統(tǒng)計測驗的效力(Power of the Test)
在四種可能的假設(shè)測驗結(jié)果中,每種結(jié)果都依賴于本質(zhì)的真實狀態(tài)和測驗結(jié)論(Every hypothesis test results in one of four possible outcomes depending on the true state of nature and the outcome of the test),如下表所示:
真狀態(tài)(True State)
| 測驗結(jié)果(Test Result)
| 錯誤類型(Type of Error)
| 本質(zhì)(of Nature)
|
|
| 無效假設(shè)為真(Null hypothesis true)
| 不否定(Not rejected)
| 無誤(No error)
| 無效假設(shè)為真(Null hypothesis true)
| 否定(Rejected)
| I類錯誤(Type I error)
| 無效假設(shè)為假(Null hypothesis false)
| 不否定(Not rejected)
| II類錯誤(Type II error)
| 無效假設(shè)為假(Null hypothesis false)
| 否定(Rejected)
| |
當(dāng)無效假設(shè)為真而被否定時發(fā)生I類錯誤Type I errors occur when the null hypothesis is rejected even though it is true),當(dāng)無效假設(shè)為假而不否定時發(fā)生第II類錯誤(Type II errors occur when the null hypothesis is not rejected when it is false)。根據(jù)每類錯誤的風(fēng)險(Depending on the risks associated with each type of error),我們能最小化類型I或類型II的錯誤(then either Type I or Type II errors can be minimized)。例如,如果假設(shè)是動物沒某種疾病而動物真的是沒這種?。╥f the hypothesis is that an animal does not have a disease and the animal does not have the disease),那么否決假設(shè)(I類錯誤)會導(dǎo)致動物被按這種病治療(then rejection of the hypothesis (Type I error) results in the animal being treated for the disease)。這可能很費錢并且還可能要做外科手術(shù)(This could be very costly and might involve surgery),或者成本很小而對動物沒傷害(or the treatment could be minimal in cost and without harmful effects on the animal)。另一方面(On the other hand),如果動物真有該病而沒否決假設(shè)(if the animal really does have the disease and the hypothesis is not rejected)(II類錯誤)(Type II error),那么動物也許不被治療(then the animal would not be treated)。不治療的代價也許是動物死亡(The cost of no treatment might be death of the animal)。
測驗的效力是1減去II類錯誤的概率(The Power of the Test is 1 minus the probability of a Type II error)。如果II類錯誤能夠?qū)е滤劳鰮p失或沉重的財政損失(If a Type II error results in death loss or heavy financial loss),那么研究人員就該使用很高的測驗效力(then the researcher should use a very high Power of the Test)。在臨床研究中測驗效力是很重要的(The Power of the Test is important in clinical studies),但是對動物繁育研究的田間數(shù)據(jù)來說并不那么嚴(yán)格(but not as critical in animal breeding research on field data)
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[ 本帖最后由 牧童 于 2007-9-8 12:25 編輯 ] |