Canadian Survey on Disability, 2017: 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, May 10, 2016) who responded that they have difficulty “sometimes,” “often,” or “always” to any of the sub-questions on activities of daily living in the long-form census questionnaire (see Textbox 3.1), which are considered CSD “filter questions”. The population covered by the long-form census questionnaire includes persons living in private dwellings^Note in the 10 provinces and 3 territories. However, for operational reasons, the population living on First Nations reserves are excluded from the CSD.

The sample for the 2017 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. These people are the most likely to have a disability and are part of the population we refer to as the YES population. The people within this population 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 with a disability.

While the CSD does not cover persons who responded “no” to the filter questions on the long-form census questionnaire (known as the NO population), a sample of these individuals is nonetheless included in the CSD data files, called the analytical files (see Section 3.8). These people are all considered to be people without a disability. A certain number of persons without a disability will also be found in the YES population. These are people 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 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, May 10, 2016. However, all the information collected during the CSD represents the population’s characteristics as measured from March to August 2017. 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 2016 Census

The sampling frame for the CSD was constructed from the Census Response Database, a preliminary database called the RDB. The database contained all responses received via the various reporting modes (Internet, paper questionnaires, personal interviews, etc.). Responses in this database are responses pre-processing and imputation by the census team. The frame had to go through a number of processing steps to ensure that all the information would be as complete as possible:

• when the age was missing for a person on the census questionnaire, it had to be imputed on the basis of responses to census long-form questions (for example, data on education, employment and income, etc.);
• various data sources were used to detect errors in telephone numbers or find missing telephone numbers or addresses;
• various data sources were used to find phone numbers associated with the household of the selected person to increase chances of contacting it;
• various data sources were used to fill in incomplete addresses to increase chances of respondents receiving the letter of introduction^Note informing them of the upcoming survey;
• preliminary weights for the census had to be derived so that estimates of the population size in each stratum could be computed for sample allocation.

3.4 Sample design

The sample design is a two-phase stratified design based on the 2016 Census. The first phase, the census itself, is the selection of the sample of households that received the long-form census questionnaire, and the second phase involves the selection of people for the CSD sample.

Phase 1

The first phase corresponds to the selection of the sample of households that received the long-form census questionnaire, approximately one in four households, systematically selected across Canada. Canadian citizens temporarily living abroad, full-time members of the Canadian Forces posted abroad, and visitors or representatives of foreign governments are excluded from the target population of the long-form census questionnaire. The following are also excluded: people living in collective dwellings (institutional and non-institutional), such as hospitals, long-term care facilities (including group homes for people with disabilities or addictions), correctional institutions or detention centres, nursing homes, residences for senior citizens, religious establishments (such as convents, monasteries or seminaries), rooming and boarding houses, hostels, Hutterite colonies, establishments offering temporary lodging (such as hotels, motels, campgrounds, YMCA, Ronald McDonald Houses, and shelters), as well as other establishments, including school residences, military bases, work camps, and ships.

There are two versions of the long-form census questionnaire: the 2A-L and the 2A-R. Questionnaire version 2A-L  is distributed to approximately one in four households in most regions of Canada and is completed by self-enumeration. In addition to the basic census demographic questions (name, sex, date of birth, legal marital status, common-law status, relationship to person 1, various language questions, and the consent question to release the data in 92 years), the 2A-L questionnaire also includes questions on labour market activity, income, education, citizenship, housing, ethnic origin, Aboriginal identity, etc. The 2A-R questionnaire is identical to the 2A-L version, but it is administered to all households in remote areas and on First Nations reserves by way of personal interview. CSD filter questions (i.e., questions on activities of daily living) are only included in the long-form questionnaire.

In sampling terminology, the first phase is a stratified systematic sample of occupied private dwellings with a constant sampling rate of ¼ in most regions of Canada and complete enumeration in remote areas and on First Nations reserves. The sampling unit for the first phase is the household.

Phase 2

In the second phase, the CSD sample was selected among individuals who reported having difficulty in response to the sub-questions about activities of daily living on the long-form census questionnaire. The sample excludes people living on First Nations reserves and those under the age of 15 as of May 10, 2016. The sampling unit for the second phase is the person.

The CSD sample was selected so that there would be a sufficiently large sample in each estimation domain and to optimize the sample allocation, as explained in section 3.5.

3.5 Estimation domains and stratification

Domains of estimation are groups of units for which estimates are targeted with an “acceptable” level of precision. The CSD domains of estimation consist of the provinces cross-classified with the following age groups:

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

Each estimation domain was then divided 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 comprise people with similar preliminary sampling weights (i.e., remote or non-remote areas) as well as 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. In order 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., vision, hearing, physical, cognitive, mental health, or other). Six strata were thus generated for each estimation domain, with three levels of severity sorted by whether a person lives in a remote area or not.

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 not all 6 strata necessarily occurred in each estimation domain. Since there are no remote areas in Prince Edward Island, Nova Scotia and New Brunswick, there were only three strata for each domain in these provinces. Conversely, since there are only remote areas in Nunavut, this territory also only had three strata.

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

3.6 Sample allocation

The sample sizes were determined 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 of an acceptable estimate. 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 (people who answered in the affirmative to the filter questions on activities of daily living in the census but have no disability according to the DSQ) in each stratum. This allocation depended in part on the long form census weights adjusted for non-response. It should be noted that at the time of allocation, those weights had not yet been calculated. Consequently, preliminary weights were calculated solely for the purposes of the allocation. However, the final census long form weights were used in the CSD weighting process. For background information on census long form weighting, see Chapter 9 of the Guide to the Census of Population, 2016.

3.7 Sample sizes

The final sample sizes for the CSD sample sent to collection (the YES sample), by province and territory, are shown in Table 3.2 below.

3.8 The NO sample

As previously mentioned, the CSD analytical file is used in part to estimate disability rates for various geographies but also to compare the characteristics of persons with and without a disability. For that purpose, the analytical file must also include a representative sample of persons without a disability, which is not the case when only the YES sample is considered.^Note A sample from the NO population therefore had to be selected, i.e. people who answered “no” (or did not answer at all) to all the filter questions on activities of daily living in the long-form census 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 sent to the field, since each individual is considered not to have a disability. The analytical file contains a large number of characteristics from the census for this sample and for the YES sample, which makes it possible to compare persons with a disability and persons without a disability. 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 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, sex, and five-year age groups, the oldest group being 75 years and over (and therefore, more detailed than 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 in order to estimate lower minimum proportions and/or to attain a lower CV (for better precision) than those 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 the proportion used for the YES population in the territories (15 years or over), and for the last two age groups in the provinces (65 to 74 years, and 75 years or over). However, for better accuracy, they were lowered slightly in the provinces for working-age groups, i.e., 15 to 24 years, 25 to 44 years, and 45 to 64 years (see Table 3.3). 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 domain of estimation.

The following table lists the NO sample sizes by province.

Since all units in the NO population are considered not to have a disability, the severity score for each unit in the file was set to 0, and the severity class was set to 0. This was done in order to calculate disability rates.

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