# Probability Sampling

### Definition

probability sample is a sample in which each population element has a known, nonzero chance of being included.

simple random sample is a probability sample in which each population element has a known and equal chance of being included in the sample and in which every combination of n population elements is a sample possibility and is just as likely to occur as any other combination of n units.

A cluster sample is a probability sample distinguished by a two-step procedure in which 1) the parent population is divided into mutually exclusive and exhaustive subsets, and 2) a random sample of subsets is selected. If the investigator then uses all of the population elements in the selected subsets for the sample, the procedure is one-stage cluster sampling. If a sample of elements is selected probabilistically from the subsets, the procedure is two-stage cluster sampling.

Area sampling is a form of cluster sample in which areas (i.e. census tracts, blocks) serve as the primary sampling units. The population is divided into mutually exclusive and exhaustive areas using maps, and a random sample of areas is selected. If all the households in the selected areas are used in the study, it is one-stage area sampling. If the areas are sub-sampled with respect to households, the procedure is two-stage area sampling.

stratified sample is a probability sample that is distinguished by the two-step procedure in which 1) the parent population is divided into mutually exclusive and exhaustive subsets, and 2) a simple random sample of elements is chosen independently from each group or subset.

systematic sample is a probability sample in which every kth element in the population is designated for inclusion in the sample after a random start.