效应值

在統計學中，效應值（英語：effect size，或譯效果量）是量化現象強度的數值。效應值實際的統計量包括了兩個變數間的相關程度、迴歸模型中的迴歸係數、不同處理間平均值的差異……等等。無論哪種效應值，其絕對值越大表示效應越強，也就是現象越明顯。效應值與特效检验的概念是互補的。在估算統計檢定力、需要的樣本數（英语：Sample size）與進行元分析時，效應值經常扮演重要角色。 在研究結果中給出效應值被視為恰當的或必須的。相對於統計學上的顯著性，效應值有利於了解研究結果的強度。特別是在社會科學和醫學研究上，效應值更顯得重要。絕對與相對效應值可以傳遞不同的訊息，又可互相補充訊息。有個心理學的研究學會鼓勵學者給出效應值： 報告主要結果時必須一併報導效應值……如果測量值的單位在實際面上是有意義的（例如每人每日抽煙的香煙根數），則我們建議採用非標準化的效應值（例如迴歸係數或平均值差異）而不是標準化的效應值（例如相關係數）。 —  L. Wilkinson and APA Task Force on Statistical Inference (1999, p. 599) 在比較平均數的情況下，效應值經常指的就是實驗結束後，實驗組與對照組之間「標準化後的平均差異程度」，依照慣例，效應值可解讀為以下幾個程度： Kelley, Ken; Preacher, Kristopher J. On Effect Size. Psychological Methods. 2012, 17 (2): 137–152. doi:10.1037/a0028086.  Wilkinson, Leland; APA Task Force on Statistical Inference. Statistical methods in psychology journals: Guidelines and explanations. American Psychologist. 1999, 54 (8): 594–604. doi:10.1037/0003-066X.54.8.594.  引文使用过时参数coauthors (帮助) Nakagawa, Shinichi; Cuthill, Innes C. Effect size, confidence interval and statistical significance: a practical guide for biologists. Biological Reviews Cambridge Philosophical Society. 2007, 82 (4): 591–605. PMID 17944619. doi:10.1111/j.1469-185X.2007.00027.x.  Ellis, Paul D. The Essential Guide to Effect Sizes: An Introduction to Statistical Power, Meta-Analysis and the Interpretation of Research Results. United Kingdom: Cambridge University Press. 2010.  Charach A, Dashti B, Carson P, et al. Attention deficit hyperactivity disorder: Effectiveness of treatment in at-risk preschoolers; long-term effectiveness in all ages; and variability in prevalence, diagnosis, and treatment. AHRQ Publication No. 12-EHC003, Agency for Healthcare Research and Quality, 2011. Cohen, Jacob. Statistical Power Analysis for the Behavioral Sciences. Routledge. 1988 [2019-03-29]. ISBN 978-1-134-74270-7. （原始内容存档于2019-08-11）.  Aaron, B., Kromrey, J. D., & Ferron, J. M. (1998, November). Equating r-based and d-based effect-size indices: Problems with a commonly recommended formula. Paper presented at the annual meeting of the Florida Educational Research Association, Orlando, FL. (ERIC Document Reproduction Service No. ED433353) Bonett, D. G. Confidence intervals for standardized linear contrasts of means. Psychological Methods. 2008, 13: 99–109. doi:10.1037/1082-989x.13.2.99.  Bonett, D. G. Estimating standardized linear contrasts of means with desired precision. Psychological Methods. 2009, 14: 1–5. doi:10.1037/a0014270.  Brooks, M.E.; Dalal, D.K.; Nolan, K.P. Are common language effect sizes easier to understand than traditional effect sizes?. Journal of Applied Psychology. 2013. doi:10.1037/a0034745.  Cumming, G.; Finch, S. A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement. 2001, 61: 530–572.  Imdadullah, M. (2014). Effect Size for dependent Sample t test. itfeature.com document on Effect Size for dependent Sample t test （页面存档备份，存于互联网档案馆） Kelley, K. Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software. 2007, 20 (8): 1–24 [2016-11-14]. （原始内容存档于2015-09-13）.  Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. Sage: Thousand Oaks, CA. Sawilowsky, Shlomo S. (2003). A Different Future For Social And Behavioral Science Research, Journal of Modern Applied Statistical Methods, Vol 2(1), 128-132. 維基學院中的相關研究或學習資源：效应值 線上應用 Copylefted Effect Size Confidence Interval R Code with RWeb service for t-test, ANOVA, regression, and RMSEA Online calculator for computing different effect sizes like Cohen's d, r, q, f, d from dependent t tests and transformation of different measures of effect size （页面存档备份，存于互联网档案馆）