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Sample Methods

In 1996, Statistics Greenland asked the Special Surveys Division of Statistics Canada to produce a feasibility study for a Survey of Living Conditions in the Arctic, using Canada as an example. The result is an October 1, 1998 report, Survey on Living Conditions in the Arctic: Inuit peoples of Labrador, Nunavik, Nunavut and the Inuvik region Feasibility Study

Included in the Feasibility Study was a consideration of sample sizes. Stat Can authors introduced the discussion with the concept of statistical reliability:

A measure suitable for specifying the reliability of survey estimates is the coefficient of variation (cv) of an estimated proportion, which expresses the standard error of the estimate as a fraction or percentage of the estimate itself. A formula for the cv is:

where:

n is the sample size, 
N is the population size, 
p is the proportion being estimated, 
deff is the design effect, and 
r is the response rate.

The design effect (deff) is a factor that is introduced to account for the relative efficiency of the sample design actually used, as compared to a simple random sample (srs). A deff of 2, for example, means that the estimates will be on average only half as precise as when using a srs design.

In order to determine the required sample size from the above formula, one can specify the level of reliability required of estimates to be produced from the survey. Statistics Canada included in its Feasibility Study the guidelines summarized in the following table:

 

Quality level

 

CV range

 

Comment

 

Acceptable

 

0.0%-16.5%

 

No warning required.

 

Marginal

 

16.6%-33.3%

 

Users should be warned about the high levels of error.

 

Unacceptable

 

33.4% and above

 

Not recommended for release.

Based on the above guidelines, Stat Can recommended for SLiCA to aim for a cv of 16.5% for proportions as low as 0.10. Proportions higher than 0.10 will have a better precision, i.e. a cv lower than 16.5%. Proportions lower than 0.10, on the other hand, will have a cv higher than 16.5% and will need to be used with caution. For this reason, 0.10 is called a minimum estimable proportion, or min p.

In all calculations, a design effect of 2.0 is used. This value appropriately represents the type of multi-stage design that is suggested here.

Please continue with Sample Size.