# Sampling

Exponent statisticians possess the requisite skills and experience to assist clients in the design, implementation, and analysis of sample surveys in diverse projects in engineering, science, business, and the law.  Statistical sampling is used in virtually every area of engineering, science, and public policy. Sampling is an efficient way to learn about a population of interest, and the statistical methodology allows for a precise assessment of the uncertainty in sample-based estimates. For more than sixty years—dating back to World War II and, in some instances, earlier—sampling has been used to audit the quality of manufactured products, to assess the accuracy of financial accounts, and to estimate the abundance and characteristics of human and animal populations.

Sampling and survey evidence also figures prominently in selected litigation—particularly in antitrust proceedings, employment discrimination cases, and toxic torts. More recent applications in electronic discovery, products liability, and construction law have expanded the legal uses of sampling. Courts have shown an increasing willingness to consider sampling in estimating damages for mass torts and class actions, for reasons of improved accuracy as well as judicial economy.

Any sample drawn for the purpose of estimating any characteristic of a population must be selected so that the sampled units can be regarded as representative of the larger population. For that reason, sampling should always be done using a random mechanism to select units. Strictly speaking, a random sample is one in which every unit of the population has a known probability of being included in the sample. The most basic form of random sampling is simple random sampling, in which every unit of the population has an equal chance of being selected for the sample. If the population can be divided into more homogeneous subpopulations, then a stratified design can be implemented in which random samples are drawn from each subpopulation, rather than from the population as a whole.

Technical experts sometimes feel they can select a representative sample by exercising their professional judgment in choosing units from the population. Such an approach was discredited in statistical studies more than seventy years ago. A judgment or “purposive” sample is vulnerable to the charge that a conscious or unconscious bias influenced the selection of units. Also, statistically derived estimates from such a sample are technically invalid, because the theory on which such estimates are based includes an assumption of random sampling from the population of interest.

Any project involving sampling should begin with a clear statement of the study objectives and an equally clear definition of the population to be sampled. One critically important step is the construction of a list of units, called a sampling “frame,” from which the sample will be selected. A common misconception is that a fixed percentage of units in the population (e.g., 10%) must be sampled to obtain reliable results. Instead, the sample size will depend on the desired level of accuracy, the unit costs of sampling, the variability of the characteristic being measured, and the number of units in the population.

Surveys of human populations can be carried out by mail, telephone, or personal interview. In such projects, care should be taken to consider and minimize potential sources of bias, such as deficiencies in coverage of the population, low response rates, and measurement errors in the survey instrument (e.g., questionnaire).

Monitoring the health of an endangered species, predicting the amount of fossil fuel resources at a new exploration site, or estimating the prevalence of a rare disease may require specialized approaches to sampling using line transects, capture-recapture methods, and spatial or adaptive designs. These techniques—developed largely in such fields as ecology, geology, and health sciences—complement the standard sampling theory and more traditional methods developed for use in the social and behavioral sciences.