the mandatory nature of the 2016 long form presumably increased the response rate. Reducing the amount of non-response is always important, as this may have a direct effect on the bias of estimates. Therefore, minimizing the non-response rate is important to keep the non-response bias as small as possible.

The combination of the one-in-four sampling fraction and the overall unweighted final response rate of 96.1% meant that the 2016 long-form sample obtained more responses overall than the 2011 NHS (which had a one-in-three sampling fraction and a response rate of 68.6%). The response rates across geographic areas were also more homogeneous. The much higher and more uniform response rate enabled the simplification of the weighting procedures.

All these features, coupled with an improved calibration procedure, meant that the maximum difference between census counts and final-weight estimates (14,493) was about 1/10 of the maximum difference for the 2011 NHS (166,801). The improvement in the calibration procedure was a mixture of choosing fewer calibration variables, larger weighting areas (i.e., SADAs) and a better selection of constraints (such as the prioritization of constraints that split the population approximately in half).

As a consequence of these improvements, the range of the final weights was reduced (compared with the 2011 NHS). This resulted in the reduction of the standard error for most characteristics. For the variables related to the calibration constraints that were selected often, the variance was reduced by virtue of the calibration method. For variables not highly related to the calibration constraints, the variance was still moderated by the limitation of the range of the weights.

Finally, the release of replicate weights implies that users can easily estimate the standard error for any particular variable of interest. For the 2011 NHS, the chosen method of variance estimation—Taylor series linearization combined with a corrective upward adjustment factor (from Monte Carlo simulation)—made computing standard errors for non-standard products difficult.

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