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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.
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The majority of textbooks, research papers and articles (including English Wikipedia articles) follow the linguistic convention of interpreting "if" as "if and only if" whenever a mathematical definition is involved (as in "a topological space is compact if every open cover has a finite subcover"). [17]
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 ...
Causality, within sociology, has been the subject of epistemological debates, particularly concerning the external validity of research findings; one factor driving the tenuous nature of causation within social research is the wide variety of potential "causes" that can be attributed to a particular phenomena.
A related concept is that of linear sufficiency, which is weaker than sufficiency but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. [1] The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic.