sufficiencia

Sufficiencia, sufficienza or sufficiency refers to the state or condition of being adequate or enough to meet a need or purpose. The term derives from Latin sufficere, “to suffice.” In everyday language it describes a level of resources, evidence, or capability that is enough to achieve a goal, without implying exclusivity or optimality. It is important to distinguish sufficiency from necessity: something can be sufficient without being required, and something can be necessary without being sufficient.

In logic and philosophy, a condition A is a sufficient condition for an outcome B if, whenever A holds, B must occur. However, A being sufficient does not exclude other conditions that could also cause B. A classic example is: having a key is a sufficient condition for opening a locked door, assuming the key fits; other keys or methods might also open the door, or B could occur by alternative routes.

In statistics, sufficiency has a precise formal meaning. A statistic T(X) is sufficient for a parameter θ if the data X, given T(X), provide no additional information about θ. The Fisher–Neyman factorization theorem characterizes this property. A common example is that, for data from a normal distribution with known variance, the sample mean (and hence the sample sum) is a sufficient statistic for the population mean.

Sufficiency also appears in policy, economics, and social sciences when discussing whether resources, evidence, or standards are adequate to meet needs or objectives. See also: sufficient condition, sufficient statistic, and sufficiency in various disciplines.