Question:
A researcher is looking at 2016 Census Dissemination Area profile data for Vancouver. She has noticed that the data for DAUID 59153188 is a bit odd. The “Total – Visible minority for the population in private households” is 105, while the “Total visible minority population” is 110. So, if the researcher is converting to percent, the percent that are visible minority are over 100 % of the population.
I am guessing that this is a quirk of the random rounding process, but it would be nice to get a more official response to this oddity?
Answer:
I love explaining random rounding to students. While you're waiting for a more official response, I know that Stat Can has a random rounding explanation for the 2016 census available here [https://www12.statcan.gc.ca/census-recensement/2016/dp-pd/prof/about-apropos/about-apropos.cfm?Lang=E#aa9].
It says (bolding mine): "To ensure confidentiality, the values, including totals, are randomly rounded either up or down to a multiple of '5' or '10.' To understand these data, you must be aware that each individual value is rounded. As a result, when these data are summed or grouped, the total value may not match the individual values since totals and sub-totals are independently rounded. Similarly, percentages, which are calculated on rounded data, may not necessarily add up to 100%."
This page [http://www12.statcan.gc.ca/census-recensement/2011/ref/DQ-QD/conf-eng.cfm]
has a fun table about random rounding – to look at with caution, because it's for the 2011 NHS and I haven't seen an equivalent explanation for 2016. According to the table, if the total Chinese population for your dissemination area was 107, then it would be randomly rounded up to 110 2 times out of 5, or down to 105 3 times out of 5. It's explained that "the random rounding algorithm uses a random seed value to initiate the rounding pattern for tables. In these routines, the method used to seed the pattern can result in the same count in the same table being rounded up in one execution and rounded down in the next."
Answer from Subject Matter:
Yes, the reason for that is due to random rounding.
Please refer to Chapter 11 – Dissemination - Guide of the Census of population, 2016 Data Suppression [http://www12.statcan.gc.ca/census-recensement/2016/ref/98-304/chap11-eng.cfm].
