本文為最近有關命中率和基本率研究（Schonemann and Thompson，1996）之延伸 。 文中修正了先前推導基本率近似值 HR1 時的錯誤前提，另提出稍較複雜之近似值 HR2。 然而在所探討的參數範圍內， HR1 與 HR2 間僅具些微差異。 本研究推導二分效標 2 × 2 列聯表的準確命中率，並將之與 HR1，HR2， 以及從泰羅二氏（ 1939 ）期望表經由貝氏定 理為連續效標推導之命中率三者比較。 整體而言，較簡單之近似值 HR1 的表現優於 HR2。 最後，本研究以整體正確分類百分比為考慮條件，推導出一個測驗若要比隨機甄選有效時， 所需要的最低效度近似值。 四十多年前，Meehl 與 Rosen （ 1955 ）即已提出警告：僅憑 效度係數本身並不足以評斷一個測驗在應用上的優劣，因為「當效標分類的基本率與百分之 五十偏離甚大時，使用一個具備中度或低度效度的測驗，將會導致錯誤臨床決定的增加」（ 原著 215 頁）。本研究結果呼應了此點關切。

　　　　　Recent work on hit rates and base rates (Schonemann and Thompson, 1996) is extended: A flawed premise in the derivation of an earlier hit rate approximation, HR1, is corrected, leading to a slightly more complicated approximation, HR2. However, over the targeted parameter region, the differences between HR1 and HR2 are small. After deriving exact hit rates for 2 × 2 contingency tables with binary criteria, they are compared with HR1 and HR2, and also with hit rates for continuous criteria inferred, via Bayes' Theorem, from Taylor and Russell's (1939) tables. Overall, the simpler approximation HR1 outperforms HR2. Finally, a new approximation is derived for the minimum validity needed that a test improves over random admissions in terms of total percent of correct classifications. More than four decades ago, Meehl and Rosen (1955) warned that validity coefficients, in isolation, are insufficient for gauging the practical merit of a test, because, "... when the base rates of the criterion classification deviate greatly from a 50 percent split, use of a test sign having slight or moderate validity will result in an increase of erroneous clinical decisions." (p. 215. Emphasis in the original). The present results corroborate these concerns.