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The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H 1, H 2, ..., H m. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant.
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between and should not depend on the quality of a third, unrelated outcome . There are several different variations of this axiom, which are generally equivalent under mild conditions.
This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses. Rejection of the null hypothesis is not necessarily the real goal of a significance tester. An adequate statistical model may be associated with a failure to reject the null; the model is adjusted until the null ...
Causality is not necessarily one-way; [dubious – discuss] in a predator-prey relationship, predator numbers affect prey numbers, but prey numbers, i.e. food supply, also affect predator numbers. Another well-known example is that cyclists have a lower Body Mass Index than people who do not cycle.
Arrow's theorem is not related to strategic voting, which does not appear in his framework, [3] [1] though the theorem does have important implications for strategic voting (being used as a lemma to prove Gibbard's theorem [15]). The Arrovian framework of social welfare assumes all voter preferences are known and the only issue is in ...
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In the existential fallacy, one presupposes that a class has members when one is not supposed to do so; i.e., when one should not assume existential import. Not to be confused with the 'Affirming the consequent', as in "If A, then B. B. Therefore A". One example would be: "Every unicorn has a horn on its forehead". It does not imply that there ...
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