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Type I error (or, error of the first kind)and Type II error (or, error of the second kind) are precise technical termsused in statistics to describe particular flaws in a testing process, where a true null hypothesis was incorrectlyrejected (Type I error) or where one fails to reject a false null hypothesis (Type IIerror).
The terms are also used in a more generalway by social scientists and others to refer to flaws in reasoning. Thisarticle is specifically devoted to the statistical meanings of those terms andthe technical issues of the statistical errors that those terms describe.
Statistical test theory
In statistical test theory the notion ofstatistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a nullhypothesis, which usually corresponds to a default "state ofnature", for example "this person is healthy", "thisaccused is not guilty" or "this product is not broken". An alternative hypothesis is the negation of null hypothesis,for example, "this person is not healthy", "this accused isguilty" or "this product is broken". Theresult of the test may be negative, relative to null hypothesis (nothealthy, guilty, broken) or positive (healthy,not guilty, not broken). If the result of the test corresponds with reality,then a correct decision has been made. However, if the result of the test doesnot correspond with reality, then an error has occurred. Due to the statistical nature of a test, the result is never,except in very rare cases, free of error. Two types of error are distinguished: type I error andtype II error.
Type I error
A type I error, alsoknown as an error of the first kind, is the wrong decision that is made when atest rejects a true null hypothesis (H0) （弃真错误）. A type I error may be compared with a so called falsepositive in other test situations. Type I error can be viewed as the error ofexcessive scepticism.
The rate of the type Ierror is called the size of the test and denoted by the Greek letter (alpha.Type I error = 
). It usually equals the significance level of a test. In thecase of a simple null hypothesis is the probability of a type I error. If thenull hypothesis is composite, is the maximum (supremum) of the possibleprobabilities of a type I error.
Type II error （纳伪）
A type II error, also known as an error ofthe second kind, is the wrongdecision that is made when a test fails to reject a false null hypothesis. A type II error may becompared with a so-called falsenegative in other test situations. Type II error can be viewed as the error of excessive credulity.
Therate of the type II error is denoted by the Greek letter (beta) and related tothe power of a test (which equals).
Whatwe actually call type I or type II error depends directly on the nullhypothesis. Negation of the nullhypothesis causes type I and type II errors to switch roles.
Thegoal of the test is to determine if the null hypothesis can be rejected. Astatistical test can either reject (prove false) or fail to reject (fail toprove false 就是TYPE TWO ERROR) a null hypothesis, but never prove it true (i.e., failing to reject a null hypothesis does not prove it true).
| Null hypothesis (H0) is true | Null hypothesis (H0) is false | |
Reject null hypothesis | Type I error | Correct outcome |
Fail to reject null hypothesis | Correct outcome | Type II error |
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