sampling, in statistics, a process or method of drawing a representative group of individuals or cases from a particular population. Sampling and statistical inference are used in circumstances in which it is impractical to obtain information from every member of the population, as in biological or chemical analysis, industrial quality control, or social surveys. The basic sampling design is simple random sampling, based on probability theory. In this form of random sampling, every element of the population being sampled has an equal probability of being selected. In a random sample of a class of 50 students, for example, each student has the same probability, 1/50, of being selected. Every combination of elements drawn from the population also has an equal probability of being selected. Sampling based on probability theory allows the investigator to determine the likelihood that statistical findings are the result of chance. More commonly used methods, refinements of this basic idea, are stratified sampling (in which the population is divided into classes and simple random samples are drawn from each class), cluster sampling (in which the unit of the sample is a group, such as a household), and systematic sampling (samples taken by any system other than random choice, such as every 10th name on a list).

An alternative to probability sampling is judgment sampling, in which selection is based on the judgment of the researcher and there is an unknown probability of inclusion in the sample for any given case. Probability methods are usually preferred because they avoid selection bias and make it possible to estimate sampling error (the difference between the measure obtained from the sample and that of the whole population from which the sample was drawn).

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inference

statistics
Also known as: statistical inference

inference, in statistics, the process of drawing conclusions about a parameter one is seeking to measure or estimate. Often scientists have many measurements of an object—say, the mass of an electron—and wish to choose the best measure. One principal approach of statistical inference is Bayesian estimation, which incorporates reasonable expectations or prior judgments (perhaps based on previous studies), as well as new observations or experimental results. Another method is the likelihood approach, in which “prior probabilities” are eschewed in favour of calculating a value of the parameter that would be most “likely” to produce the observed distribution of experimental outcomes.

In parametric inference, a particular mathematical form of the distribution function is assumed. Nonparametric inference avoids this assumption and is used to estimate parameter values of an unknown distribution having an unknown functional form.

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