Sufficiencies

Sufficiencies refer to conditions or quantities that meet the required standard for a given purpose. In everyday use, something is sufficient if it satisfies the need, but it may not be excessive. In philosophy and logic, a sufficient condition for a proposition is one that, if true, guarantees the proposition, while a necessary condition is required for the proposition but may not be enough on its own. Distinguishing between sufficient and necessary conditions clarifies arguments and explanations.

In statistics, sufficiency has a precise meaning: a statistic is sufficient for a parameter if it preserves all information needed to compute the parameter from the data. The Fisher–Neyman factorization theorem provides a practical criterion: a statistic T(X) is sufficient for θ if the joint density can be factored as g(T(x), θ) h(x). Examples include the sample mean for normal distributions with known variance and certain exponential families.

In law and evidence, sufficiency describes whether the available evidence is adequate to support a conclusion or verdict. Standards vary by jurisdiction and context, but generally a decision requires evidence that would persuade a reasonable person under the applicable standard, such as a preponderance of the evidence or beyond a reasonable doubt.

In nutrition and medicine, sufficiency refers to meeting recommended dietary requirements or clinical thresholds for nutrients. An insufficiency indicates levels below those thresholds, potentially affecting health. Public health policies use the concept of sufficiency to set targets and assess population health.