Canadian Survey on Disability, 2022: Concepts and Methods Guide
3. Sample design of the Canadian Survey on Disability

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3.1 Target population and coverage

The population covered by the Canadian Survey on Disability (CSD) consists of all persons aged 15 and over  (on Census Day in 2021, May 11, 2021) who responded that they have difficulty “sometimes,” “often” or “always” to any of the sub-questions on activities of daily living in the census long-form questionnaire (see Textbox 3.1). These questions are considered CSD “filter questions”. The population covered by the census long-form questionnaire includes persons living in private dwellings^Note in the 10 provinces and the 3 territories. For operational reasons, the population living on First Nations reserves is excluded from the CSD.

The sample for the 2022 CSD was selected from the list of all individuals who responded in the affirmative to at least one of the census filter questions on activities of daily living. They are the most likely to have a disability and are part of the population we refer to as the YES population. Among these individuals, those whose activities are limited as a result of a long-term condition or health issue (as determined through the CSD’s Disability Screening Questions [DSQ]) are part of the target population of persons who have a disability.

While the CSD does not cover persons who responded “no” to the filter questions on the census long-form questionnaire (known as the NO population), a sample of these individuals is nonetheless included in the CSD data file, called the analytical file (see Section 3.9). They are all considered to be persons without a disability. A certain number of persons without a disability will also be found in the YES population; they are individuals who did not report any activity limitations in the DSQ module of the CSD (also called “false positives”). As we will see later, the sample of persons without a disability included in the analytical file is used in two ways: to calculate disability rates and to compare the census characteristics of persons with and without a disability.

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3.2 Reference period

The CSD represents the population aged 15 and over on Census Day in 2021, May 11, 2021. However, the information collected during the CSD represents this population’s characteristics as measured from June to November 2022. To understand how these two reference periods affect the use and interpretation of CSD data, refer to Section 6.2.

3.3 Sampling frame created from the 2021 Census

The sampling frame for the CSD was constructed from the Census Response Database (RDB), a preliminary database containing all responses received via the various reporting modes (Internet, paper questionnaires, personal interviews, etc.). Responses in this database have not been processed or imputed by the census team. A number of processing steps are therefore required for creating the CSD sampling frame, to ensure that the information is as complete as possible, namely

• imputing the age when it was missing for a person on the census questionnaire, based on responses on the long-form questionnaire (e.g., data on education, employment and income, etc.)
• using various data sources to detect errors in telephone numbers or find missing addresses or telephone numbers
• using various data sources to find phone numbers associated with the household of the selected person to increase chances of contacting them
• using various data sources to fill in incomplete addresses to increase chances of respondents receiving the letter of introduction^Note informing them of the upcoming survey
• calculating preliminary weights for the census to estimate the population size in each stratum for sample allocation.

3.4 Sample design

The sample design is a two-phase stratified design based on the 2021 Census. The first phase is selecting the sample of households that receives the census long-form questionnaire as part of the census itself, and the second phase involves selecting individuals for the CSD sample.

Phase 1

The first phase involves selecting the sample of households that receives the census long-form questionnaire, i.e., approximately one in four households across Canada, systematically across Canada. Canadian citizens temporarily living abroad, full-time members of the Canadian Armed Forces stationed abroad, and visitors or representatives of foreign governments are excluded from the target population of the census long-form questionnaire. Also excluded are those living in collective dwellings (institutional or non-institutional). Collective dwellings include hospitals, residences for seniors, residential care facilities such as group homes for persons with a disability or an addiction, shelters, correctional and custodial facilities, lodging and rooming houses, religious establishments, Hutterite colonies, establishments offering temporary accommodation services,^Note and other establishments.^Note For more information on collective dwellings, see the Dictionary of the Census of Population, 2021.

