Sampling Bias

Sampling Bias for Averages

For survey researchers, sampling biases for averages derive from three sources: (1) imperfect sampling frames, (2) nonresponse bias, and (3) measurement error. Mathematical statisticians may also consider biases due to sources such as using the sample size (n) instead of n - 1, or using a sample statistic (e.g. s2) to estimate a population parameter (e.g. σ2), but these tend to be of academic interest and of less interest to practical research concerns; therefore, these will not be considered in this entry.

Imperfect sampling frames occur frequently in research and can be classified into four general categories: (1) frames where elements are missing, (2) frames where elements cluster, (3) frames that include foreign elements, and (4) frames with duplicate listings of elements. For example, household telephone surveys using random-digit dialing samples for landline telephones exclude households that are cell phone only (missing elements), include telephone numbers in some dwelling units that include more than a single household (element cluster), include some telephone numbers that are dedicated solely to fax machines (foreign elements), and include some households with more than a single landline telephone number (duplicate listings). All of these can cause sampling bias if they are not taken into account in the analysis stage.

Sampling bias due to nonresponse results from missing elements that should have been included in the sample but were not; these can be classified as noncontact (missing), unable to answer, or refusal. Noncontacts are those elements that are selected into the sample but cannot be located or for which no contact can be made; whereas the unable-to-answer either do not have the necessary information or the required health or skills to provide the answer, refusals are elements that, once located, decline to participate. Each will contribute to sampling bias if the sampled nonre-sponding elements differ from the sampled elements from which data are gathered. This sampling bias for averages can be characterized as follows:

As can be seen, when the number of nonresponse represents a small proportion of the total sample, or when there is a small difference between those who respond and those who do not, the resulting sampling bias will be small or modest. If it is possible to place bounds on the averages (such as with probabilities and proportions), researchers can quantify the possible range of sampling bias.

The third source of sampling bias for averages results from measurement error—that is, when what is measured among the sample elements differs from what researchers actually wished to measure for the target population. Measurement error, however, can be divided into random error and consistent bias; only consistent bias results in sampling bias, as random error will appear as sampling variance. These components of measurement error can be represented

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