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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Statistical proof ： ウィキペディア英語版 Statistical proof Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypothesis, the experimental data, the facts, the test, and the odds. Proof has two essential aims: the first is to convince and the second is to explain the proposition through peer and public review. The burden of proof rests on the demonstrable application of the statistical method, the disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world. There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelihood function, or positivism versus critical rationalism. These methods of reason have direct bearing on statistical proof and its interpretations in the broader philosophy of science.〔 A common demarcation between science and non-science is the hypothetico-deductive proof of falsification developed by Karl Popper, which is a well-established practice in the tradition of statistics. Other modes of inference, however, may include the inductive and abductive modes of proof. Scientists do not use statistical proof as a means to attain certainty, but to falsify claims and explain theory. Science cannot achieve absolute certainty nor is it a continuous march toward an objective truth as the vernacular as opposed to the scientific meaning of the term "proof" might imply. Statistical proof offers a kind of proof of a theory's falsity and the means to learn heuristically through repeated statistical trials and experimental error.〔 Statistical proof also has applications in legal matters with implications for the legal burden of proof. == Axioms == There are two kinds of axioms, 1) conventions that are taken as true that should be avoided because they cannot be tested, and 2) hypotheses. Proof in the theory of probability was built on four axioms developed in the late 17th century: #The probability of a hypotheses is a non-negative real number: $\backslash bigg\backslash$; #The probability of necessary truth equals one: $\backslash bigg\backslash$; #If two hypotheses h1 and h2 are mutually exclusive, then the sum of their probabilities is equal to the probability of their disjunction: $\backslash bigg\backslash$; #The conditional probability of h1 given h2 $\backslash Bigg\backslash$ is equal to the unconditional probability $\backslash bigg\backslash$ of the conjunction h1 and h2, divided by the unconditional probability $\backslash bigg\backslash$ of h2 where that probability is positive $\backslash bigg\backslash \; \backslash bigg\backslash \}$, where $\backslash bigg\backslash$. The preceding axioms provide the statistical proof and basis for the laws of randomness, or objective chance from where modern statistical theory has advanced. Experimental data, however, can never prove that the hypotheses (h) is true, but relies on an inductive inference by measuring the probability of the hypotheses relative to the empirical data. The proof is in the rational demonstration of using the logic of inference, math, testing, and deductive reasoning of significance.〔〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Statistical proof」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.