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In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is the failure to reject a false null hypothesis (a "false negative"). More simply stated, a type I error is detecting an effect that is not present, while a type II error is failing to detect an effect that is present. The terms "type I error" and "type II error" are often used interchangeably with the general notion of false positives and false negatives in binary classification, such as medical testing, but narrowly speaking refer specifically to statistical hypothesis testing in the Neyman–Pearson framework, as discussed in this article. ==Definition== In statistics, a null hypothesis is a statement that one seeks to nullify with evidence to the contrary. Most commonly it is a statement that the phenomenon being studied produces no effect or makes no difference. An example of a null hypothesis is the statement "This diet has no effect on people's weight." Usually an experimenter frames a null hypothesis with the intent of rejecting it: that is, intending to run an experiment which produces data that shows that the phenomenon under study does make a difference. In some cases there is a specific alternative hypothesis that is opposed to the null hypothesis, in other cases the alternative hypothesis is not explicitly stated, or is simply "the null hypothesis is false" – in either event this is a binary judgment, but the interpretation differs and is a matter of significant dispute in statistics. A type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. Usually a type I error leads one to conclude that a supposed effect or relationship exists when in fact it doesn't. Examples of type I errors include a test that shows a patient to have a disease when in fact the patient does not have the disease, a fire alarm going off indicating a fire when in fact there is no fire, or an experiment indicating that a medical treatment should cure a disease when in fact it does not. A type II error (or error of the second kind) is the failure to reject a false null hypothesis. Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; a fire breaking out and the fire alarm does not ring; or a clinical trial of a medical treatment failing to show that the treatment works when really it does. In terms of false positives and false negatives, a positive result corresponds to rejecting the null hypothesis (or instead choosing the alternative hypothesis, if one exists), while a negative result corresponds to failing to reject the null hypothesis (or choosing the null hypothesis, if phrased as a binary decision); roughly "positive = alternative, negative = null", or in some cases "positive = null, negative = alternative", depending on the situation & requirements, though exact interpretation differs. In these terms, a type I error is a false positive (incorrectly choosing alternative hypothesis instead of null hypothesis), and a type II error is a false negative (incorrectly choosing the null hypothesis instead of the alternative hypothesis). When comparing two means, concluding the means were different when in reality they were not different would be a Type I error; concluding the means were not different when in reality they were different would be a Type II error. Various extensions have been suggested as "Type III errors", though none have wide use. All statistical hypothesis tests have a probability of making type I and type II errors. For example, all blood tests for a disease will falsely detect the disease in some proportion of people who don't have it, and will fail to detect the disease in some proportion of people who do have it. A test's probability of making a type I error is denoted by α. A test's probability of making a type II error is denoted by β. These error rates are traded off against each other: for any given sample set, the effort to reduce one type of error generally results in increasing the other type of error. For a given test, the only way to reduce both error rates is to increase the sample size, and this may not be feasible. These terms are also used in a more general way by social scientists and others to refer to flaws in reasoning.〔Cisco Secure IPS – Excluding False Positive Alarms http://www.cisco.com/en/US/products/hw/vpndevc/ps4077/products_tech_note09186a008009404e.shtml〕 This article is specifically devoted to the statistical meanings of those terms and the technical issues of the statistical errors that those terms describe. 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「Type I and type II errors」の詳細全文を読む スポンサード リンク
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