型一錯誤與型二錯誤

型一錯誤型二錯誤(英語:Type I error & Type II error)為统计学推論統計學統計術語,表示統計學假說檢定中的两种錯誤。

簡介

假說檢定中,有一種假說稱為“零假设”,記為,假說检验的目的是利用統計的方式,推翻虛無假說的成立,也就是對立假說(Alternative hypothesis,記為)成立。

假說檢定涉及選擇兩個相互競爭的命題,稱為零假設(Null hypothesis),用H0表示,另一種對立假說(Alternative hypothesis),用H1表示。

如果測試結果與現實相符,則做出了正確的決定。但是,如果測試結果與實際不符,則發生錯誤。發生錯誤的情況有兩種:零假設為真,而我們拒絕H0。 另一方面,對立假說H1為真,而我們不拒絕H0。 兩種錯誤分別稱為:型一錯誤、型二錯誤[1]

  • 若零假设事實上成立,但統計檢驗的結果拒絕零假设(接受對立假說),這種錯誤稱為型一錯誤
  • 若零假设事實上不成立,但統計檢驗的結果不拒絕零假设,這種錯誤稱為型二錯誤[2]
真實情況
(虛無假說)為真 (對立假說)為真
根據研究結果的判斷 拒絕 錯誤判斷
偽陽性型一錯誤
發生機率α(顯著水準
正確判斷
發生機率1-β(檢定力
不拒絕 正確判斷
發生機率1-α
錯誤判斷
偽陰性型二錯誤
發生機率β

舉例

  • 概念上類似於法庭審判中的判決。零假設對應於被告的立場:正如他在被證明有罪之前被假定為無罪一樣,在數據提供反對它的令人信服的證據之前,零假設也被假定為真。 對立假說對應於反對被告的立場。 具體來說,零假設還涉及不存在差異或不存在關聯。
  • 以利用驗孕棒驗孕為例,此時沒有懷孕為零假设。若用驗孕棒替一位未懷孕者驗孕,結果呈已懷孕,此即型一錯誤。若用驗孕棒替一位已懷孕者驗孕,結果呈未懷孕,此即型二錯誤。

交叉錯誤率

交叉錯誤率 (CER) 是型一錯誤和型二錯誤相等的點,代表了衡量生物識別有效性的最佳方法。 具有較低CER值的系統比具有較高CER值的系統提供更高的準確度。[來源請求]

偽陽性和偽陰性

在偽陽性和偽陰性方面,陽性結果對應於拒絕零假设,而陰性結果對應於未能拒絕零假设; “偽”表示得出的結論不正確。 因此,型一錯誤相當於偽陽性,型二錯誤相當於偽陰性。[來源請求]

參考

  1. ^ A modern introduction to probability and statistics : understanding why and how. Dekking, Michel, 1946-. London: Springer. 2005. ISBN 978-1-85233-896-1. OCLC 262680588. 
  2. ^ cheng, ayo. 型一錯誤 型二錯誤. myweb.nutn.edu.tw. [2012-02-10]. (原始内容存档于2011-12-16). 

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