Sampling Error

Populations and Samples

Which candidate do voters prefer in an upcoming election? What is the average level of formal education among American adults at least 25 years old? Considerable research tries to ascertain the value of some characteristic in a well-defined population. Researchers call the value of a selected characteristic in the population, such as a preference for “Candidate X,” a population parameter.

A population is the entire collection of cases, elements, or people that the researcher plans to study, such as all U.S. registered voters in November 2008. Notice the precision in the example population definition—it is specific to a particular quality such as voter status, location, and time. If a population is small, cooperative, and accessible, then collecting information is straightforward. For example, a small county has an address list of all registered voters. Such a list is called a population frame, and researchers ensure that it is as complete as possible. Collecting information from all population elements is called a census.

Most often, however, the population is too large, geographically dispersed, or unwieldy to collect information efficiently from every single element. When the United States conducts its decennial population census, it can take a year to collect the information; even with such a massive effort, the U.S. Census undercounts some population segments, spending additional time making corrections. Thus, much research gathers [Page 1313]information from a sample (i.e., a specified subpart or subset of the population). The value of a selected characteristic in a sample is called the sample estimate or the sample statistic. For example, surveys are gathered about voter preferences using samples prior to elections. Sampling error forms an integral part of generalizing from a sample to the larger population because the exact population value is typically unknown.

Many studies predict the population parameter from a sample estimate. However, because sample estimates rely on only a subset of population cases, the estimates will vary across the samples. If the sample is carefully selected using probability methods comparable with a lottery, most estimates will be close to the population parameter, but a few will deviate sharply from the population value. The study of this sample variability comprises much of the study of sampling error.

Types of Error in Parameter Estimation

Research practitioners distinguish two major sources of error in estimating population parameters. First is systematic error or bias, which is often hidden and thus uncontrolled. An example is the scale that always weighs its user 5 lb too light. Poundage loss or gain is reflected in the scale results—but always 5 lb under the true weight. Given a strong focus on sampling error, bias is often critically neglected. Strategies used to minimize bias include careful measurement (e.g., a correctly calibrated scale), using several different measures, and a probability sample.

...