There are two versions of the census long-form questionnaire: the 2A-L questionnaire and the 2A-R questionnaire. The 2A-L questionnaire is sent to approximately one in four households in most regions of Canada. In addition to the basic census demographic questions (name, sex at birth and gender, date of birth and age, legal marital status, common-law status, relationship to Person 1, various questions on knowledge of official languages, languages spoken at home, first language learned, education in the minority official language, and the question on Canadian military experience), the 2A-L questionnaire also includes questions on labour market activity, income, education, citizenship, housing, ethnic or cultural origin, religion, Indigenous identity, and so on. The 2A-R questionnaire is similar to the 2A-L questionnaire and targets all households in First Nations communities, Métis Settlements, Inuit regions and other remote areas.^Note Only the long-form questionnaire includes the question on activities of daily living, i.e., the CSD filter questions.

More precisely, the first phase is a stratified systematic sample of occupied private dwellings selected with a constant sampling fraction of 1/4 in most regions of Canada and a complete enumeration in remote areas. The sampling unit for the first phase is the household.

Phase 2

In the second phase, the CSD sample was selected from individuals who reported difficulties in their answers to the activities of daily living sub-questions on the census long-form questionnaire. Excluded from the sample were individuals living on First Nations reserves and those aged younger than 15 years as of May 11, 2021. The sampling unit for the second phase is the person.

The CSD sample was selected to ensure sufficient sample sizes in each of the estimation domains and to optimize sample distribution, as explained in Section 3.5.

3.5 Estimation domains and stratification

Domains of estimation are groups of units for which estimates must be produced with an adequate level of precision. The CSD domains of estimation consist of the provinces cross-classified with the following age groups:

• 15 to 24 years
• 25 to 44 years
• 45 to 64 years
• 65 to 74 years
• 75 years and over.

For Prince Edward Island, the first two age groups had to be combined because of their very small population sizes. For each of the three territories, the estimation domain includes a single age group (15 years and over).

Each estimation domain was then subdivided into strata. Stratification makes the sampling strategy efficient, ensures that the sample sizes are adequate for the known areas of interest and helps prevent a “bad” sample from being selected. The census sample design was taken into account when establishing strata for each domain. The strata group individuals with similar preliminary sampling weights (i.e., remote or non-remote areas) and similar degrees of potential disability severity.^Note The degree of severity used for stratification purposes reflects the answers to the filter questions on activities of daily living. To group individuals with a similar probability^Note of having a disability, three severity classes were created based on the answers (i.e., “no,” “sometimes,” “often” or “always”) to each filter question (i.e., seeing, hearing, physical, cognitive, mental health or other). Six strata were thus generated for each estimation domain, with three levels of severity cross-classified by whether a person lives in a remote or non-remote area.

Hence, each estimation domain was divided into six possible strata defined as follows:

• non-remote area—mild severity
• non-remote area—moderate severity
• non-remote area—high severity
• remote area—mild severity
• remote area—moderate severity
• remote area—high severity.

Note that these six strata were not always present in each estimation domain. Since there are no remote areas in Prince Edward Island, there were only three strata in each domain in this province. In addition, there are only three strata in Nunavut, because there are only remote areas in this territory.

All persons meeting the conditions for the CSD frame were then classified into these estimation domains and strata before sample selection.

3.6 Sample allocation

The sample units were allocated in such a way that, for each estimation domain, one could estimate a minimum proportion with a maximum coefficient of variation (CV) of 16.5%. At Statistics Canada, 16.5% is often used as the upper limit for the CV to allow the corresponding estimate to be considered of adequate quality. The minimum proportion to estimate in each estimation domain is shown in the table below. A design effect of 1.2 was assumed for these calculations. In other words, it was assumed that, in the estimation domains, the variance that would be obtained with the CSD’s sample design would be 20% higher than the variance that would be obtained if a simple random sample of the same size in each domain was selected.

