心理測驗命中率與基本率之新結果

Some New Results on Hit Rates and Base Rates in Mental Testing

本文為最近有關命中率和基本率研究（Schönemann and Thompson, 1996）之延伸。文中修正了先前推導基本率近似值HRI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 (Schönemann 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 HR I and HR2 are small. After deriving exact hit rates for 2x2 contingency tables with binary criteria, they are compared with HR I and HR2. and also with hit rates for continuous criteria infer red, via Bayes' Theorem, from Taylor and Russell's (1939) table s. Overall, the simpler approximation HR I 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 in sufficient for gauging the practical merit of a test, be ca use, ' ... 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.