How can a survey covering only a small sample allow for findings to be made about the total population?
A good example can be found in Statistics SA's recently released general household survey.
The way the sample for the survey is constructed is critical in assessing the credibility of the information.
For the 2003 survey, a multi-stage stratified sample was drawn using probability proportional to size principles.
This sample was drawn from the master sample that Stats SA uses for its regular household surveys.
The master sample is drawn from the database of enumeration areas established during the demarcation phase of the population census. Small enumeration areas are combined to form primary sampling units of at least 100 households.
The sampling procedure involves explicit stratification by province, and urban and non-urban areas. For the general household survey, 3 000 sampling units were selected. In each selected unit a systematic sample of 10 dwelling units was drawn, resulting in a sample of about 30 000.
Once the information has been collected, it is then weighted to population estimates. Thus, one can comfortably say that one element in a sample represents a specified number of elements in the population with similar characteristics.
However, sample surveys always involve some margin of error. The measure usually used to indicate the probable difference between a sample estimate and the corresponding total population figure is the standard error.
The first is the sample size. Generally speaking, the larger the sample size, the more precise the estimate and the smaller the standard error.
Consequently, in a national survey, one expects more precise estimates at the national level than at the provincial level.
The second factor is the variability between households of the parameter of the population being estimated - for example, the number of unemployed people in the household. The way this standard error is calculated is demonstrated in Stats SA's report on the survey.
The general household survey itself collected information on a variety of subjects including education, health, employment, births, access to services and facilities, the environment, and quality of life.
As a result, it provides data that can be used to measure the trajectory of development and the impact of various government programmes and projects, especially when comparing the 2002 and 2003 surveys.
The results of the 2003 general household survey provide a good example of the way in which a survey based on a small sample can be used to identify important trends among the population as a whole.
Pali Lehohla is the statistician-general and head of Statistics SA. For more information on Stats SA and its outputs, including the report on the general household survey, visit www.statssa.gov.