Sampling (statistics)

Sampling is the selection of a subset of individuals from a statistical population to estimate characteristics of the whole population. It is a fundamental technique in statistics, quality assurance, and survey methodology, used to gather information when measuring an entire population is infeasible or too costly. The subset, known as a statistical sample, is intended to reflect the broader population, and statisticians strive to collect samples that are representative. Sampling offers lower costs and faster data collection compared to a census; in many cases, collecting data from the entire population is impossible, such as measuring all stars in the universe. Each observation records properties like weight, location, colour, or mass of independent objects. In survey sampling, weights may adjust for the sample design, especially in stratified sampling. Results from probability and statistical theory guide the practice, and sampling is widely used in business and medical research. Acceptance sampling determines if a production lot meets specifications.

The concept of random sampling by lots is ancient, mentioned several times in the Bible. In 1786, Pierre Simon Laplace estimated France’s population using a sample and a ratio estimator, computing probabilistic error estimates. His work used Bayes’ theorem with a uniform prior and assumed a random sample. Alexander Ivanovich Chuprov introduced sample surveys to Imperial Russia in the 1870s. In the US, the 1936 Literary Digest presidential poll failed due to severe bias; over two million responses came from magazine subscription lists and telephone directories, which were heavily biased toward Republicans, making the large sample deeply flawed. Since the 2015 election, Singapore has adopted sample counts to reduce speculation and misinformation, with a reported 4% margin of error at a 95% confidence interval, though these are separate from official results.

Defining the population is crucial. A population includes all items or people with the desired characteristics. Often, the sampled population differs from the target population due to frame issues, and sometimes they are entirely separate—for instance, studying rats to understand human health. Sampling may also occur over time or space, such as examining supermarket staffing at various times or penguin hunting grounds. In some cases, the population is a th