Sufficient

Sufficient is an adjective meaning adequate or enough to meet a need or purpose. In everyday usage, phrases such as sufficient funds or sufficient evidence are common. In technical contexts the term takes on specific meanings in logic and statistics, among other fields. The related noun sufficiency is used to denote the quality of being sufficient.

Etymology: The word derives from Latin sufficientem, from sufficere, meaning to meet a need or to be adequate.

In logic and philosophy, a condition is said to be sufficient for a given result if, whenever the condition holds, the result follows. It is not, however, required; a result may still occur by other means. A famous distinction within such reasoning is between sufficient conditions and necessary conditions: a condition can be sufficient without being necessary, and vice versa. For example, turning a lock with a key is a sufficient condition to open a door, but not the only possible way to open it.

In statistics, sufficiency refers to information: a statistic is sufficient for a parameter if the observed data provide no additional information about the parameter beyond the statistic. More formally, T(X) is sufficient for theta if the joint distribution of the sample X, given T(X), does not depend on theta. The Fisher–Neyman factorization theorem gives a practical criterion. Common examples include the sample sum for a Bernoulli or binomial model, and the sample mean for a normal model with known variance. A minimal sufficient statistic is a smallest data reduction that preserves all information about theta.

See also: necessary condition, sufficiency, sufficient statistic, factorization theorem.