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In inferential statistics the null hypothesis usually refers to a general statement or default position that there is no relationship between two measured phenomena, or no difference among groups. Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science, and gives a precise sense in which a claim can be proven false. The null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted ''H''0 (read “H-naught”, "H-null", or "H-zero"). The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected on the basis of data that is significantly unlikely if the null is true, but the null hypothesis is never accepted or proved. This is analogous to a criminal trial, in which the defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree). In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and the two hypotheses are distinguished on the basis of data, with certain error rates. Proponents of each approach criticize the other approach. Nowadays, though, a hybrid approach is widely practiced and presented in textbooks. The hybrid is in turn criticized as incorrect and incoherent—for details, see Statistical hypothesis testing. Statistical inference can be done without a null hypothesis, thus avoiding the criticisms under debate. An approach to statistical inference that does not involve a null hypothesis is the following: for each candidate hypothesis, specify a statistical model that corresponds to the hypothesis; then, use model selection techniques to choose the most appropriate model.〔.〕 (The most common selection techniques are based on either Akaike information criterion or Bayes factor.) ==Principle== Hypothesis testing requires constructing a statistical model of what the world would look like given that chance or random processes alone were responsible for the results. The hypothesis that chance alone is responsible for the results is called the ''null hypothesis''. The model of the result of the random process is called the ''distribution under the null hypothesis''. The obtained results are then compared with the distribution under the null hypothesis, and the likelihood of finding the obtained results is thereby determined.〔Stockburger D.W. (2007), "Hypothesis and hypothesis testing", ''Encyclopedia of Measurement and Statistics'' (editor—Salkind N.J.), Sage Publications.〕 Hypothesis testing works by collecting data and measuring how likely the particular set of data is, assuming the null hypothesis is true, when the study is on a randomly-selected representative sample. The null hypothesis assumes no relationship between variables in the population from which the sample is selected. If the data-set of a randomly-selected representative sample is very unlikely relative to the null hypothesis (defined as being part of a class of sets of data that only rarely will be observed), the experimenter rejects the null hypothesis concluding it (probably) is false. This class of data-sets is usually specified via a test statistic which is designed to measure the extent of apparent departure from the null hypothesis. The procedure works by assessing whether the observed departure measured by the test statistic is larger than a value defined so that the probability of occurrence of a more extreme value is small under the null hypothesis (usually in less than either 5% or 1% of similar data-sets in which the null hypothesis does hold). If the data do not contradict the null hypothesis, then only a weak conclusion can be made: namely, that the observed data set provides no strong evidence against the null hypothesis. In this case, because the null hypothesis could be true or false, in some contexts this is interpreted as meaning that the data give insufficient evidence to make any conclusion; in other contexts it is interpreted as meaning that there is no evidence to support changing from a currently useful regime to a different one. For instance, a certain drug may reduce the chance of having a heart attack. Possible null hypotheses are "this drug does not reduce the chances of having a heart attack" or "this drug has no effect on the chances of having a heart attack". The test of the hypothesis consists of administering the drug to half of the people in a study group as a controlled experiment. If the data show a statistically significant change in the people receiving the drug, the null hypothesis is rejected. 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「Null hypothesis」の詳細全文を読む スポンサード リンク
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