A method of optimal allocation among the strata in a particular domain was used, taking into account the expected non-response and the expected false positive rate (individuals who answered in the affirmative to the filter questions on activities of daily living in the census but have no disability according to the CSD) in each stratum. This allocation depended in part on the census long-form questionnaire weights adjusted for non-response. It should be noted that at the time of allocation, these weights had not yet been calculated. Consequently, preliminary weights were calculated solely for the purposes of the allocation. However, the final census long-form questionnaire weights were used in the CSD weighting process. For background information on census long-form questionnaire weighting, see Chapter 12 of the Guide to the Census of Population, 2021.

3.7 Oversample of Veterans

The 2022 CSD sample design includes an oversampling of Veterans to enable the production of statistics on the population of Veterans who have a disability. Once the sampling plan had been determined for the main needs of the survey, the oversampling plan was established to meet the analytical needs for the population of Veterans who have a disability. For this population, it must be possible to produce national estimates by veteran status and gender. The oversample estimation domains were therefore defined as the veteran status cross-classified with gender (Man+ and Woman+). Strata were created within each estimation domain by cross-classifying the three levels of severity with whether a person lives in a remote area or not.^Note The veteran oversample units were distributed so that, for each estimation domain, a minimum proportion of 5% could be estimated with a maximum CV of 16.5%. A design effect of 1.2 was used. The size of the oversample of Veterans sent for collection is 4,001.

3.8 Sample sizes

Table 3.2 below shows the final sample sizes of the CSD sample sent for collection (YES sample, i.e., main sample, and veteran oversample) by province and territory.

3.9 NO sample

As previously mentioned, the CSD analytical file is used in part to estimate disability rates for various geographies and to compare the characteristics of persons with and without a disability. For this purpose, the analytical file must also include a representative sample of persons without a disability, and this is not the case when only the YES sample is considered.^Note A sample from the NO population was therefore selected, i.e., individuals who answered “no” (or did not provide an answer) to all the filter questions on activities of daily living in the census long-form questionnaire. The underlying assumption here is that the members of the census NO population are less likely to have a disability or that, if they have a disability, it is very mild.

The NO sample was not the object of data collection, since each individual is considered to have no disability. The analytical file contains a large number of characteristics from the census for this sample, as for the YES sample, making it possible to compare the characteristics of persons with a disability and persons without a disability according to census data. With this NO sample, analysts are also able to produce the denominators required to calculate the disability rates for a number of subgroups of the Canadian adult population.

To keep the analytical file from getting too large, a sample of the NO population was selected instead of taking the entire population. To select the sample, the population was stratified by province, gender and five-year age groups, with the oldest group being 75 years and over . Age stratification is therefore more detailed than for the YES sample. The census sample design was also taken into account for the NO sample since the strata were then subdivided based on remote and non-remote areas.

The NO sample size was established to estimate lower minimum proportions and/or to attain a lower CV (for better precision) than what was established for the YES sample. A minimum proportion to estimate and a CV to attain were set for each domain to ensure the total sample size was roughly 140,000 individuals—a size with which estimates of adequate quality can be produced. The minimum proportions used to calculate the sample sizes for the NO population were the same as those used for the YES population for the two oldest age groups in the provinces (65 to 74 years, and 75 years and over). However, the minimum proportion was lowered by 2 percentage points (i.e., set to 7.0%) for the other age groups in the provinces to improve accuracy for working-age groups (i.e., 15 to 24 years, 25 to 44 years and 45 to 64 years). In the territories (15 years and over), the minimum proportion was lowered by 1 percentage point (i.e., set to 8.5%) (see Table 3.3). The CV targets were reduced to 6.5% across most of the domains^Note (compared with 16.5% in all domains for the YES sample) since a larger sample size was possible for the NO population. This offers the advantage of producing a sample with a relatively stable size per domain, thereby improving the accuracy of the estimators at the domain level. The table below lists the minimum proportions to estimate for each estimation domain.

The following table presents the NO sample sizes by provincee.

Since all units in the NO population are considered to have no disability, the severity score for each unit in the file was set to 0, and the severity class was set to 0. This treatment enables the calculation of disability rates.

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