Within-Unit Coverage Error

Within-unit coverage error refers to the bias, variance, or both, that may result when the respondents who are selected from within a sampling unit, and from whom data are gathered, differ in non-negligible ways from those who were missed from being selected but in theory should have been selected.

Many probability sample surveys are made up of a target population of individuals that belong to one sampling unit. But often these surveys use a two-stage design in which the unit is sampled first, and then a respondent (or more than one) from within the unit is selected to be interviewed. One example is a household or a unit within an organization, from which one person or a subset of persons per sampling unit is surveyed. These surveys usually select randomly one or more persons among all eligible persons that belong to a certain sampling unit according to some a priori definition. Within-unit coverage error can occur when one or more eligible persons within a selected sampling unit have a zero chance of selection, have a 100% (certain) chance of being selected, or have some other disproportionate chance of being selected, for example, because they belong to more than one sampling unit.

Within-unit coverage problems that might lead to error can therefore be defined as the difference between the sampling frame and the target population at the level of the individual residents. Within-unit undercoverage problems occur if people that are in fact eligible and should be counted as sampling unit members have no chance or less chance of being selected because they are not "recognized" by the informant or the selection technique as being a sampling unit member or they are not mentioned at all when sampling unit members are listed for the respondent selection process. The undercoverage problem arises because these persons are part of the target [Page 963]population but do not have a correct chance (probability) of being part of the frame population. Persons are said to be overcovered if they are listed in the frame population more than once and therefore have more than one chance to be selected into the sample but are only represented once in the target population.

Within-unit coverage error includes a bias as well as an error variance component. In both cases, within-unit coverage error is a property of a statistic, not a survey. Within-unit coverage bias in a statistic of interest occurs only if the members of the population that are not covered (or are overcovered) are different from those who are covered (or are only covered once) with regard to the statistic of interest. Therefore, there are two conditions that have to be met to produce within-unit coverage bias in a statistic of interest. The first condition is a difference between the sampling frame and the target population—subsets of the population are overcovered or undercovered. The second condition entails a difference of those people overcovered or undercovered from the rest of the target population with regard to the statistic of interest. Each condition is necessary but not sufficient to produce coverage error.

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