效應值

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。^[1]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。效應值與特效檢定的概念是互補的。在估算統計檢定力、需要的樣本數（英語：Sample size）與進行統合分析時，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。^[2][3]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。^[4]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遞移不同的訊息，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（例如每人每日抽菸的香菸根數），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：

效應值	d[5]	r[6]
較小	0.2	0.10
中等	0.5	0.30
較大	0.8	0.50

參考文獻

1. Kelley, Ken; Preacher, Kristopher J. On Effect Size. Psychological Methods. 2012, 17 (2): 137–152. doi:10.1037/a0028086.
2. 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. 引文使用過時參數coauthors (幫助)
3. 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.
4. 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.
5. 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.
6. Cohen, Jacob. Statistical Power Analysis for the Behavioral Sciences. Routledge. 1988 [2019-03-29]. ISBN 978-1-134-74270-7. （原始內容存檔於2019-08-11）.

延伸閱讀

• 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 （頁面存檔備份，存於網際網路檔案館）
• Kelley, K. Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software. 2007, 20 (8): 1–24 [2016-11-14]. （原始內容存檔於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.

外部連結

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 （頁面存檔備份，存於網際網路檔案館）