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3.  Sampling in Canadian censuses

3.1 The history of sampling in the Canadian census
3.2 The sampling scheme used in the 2006 Census

In the context of a census of population, sampling refers to the process whereby certain characteristics are collected and processed only for a random sample of the dwellings and persons identified in the complete census enumeration. Tabulations that depend on characteristics collected only on a sample basis are then obtained for the whole population by scaling up the results for the sample to the full population level. Characteristics collected on all dwellings or persons in the census will be referred to as 'basic characteristics' while those collected only on a sample basis will be known as 'sample characteristics.'

3.1  The history of sampling in the Canadian census

Sampling was first used in the Canadian census in 1941. A housing schedule was completed for every tenth dwelling in each census subdistrict. The information from 27 questions on the separate housing schedule was integrated with the data in the personal and household section of the population schedule for the same dwelling, thus allowing cross-tabulation of sample and basic characteristics. Also in the 1941 Census, sampling was used at the processing stage to obtain early estimates of earnings of wage-earners, of the distribution of the population of working age, and of the composition of families in Canada. In this case, a sample of every tenth enumeration area across Canada was selected and all population schedules in these areas were processed in advance.

Again in 1951, the census of housing was conducted on a sample basis. This time every fifth dwelling (those whose identification numbers ended in a 2 or 7) was selected to complete a housing document containing 24 questions. In the 1961 Census, persons 15 years of age and over in a 20% sample of private households were required to complete a Population Sample Questionnaire containing questions on internal migration, fertility and income. Sampling was not used in the smaller censuses of 1956 and 1966.

The 1971 Census saw several major innovations in the method of census-taking. The primary change was from the traditional canvasser method of enumeration to the use of self-enumeration for the majority of the population. This change was prompted by the results of several studies in Canada and elsewhere (Fellegi [1964]; Hansen et al. [1959]) that indicated that the effect of the enumerator was a major contribution to the variance 1 of census figures in a canvasser census. Thus the use of self-enumeration was expected to reduce the variance of census figures through reducing the effect of the enumerator, while at the same time giving the respondent more time and privacy in which to answer the census questions—factors which might also be expected to yield more accurate responses.

The second aspect of the 1971 Census that differentiated it from any earlier census was its content. The number of topics covered and the number of questions asked were greater than in any previous census. Considerations of cost, respondent burden, and timeliness versus the level of data quality to be expected using self-enumeration and sampling led to a decision to collect all but certain basic characteristics on a one-third sample basis in the 1971 Census. In all but the more remote areas of Canada, every third private household received the 'long questionnaire' which contained all the census questions, while the remaining private households received the 'short questionnaire' containing only the basic questions covering name, relationship to head of household, sex, date of birth, marital status, mother tongue, type of dwelling, tenure, number of rooms, water supply, toilet facilities, and certain census coverage items. All households in pre-identified remote enumeration areas and all collective dwellings2 received the long questionnaire. A more detailed description of the consideration of the use of sampling in the 1971 Census is given in Sampling in the Census (Dominion Bureau of Statistics [1968]).

The content of the 1976 Census was considerably less than that of the 1971 Census. Furthermore, the 1976 questionnaire did not include the questions that cause the most difficulty in collection (e.g., income) or that are costly to code (e.g., occupation, industry, and place of work). Therefore, the benefits of sampling in terms of cost savings and reduced respondent burden were less clear than for the 1971 Census. Nevertheless, after estimating the potential cost savings to be expected with various sampling fractions, and considering the public relations issues related to a reversion to 100% enumeration after a successful application of sampling in 1971, it was decided to use the same sampling procedure in 1976 as in 1971.

Most of the methodology used in the 1971 and 1976 censuses was kept for the 1981 Census, except that the sampling rate was reduced from every third occupied private household to every fifth. Studies done at the time showed that the resulting reduction in data quality (measured in terms of variance) would be tolerable, and would not be significant enough to offset the benefits of reduced cost, response burden, and improved timeliness (see Royce [1983]). The one-in-five sampling rate has been maintained for every census since 1981.

3.2  The sampling scheme used in the 2006 Census

A wealth of information was collected from everyone in Canada on Census Day, May 16, 2006. The bulk of the information was acquired on a sample basis. In all self-enumeration areas, a one-in-five sample of occupied private dwellings was selected to receive a long questionnaire (Form 2B) while the non-sampled occupied private dwellings received a short questionnaire (Form 2A). Basic questions on age, sex, marital status, common-law status, mother tongue, relationship to the household reference person (Person 1) were asked of all respondents, as well as the type of dwelling. Additional information on the dwelling, plus socio-economic questions, was asked on a sample basis. The usual residents of an occupied dwelling are called a household, so the terms household and occupied dwelling will be used interchangeably in this report.

All dwellings in those areas enumerated in person by the canvasser method (generally remote areas or Indian reserves) received the Form 2D.

Most persons in collective dwellings received a long form (usually a Form 3B except for those in Hutterite colonies and senior units that received a Form 2B). The following persons in collective dwellings, however, were not asked the sample questions (i.e., a form 3A was used):

  • inmates in correctional and penal institutions or jails
  • patients in general hospitals, special care homes, and collective dwellings or institutions for senior citizens, the chronically ill or psychiatric institutions
  • children in orphanages and children's homes or young offenders facilities
  • people in shelters.

A senior unit is an accommodation within a collective residence for senior citizens that contains one or more senior citizens judged capable of completing a census form. In the 2001 Census, as described in point (b) above, these persons were not asked the sample questions. New for 2006, a random sample of 1 in 5 of these senior units was selected and they were provided with a long form to complete. The other senior units were provided with a short form to complete. These senior units were treated as if they were private dwellings that had been subject to sampling by the 2006 Census weighting system, and are included in the various tables provided in this report. There were 40,755 senior units containing 47,540 persons in 2006. Note, however, that a senior unit is not a household or a dwelling; the seniors' residence facility as a whole is one household and one dwelling. Furthermore, these numbers are lower than the true counts because of problems during collection and processing, where some residences for senior citizens were misclassified as nursing homes. As a result, data quality for senior units alone is poor, and should be used with caution.

Section 1.2 discusses the various methods of census collection. Each dwelling, regardless of collection method, was assigned a Visitation Record (VR) number. The VR number was used to determine which type of census questionnaire (i.e., Form 2A or 2B) would be delivered. Every fifth dwelling was selected to be part of the census sample, and was given a long form. The remaining four-fifths were given a short form.

In sampling terminology, the census sample design can be described as a stratified systematic sample of private occupied dwellings using a constant one-in-five sampling rate in all strata (CUs). As a sample of persons, it can be regarded as a stratified systematic cluster sample with dwellings as clusters. For a more detailed description of the concepts and terminology of sampling, see Cochran (1977) or Sarndal, Swensson and Wretman (1992).

Notes:

  1. The 'variance' of an estimate is a measure of its precision. Variance is discussed more fully in Chapter 9.
  2. A collective dwelling is a dwelling used for commercial, institutional or communal purpose, such as hotels, hospitals and work camps.

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