In statistics, in the theory relating to sampling from finite populations, the inclusion probability of an element or member of the population is its probability of becoming part of the sample during the drawing of a single sample.
Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the "first-order inclusion probability" to distinguish it from the "second-order inclusion probability", i.e. the probability of including a pair of elements.
Generally, the first-order inclusion probability of the ith element of the population is denoted by the symbol πi and the second-order inclusion probability that a pair consisting of the ith and jth element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by πij.
- Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, ISBN 0-387-40620-4