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In biological research, experiments or tests are often used to study predicted causal relationships between two phenomena. [1] These causal relationships may be described in terms of the logical concepts of necessity and sufficiency. Consider the statement that a phenomenon x causes a phenomenon y.
For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant. Mathematically speaking, necessity and sufficiency are dual to one another.
Necessary condition analysis (NCA) is a research approach and tool employed to discern "necessary conditions" within datasets. [1] These indispensable conditions stand as pivotal determinants of particular outcomes, wherein the absence of such conditions ensures the absence of the intended result.
Once the sample mean is known, no further information about μ can be obtained from the sample itself. On the other hand, for an arbitrary distribution the median is not sufficient for the mean: even if the median of the sample is known, knowing the sample itself would provide further information about the population mean. For example, if the ...
Pages in category "Necessity and sufficiency" The following 5 pages are in this category, out of 5 total. This list may not reflect recent changes. ...
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the ...
Sufficiency: the solution pair , (,) satisfies the KKT conditions, thus is a Nash equilibrium, and therefore closes the duality gap. Necessity: any solution pair x ∗ , ( μ ∗ , λ ∗ ) {\displaystyle x^{*},(\mu ^{*},\lambda ^{*})} must close the duality gap, thus they must constitute a Nash equilibrium (since neither side could do any ...
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. [1] The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the data only through a complete , sufficient statistic is the unique ...