1. Measurement errors Marina Signore
Measurement of the quality of statistics
3-5 October 2012
Marina Signore
Istat
Division "Metadata, Quality and R&D Projects", Chief

2. Coverage errors
In a survey the objective of the inference are some characteristics of the (finite) target population
In general to achieve this goal we need to:
  draw a sample of units from a list;
identify the corresponding population elements;
contact and observe them.
Coverage errors are errors of nonobservation related to the frame that is supposed to list all the units in the target population.
A frame, also said sampling frame, is a collection of units to which are associated the population elements (e.g. database) .

3. Coverage errors
The ideal frame should contain units that are linked only with the elements of the target population, i.e. the population under investigation. Usually, the frame population is different from the target population due to frame imperfections, called coverage errors. Remark: Sometimes the concept of survey population is introduced. It refers to the “realistic target population” or “the population that can realistically be studied”. The population for which a good frame can be constructed with the given budged constraint (Särndal et al., 1992, Section 14.7)

4. Coverage errors Five types of frame imperfections: Undercoverage
Undercoverage
some target population elements do not have a link to any unit in the frame
They can never be selected in the sample.
Overcoverage
Some units in the frame are linked with elements that do not belong to the target population (out of scope or ineligible units). The frame presents overcoverage.
ineligible units, when encountered in the sample, have to be discarded (the sample size reduces)

5. Coverage errors Duplicate listings
Some target population units have links to more than one frame unit
Duplicated units have a higher probability of being selected than the one assigned by the sampling design.
 Accuracy/timeliness of frame information
The frame information is not detailed enough or not up-to-date to allow access to some population elements
some units can not be contacted and observed (a kind of undercoverage)
Errors in auxiliary information
The frame contains auxiliary variables that can be used for the stratification, PPS sampling, or ratio estimation, but these information are affected by errors
possible loss of precision of survey estimates that make use of these information

6. Impact of frame errors Impact of frame errors on survey estimates
Undercoverage is considered the more damaging frame error.
The undercoverage can introduce a high noncoverage bias into final survey estimates.