Error of Nonobservation

Sampling Error

Inference from sample surveys assumes that an underlying population is being studied and that samples are taken from this underlying population. Sample statistics, including sampling errors, are calculated to determine the variability of a statistic as measured in a survey compared to the actual or true value of that statistic in the population.

Since not all members of a population are included in a sample, survey statistics are usually different from population values. For any population, there are all sorts of possible combinations of records that might be included in any particular sample. In many cases, the results of a survey will be close to what would be found in an underlying population; in some cases they may be far off. The sampling error is traditionally taken as a measure of how the statistics obtained from any particular survey might differ or vary from those of the actual underlying population.

In terms of understanding errors of nonobservation, sample errors from probability samples primarily refer to errors regarding certainty about how close a survey statistic comes to the actual value of the statistic in an underlying population. That is, nonobservational errors due to sampling primarily impact the variability of survey statistics or the precision of the survey measure. Although there is almost always error in the form of variance, because survey results are rarely exactly in line with population statistics, these variable errors are random and thus cancel each other out across many samples.

The characteristics of sampling error are primarily mathematical and are based on several assumptions. Sampling statistics assume that a sample of respondents or other units is taken from an underlying collection, list, or frame of all members of a population. [Page 237]Sampling statistics also assume that data are collected from all selected records. Moreover, probability sampling assumes that all sampled records have a known, nonzero probability of being selected.

Nonprobability samples select respondents in ways that do not permit the understanding of the specific probability that sampled members of the population are included in the sample. Convenience samples, for example, select respondents that are easily accessible to the researcher while excluding others. These sampling methods can lead to bias, when the results of measured statistics systematically differ from population values, usually in unknown ways. Bias or systematic error can also occur in scientific samples when different sample records are selected with varying likelihoods or probabilities of selection, but this bias can be adjusted for with simple mathematical adjustments known as sample weights.

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