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Sampling (statistics)

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Sampling is a vital tool used in statistics, quality assurance, and survey methodology. It involves selecting a subset of individuals from a larger group, known as a statistical population. This subset is called a sample. The primary goal is for the sample to reflect the characteristics of the entire population. Measuring every single member of a population is often impossible or impractical. For example, it is impossible to measure the size of every star in the universe. Sampling provides faster data collection and lower costs. It allows researchers to gain insights when studying a whole population is infeasible.

To begin sampling, a researcher must first define the population. A population includes all people or items with the specific characteristics being studied. Sometimes this definition is simple, such as a batch of manufactured material. In these cases, the batch is the population, and a manufacturer uses acceptance sampling to see if the lot meets specifications. Other times, populations are defined by time or space. A study on endangered penguins might look at hunting grounds over a specific period. A researcher might even study a "superpopulation." This is a larger group that does not yet exist, such as everyone in a country who might one day use a new medical program.

Simple random sampling
Simple random sampling

A successful sample requires a sampling frame. A frame is a way to identify every element in a population so they can be selected. The most straightforward frame is a list, such as an electoral register or a telephone directory. Without a proper frame, it is difficult to ensure every member has a chance to be included. For instance, there is no way to identify every rat in existence. However, a list of names provides a clear way to pick individuals for a survey. A good frame helps researchers avoid leaving certain groups out entirely.

There are two main types of sampling: probability and nonprobability sampling. In probability sampling, every unit in the population has a known chance of being selected. This allows statisticians to use mathematical theory to produce unbiased estimates. One method is simple random sampling, where every subset of the frame has an equal chance of selection.

Simple random sampling
Simple random sampling

Other methods include systematic sampling, stratified sampling, and cluster sampling.

Systematic sampling
Systematic sampling
Stratified sampling
Stratified sampling
Cluster sampling
Cluster sampling

In stratified sampling, the population is divided into groups to ensure representation. Researchers can also apply weights to the data to adjust for the specific design used.

Nonprobability sampling occurs when some elements have no chance of being selected. In these cases, the probability of selection cannot be accurately determined. This often happens through convenience sampling, where researchers pick whoever is easiest to reach. For example, interviewing the first person who answers a door is nonprobability sampling. This is because certain people, like those who stay home more often, are more likely to be picked. This creates exclusion bias, which limits how much information the sample can provide. Because the selection is not random, researchers cannot easily estimate sampling errors.

Stratified sampling
Stratified sampling

The history of sampling includes both great discoveries and famous mistakes. In 1786, Pierre Simon Laplace used a sample to estimate the population of France. He used a ratio estimator and Bayes' theorem to compute probabilistic estimates of error. In the 1870s, Alexander Ivanovich Chuprov introduced sample surveys to Imperial Russia. However, sampling can fail if the frame is biased. In 1936, the Literary Digest tried to predict a US presidential election. They used a massive sample of over two million people from magazine lists and phone books. Because these lists were biased toward Republicans, the prediction was deeply flawed.

Today, sampling remains essential across many different fields. In Singapore, officials use sample counts during elections to reduce misinformation. These counts provide an indicative result with a 4% margin of error at a 95% confidence interval. In business, companies use sampling to check the electrical conductivity of materials like copper. Even in casinos, people like Joseph Jagger have used sampling to study the behavior of roulette wheels. Whether studying human health through rats or checking product quality, sampling turns the impossible task of measuring everything into a manageable science.

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