The census of Canada, being an actual counting procedure, is an essential underpinning to the myriad surveys, studies and polls that all claim to be based on representative samples. That is why Munir Sheikh, the former chief statistician of Canada, said that a voluntary survey cannot be a substitute for a mandatory census.
Everyone knows what counting is, but the word "statistics" has a range of meanings. In the strict sense of the term, it is a branch of mathematics that is closely connected with the study of probability.
Consequently, the census is not really statistical; it does not declare what is likely, or try to identify risk factors for this or that undesirable event. Instead, it tries to count the whole population in Canada.
If a sample is to be representative, the relative proportions of different groups inside the sample need to be much the same as those proportions in the entire population. But the numbers in those subgroups - say, how many cars were sold in Manitoba in May - are often quite small, so that what the samples really tell us becomes quite shaky.
That's where the mandatory element of the long-form questionnaire becomes important. By requiring responses, Statistics Canada is able to ensure that the samples are sufficiently representative of the population, and therefore the numbers in those small subgroups are more reliable than they would be otherwise.
Even then, the outcome is of course imperfect, and Statistics Canada uses other statistical tests to make the census more accurate. But because these tests are done on a large, reliable base of data, the necessary adjustments are small.
That means that counting and statistics are complementary; they serve as tests for each other. Statistics Canada's reliable count is made even more authoritative by its use of statistics.
The census is a vast, lumbering operation, but it is, in essence, the biggest and best count in the country. It helps ensure that surveys done with much smaller samples are as accurate as possible.
Modern societies depend heavily on all sorts of surveys. There is a huge demand for and supply of statistics, which is all the more reason to have ways of evaluating them. The census allows that evaluation.
Because surveys and censuses are interdependent, but very different creatures, Mr. Sheikh is right that a survey is no substitute for the long-form questionnaire. The Conservative government should recognize its mistake and restore the established practice for the 2011 census.