《统计学知识(一类错误和二类错误)》由会员分享，可在线阅读，更多相关《统计学知识(一类错误和二类错误)（15页珍藏版）》请在金锄头文库上搜索。
1、In statistics, the terms Type I error (also, a error, or false positive) and type II error(B error, or a false negative) are used to describe possible errors made in a statistical decision process. In 1928, Jerzy Neyman (1894-1981) and Egon Pearson (1895T980), both eminent statisticians, discussed t
2、he problems associated with deciding whether or not a particular sample may be judged as likely to have been randomly drawn from a certain population (1928/1967, p.1): and ide nti fied two sources of error, namely:(a ) the error of rejecting a correct null hypothesis, and(p ) the error of not reject
3、ing a false null hypothesisIn 1930, t hey elabora tedon t hese t wo sources of error, remarking that intesting hypo theses two considerations must bekept in view, (1) we must be able to reduce the chance of rejecting a true hypothesis to as low a value as desired; (2) the test must be so devised tha
4、t it will reject the hypothesis tested when it is likely to be falseEWhen an observer makes a Type I error in evaluating a sample against its parent population, s/he is mistakenly thinking that a statistical difference exists when in truth there is no statisti cal difference (or, to put anot her way
5、, the null hypo thesis is t rue but was mis takenly rejected). For example, imagine that a pregnancy test has produced a positive result (indica ting that the woman t aking the test is pregna nt); if the woman is actu ally not pregna nt though, then we say the test produced a false positive. A Type
6、II error, or a false negative, is the error of failing to reject a null hypothesis when the alternative hypothesis is the true state of nature. For example, a type II error occurs if a pregnancy test reports negative when the woman is, in fact, pregnant.Statistical error vs. systematic errorScientis
7、ts recognize two different sorts of error:芮 Statistical error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value (see errors and residuals in statistics) that is caused byrandon, and inherently unpredictable fluctuations in the me
8、asurement apparatus or the system being studied.m Systematic error: the difference between a computed, estimated, or measured value and the true, specified, or theoretically correct value that is caused by non-random fluctuations from an unknown source (seeuncertainty), and which, once identified, c
9、an usually be elimina ted.tsiStatistical error: Type I and Type IIStatisticians speak of two significant sorts of statistical error. The context is that there is a null hypothesis which corresponds to a presumed default state of nature, e.g., that an individual is free of disease, that an accused is
10、 innocent, or that a potential login candidate is not authorized. Corresponding to the null hypothesis is an alternative hypothesis which corresponds to the opposite situation, that is, that the individualhas the disease, that the accused is guilty, or that the login candidate is an authorized user.
11、 Thegoal is to determine accurately if the null hypothesis can be discarded in favor of the alternative. A test of some sort is conducted (a blood test, a legal trial, a login attempt), and data is obtained. The result of the test may be negative (that is, it does not indicate disease, guilt, or aut
12、horized identity). On the other hand, it may be positive (that is, it may indicate disease, guilt, or identity). If the result of the test does not correspond with the actual state of nature, then an error has occurred, but if the result of the test corresponds with the actual state of nature, then
13、a correct decision has been made. There are two kinds of error, classified as Type I error and Type II error, depending upon which hypo thesis has incorrectly been identified as the true state of nature.Type I errorType I error, also known as an error of the first kind, an a error, or a false positi
14、ve: the error of rejec ting a null hypo thesis when it is actu ally t rue. Plainly speaking, it occurs when we are observing a difference when in truth there is none. Type I error can be viewed as the error of excessive skepticism.Type II errorType II error, also known as an error of the second kind
15、, a B error, or a false negative： the error of failing to reject a null hypothesis when it is in fact false. In other words, this is the error of failing tobserve a difference when in truththere is one. Type II error can be viewed as the error of excessive gullibility.See Various proposals for furth
16、er extension, below, for additional terminology.Understanding Type I and Type II errorsHypothesis testing is theart of testing whether a variation between twosample distributions can be explained by chance or not. In many practical applications Type I errors are more delicate than Type II errors. In these cases, care is usually focused on minimizing the occurrence of this statistical error. Suppose, the probability f
