A *random sample* is a subset of individuals selected at random from a larger population, where each individual in the population has a known and non-zero chance of being chosen. Sampling refers to the process of selecting a sample. Although the concept of random sampling is central to much of statistical theory, in practice it is rare. For example, in surveys involving humans, it is usually not practical to contact most people, let alone to compel them to participate if randomly selected.

Consequently, many alternatives exist to random sampling. A sample that is not a random sample is known as a non-random or non-probability sample. Specific types of non-random sampling include quota sampling, convenience sampling, volunteer sampling, purposive sampling, and snowball sampling. It is common practice to use as much randomization as possible when employing these techniques, in the hope that the resulting sample approximates the qualities of a random sampling.

## Quota sampling

The main alternative to random sampling is *quota sampling. *This involves specifying required sub-samples, and obtaining these in a cost-effective way (e.g., obtaining 50 males under 30, 50 females under 30, 50 males 30 or older, and 50 females 30 or older).

## Convenience sampling

*Convenience sampling* refers to approaches where considerations of simplicity rather than randomness determine which observations are selected in a sample. Common examples of this would be conducting interviews in high-traffic locations, or among students.

## Volunteer sampling

*Volunteer sampling *involves asking for people to volunteer to participate. This could be via phone and text message-based campaigns run by TV and radio stations, or questionnaires on newspaper websites.

## Purposive sampling

*Purposive sampling* involves obtaining a sample such that it maximizes the quality of the information obtained from a sample, rather than representing the population at large. For example, whereas a *simple random sample* may obtain 50% men and 50% women, a purposive sample may seek to represent all genders (including transgender people). Samples designed to maximize variation within the sample, expert samples, and samples of “typical” people are all types of purposive samples.

## Snowball sampling (referral sampling)

*Snowball sampling *is a technique where a respondent nominates other people to participate in the study. It is useful in situations where participants for a study are hard to find (e.g., studies of illegal drug users, people with HIV),

## Statistical analysis of non-random samples

In theory, a non-random sample can be just as representative as a random sample. However, the benefit of random sampling is that the level of uncertainty (sampling error) is quantifiable using statistical theory. There is typically no mechanism for quantifying the extent to which conclusions from a random sample may diverge from the population. For this reason, the statistical literature often describes non-probability samples as mistakes.

Nevertheless, when significant randomization does occur within non-random samples, they can have properties that are closer to random samples. For example, with s quota sampling, if randomly contacting people and continuing to do so until all quotas are met, this approach can lead to a sample that is approximately random (Seymour Sudman, *Applied Sampling*, Academic Press, 1976).

In practice, nearly all samples are non-probability samples. For example, in the case of political polling, some people are not contactable, and others refuse to participate. As a result, all political polls are convenience samples. This is true of just about all samples of living organisms. Factories are one of the only real-world instances where random samples are possible.

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