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In statistics, the ''p''-value is a function of the observed sample results (a statistic) that is used for testing a statistical hypothesis. More specifically, the ''p''-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, assuming that the hypothesis under consideration is true.〔Hubbard, R. (2004). Blurring the Distinctions Between p’s and a’s in Psychological Research, Theory Psychology June 2004 vol. 14 no. 3 295-327〕 Here, "more extreme" is dependent on the way the hypothesis is tested. Before the test is performed, a threshold value is chosen, called the significance level of the test, traditionally 5% or 1% and denoted as ''α''. If the ''p''-value is equal to or smaller than the significance level (''α''), it suggests that the observed data are inconsistent with the assumption that the null hypothesis is true and thus that hypothesis must be rejected (but this does not automatically mean the alternative hypothesis can be accepted as true). When the ''p''-value is calculated correctly, such a test is guaranteed to control the Type I error rate to be no greater than ''α''. Since ''p''-value is used in frequentist inference (and not Bayesian inference), it does not in itself support reasoning about the probabilities of hypotheses but is only as a tool for deciding whether to reject the null hypothesis. Statistical hypothesis tests making use of ''p''-values are commonly used in many fields of science and social sciences, such as economics, psychology, biology, criminal justice and criminology, and sociology.〔Babbie, E. (2007). The practice of social research 11th ed. Thomson Wadsworth: Belmont, California.〕 Misuse of this tool continues to be the subject of criticism. ==Basic concepts== The ''p''-value is used in the context of null hypothesis testing in order to quantify the idea of statistical significance of evidence. Null hypothesis testing is a reductio ad absurdum argument adapted to statistics. In essence, a claim is shown to be valid by demonstrating the improbability of the consequence that results from assuming the counter-claim to be true. As such, the only hypothesis that needs to be specified in this test and which embodies the counter-claim is referred to as the null hypothesis. A result is said to be statistically significant if it can enable the rejection of the null hypothesis. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis. However, unless there is a single alternative to the null hypothesis, the rejection of null hypothesis does not tell us which of the alternatives might be the correct one. For instance, if the null hypothesis is assumed to be a standard normal distribution N(0,1), the rejection of this null hypothesis can either mean (i) the mean is not zero, or (ii) the variance is not unity, or (iii) the distribution is not normal, depending on the type of test performed. However, supposing we manage to reject the zero mean hypothesis, the null hypothesis test does not tell us which non-zero value we should adopt as the new mean. In statistics, a statistical hypothesis refers to a probability distribution that is assumed to govern the observed data. If is a random variable representing the observed data and is the statistical hypothesis under consideration, then the notion of statistical significance can be naively quantified by the conditional probability , which gives the likelihood of the observation if the hypothesis is ''assumed'' to be correct. However, if is a continuous random variable and an instance is observed, Thus, this naive definition is inadequate and needs to be changed so as to accommodate the continuous random variables. Nonetheless, it helps to clarify that ''p''-values should not be confused with probability on hypothesis (as is done in Bayesian Hypothesis Testing) such as the probability of the hypothesis given the data, or the probability of the hypothesis being true, or the probability of observing the given data. 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「P-value」の詳細全文を読む スポンサード リンク
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