Survey Sampling and Sampling Frames

Study Notes

A population is a set of elements of interest.
A study variable is an attribute of interest associated to each element in the population.
A survey is a statistical investigation whose goal is to describe a population of elements by one or more characteristics or parameters.
In principle, a survey could measure every study variable associated with every element in the population.
However, in practice, a survey will select a sample of the population and measure the study variables associated with the selected sample.
A sampling frame is any material or device used to obtain observational access to the population of interest.
Ideally, the frame also contains some additional variables associated to the elements. These variables are called auxiliary variables.
In the first two examples above, a sampling frame can be a file having households in rows and variables in columns. Among the variables there should be some that allow to identify a household —e.g. the personal identification number of the head of the household— and some that allow to establish contact with the households —e.g. the telephone number of the head of the household.
An auxiliary variable may be the number of members of the household.
In the second example, a sampling frame can be a file having patients in rows and variables in columns. In the third example, a sampling frame can be some device that allows for selecting arbitrary points within the boundaries of the region of interest where each point is identified by its latitude and longitude. In the fourth example, a sampling frame is any device that allows for selecting points within the interval (0 , 1).