# Weighted Sample

**DOI:**https://doi.org/10.1007/978-1-4614-6439-6_1082-2

## Definition

In a weighted sample, not all sample observations contribute equally to the estimate of a population parameter.

Investigators are often interested in estimating quantities (such as means, counts, or proportions) in a population by using a representative sample selected from that population. Probability samples, defined as samples in which each sampling unit has a known, nonzero probability of selection based on the sampling design, allow investigators to compute estimates of population parameters. The most straightforward type of probability sampling design, a simple random sample (SRS), is a selection method in which each sample has the same probability of being selected. In an SRS, the probability of selection of each member in the population is the same.

*n =*sample size,

*N =*population size. Also, let {

*Y*

_{1}, …,

*Y*

_{N}} be the population values and {

*y*

_{1}, …,

*y*

_{n}} be the sample values. We define the...

## References and Further Reading

- Foreman, E. K. (1991).
*Survey sampling principles*. New York: M. Dekker.Google Scholar - Kish, L. (1965).
*Survey sampling*. New York: Wiley.Google Scholar - Korn, E. L., & Graubard, B. I. (1995). Examples of differing weighted and unweighted estimates from a sample survey.
*The American Statistician, 49*(3), 291–295.Google Scholar