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For rate and ratio statistics, correct identification of Indigenous people is needed for both the numerator (e.g. number of events) and denominator (e.g. number of people at risk). For many commonly used measures of population health, the data in the numerator and denominator come from different sources. For example, death rates are typically calculated using the number of deaths notified to the Registrar of Births, Deaths and Marriages (or to an equivalent office) divided by the estimated population (based ultimately on census data). It is important that the measurement of Indigenous status be comparable from one data source to another. This means that the same question should be used across collections.
There is good evidence that it matters what you ask. For example, as has been the experience in the US and New Zealand, different numbers of people can be categorised in different population sub-groups depending on whether they are asked to report descent or self-identification.
In Australia, the government has come up with a "Working Definition" of Aboriginal and Torres Strait Islander. This definition is based on the three elements of descent, self-identification and community acceptance. A person is considered to be Aboriginal or Torres Strait Islander if he or she: 1) has Aboriginal or Torres Strait Islander ancestors; 2) identifies as an Aboriginal or Torres Strait Islander person; and 3) is accepted as such by the community in which he or she lives.
The second element of this definition (or a combination of the first two) is the most useful in practice. The third element of community acceptance is used to determine eligibility for a few government programs, but it is not suitable for use in standard data collections, such as surveys, censuses or administrative collections.