Not surprisingly, the sampling texts devote the majority of the content to sampling error. There are tradeoffs with other sources of error, however. Nonresponse, for example, is quite directly related to sampling; one could start with a much larger sample size and achieve more completed interviews at the expense of potential nonresponse error.
Within a total survey error paradigm the role of the statistician becomes different. A sampling statistician could not just optimize and fix a sample design based on sampling variance. Instead, other error sources need to be considered in the initial sampling design. Furthermore, the statistician needs to be involved during data collection in order to help optimize outcomes for the multiple sources of error and their interactions, especially utilizing information that could not be available prior to conducting the study.
An example of this is the use of replicate samples, where the initial sample is divided into random subsamples and released as needed depending on eligibility, contact, and refusal rates. This could be done separately within strata of interest. Another example is the subsampling of nonrespondents for another phase of data collection during the study. The sampling statistician’s involvement can be also extended to other sources of error, to include measurement error, such as exerting control over the allocation across sampling frames, particularly when each sampling frame is closely tied to the use of a particular mode of data collection.
This presents challenges to the survey statistician and to the data collection team. It requires greater coordination of data collection efforts with sampling. Which cases should receive a different treatment and when? The survey statistician needs to be also privy of the data collection process – from typical changes in participation over the course of data collection to particular changes that are implemented in order to account for such interventions.
