效应值
在统计学中，效应值（英语：effect size，或译效果量）是量化现象强度的数值。[1]效应值实际的统计量包括了两个变数间的相关程度、回归模型中的回归系数、不同处理间平均值的差异……等等。无论哪种效应值，其绝对值越大表示效应越强，也就是现象越明显。效应值与特效检验的概念是互补的。在估算统计统计功效、需要的样本数与进行元分析时，效应值经常扮演重要角色。
在研究结果中给出效应值被视为恰当的或必须的。[2][3]相对于统计学上的显著性，效应值有利于了解研究结果的强度。[4]特别是在社会科学和医学研究上，效应值更显得重要。绝对与相对效应值可以传递不同的讯息，又可互相补充讯息。有个心理学的研究学会鼓励学者给出效应值：
报告主要结果时必须一并报导效应值……如果测量值的单位在实际面上是有意义的（例如每人每日抽烟的香烟根数），则我们建议采用非标准化的效应值（例如回归系数或平均值差异）而不是标准化的效应值（例如相关系数）。
— L. Wilkinson and APA Task Force on Statistical Inference (1999, p. 599)
在比较平均数的情况下，效应值经常指的就是实验结束后，实验组与对照组之间“标准化后的平均差异程度”，依照惯例，效应值可解读为以下几个程度：
| 效应值 | d[5] | r[6] |
|---|---|---|
| 较小 | 0.2 | 0.10 |
| 中等 | 0.5 | 0.30 |
| 较大 | 0.8 | 0.50 |
参考文献
- ^ 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.
- ^ 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）.
延伸阅读
- 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.
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