心理学常用效应量的选用与分析

1、DOI: 10.3724/SPJ .1042.2011.018682011. Vol. 19. No. 12. 1868-1878Advances in Psychological Science心理学常用效应量的选用与分析*郑昊敏I温忠麟I吴艳2C510631） （2,510420）摘 要 效应童在童化方面弥补了零假设检絵的不足.除了报告检验结果外许多期刊还要求在研究报告中包括效应童.效应量可以分为三大类别：差异类、和关类和俎査叠类.它们在不同的研究没计（如单因素机$因素祿试间.被试内和泯合实脸设计）或在不同的软据条件下（如小样本.方差异质等）可能有不同的计算方法和用法.但许多牧应童可以和互

2、转换。我们梳理出一个农格有功应用工作者根据研究目的和研究类型选用合适的效应旻关键词 牧应童；担异；和关；纽重业分类号 B841.2(effect size)(,Wilkinson& Task Force on Statistical Inference. 1999; APA. 2001; Rosnow & RosenthaL 2003. 2009)(Ruscio. 2008)(Kirk. 1996);(Hunter & Schmidt. 2004);(Cohen. 1988)(2010)(2011)(Lipsey& Wilson, 2000)(1)(differ

3、ence-type), (2)(correlation-type ). (3)(group-overlaph1(R21效应帛的类型(Snyder & Lawson. 1993),:2010-11-10(30870784)(11JJD190005): Email: wenzl1868(Glass, 1976).1 21869表1效应呈分类Cohen d . Glass AHedge gr 怙 rh9 Cramer V/rntfAflImprovemenl-Over-Chance indexIrf. R2. rf, ar. r2效应最的计算2.1差异类效应星(3)(3)(3)(3)(q-l

4、)s：+(2T)s；人 nl + ft2Spooled(1) Cohen d,Cohen (1969) Glass (1976)2.1.1单因素实验设计(3)(3)(contrast, Keppel & Wickenst 2004; Kline. 2004;Bonett. 200&, 2006) if/ =+ + c匕J “ i / =Cj + + cj = 0,a bc儿一 “b( Olcjnik &Algina. 2000)6 = if/a(1)a(pooled standard deviation)Cohen (1969) dCohen d( ),Cohen (1

5、969) d=02 d=05d=08,58% 69%79%14.7% 33.0%47.4% .Cohen0.05,( Thompson, 2001).(3)(3) Hedges gS =(yi-y2)/s pooled(3)(3)1969)Hedges (1981) g , spo<>ld(Cohen,(MSE)(3)(2)(Hedges, 1981)pooled(Wj _l)s+ + 仞 _1R-(”一 1)+(巧一 1)(3)187019187019Hi +n2 -2(7)A(al)(Bird. 2004)2B-Glass (a2);(bl).y 4ab.abl.a2b.alb

6、2(b2)(8)187019Glass 2ab(Rosenthal. 1991)刁（丘+几3）- =（兀如+元2b2）yab)187019187019(Vacha-Haase &厅（兀+%2引）一牙（兀3 +%2b2）（°）187019Thompson. 2004)(Glass MeGaw, &Smith. 1981)(Olejnik & Algina. 2000)(1)(Rosnow & Rosenthal. 2003), d5 Hedges Olkin (1985)c(n»)=I 一 -d ( ni = Wj +- 2 人4w-1(加=”

7、2 -1)2.1.2多因素实验设计(Olejnik & Algina. 2000).( ) () .(Olejnik &Algina. 2000) ，Spool祕() , (Cohen 1969:Glass, 1976; Hedges, 1981)SpOOl&q 2.1.1 ( © /) (hby),SpooXd187219SpooSd(fli ai)2.2相关类效应呈(Ferguson. 2009).(Cohen, 1969: Glass 1976: Hedges, 1981)Spool”Spool詔187219187219(Rosenthal. Rosno

8、w. & Rubin. 2000) ,(223)(Rosenthal et al.9 2000) ， d g(Rosnow &Rosenthal, 2003)2.2.1常用的相关系数指标 2006)187219187219(Olejnik & Algina, 2000)187219(1) r rFishcr-r. (Rosenthal1991)(2) pbrpbAlgina. 2000)2.1.3小结(Olejnik &(Cohen. 1965: Friedman, 1968),rpb=t2/(t2 + df)f2(11)It df - n-.df = ?i|+

9、 小2Cohen (1988),=0.010 安=0.059 rjb =0.138(3) Cramer VCramer VR2 (), rf( Pearson. 1905),2 (Kelly. 1935) ci (Hays. 1963)(1)用187219187219Z (Z(14) = lZ2M-l)P(12),k(2006)(4) 0(Phi)(Cohen. 1965: Friedman. 1968)(13)p ，hn0= Z/>/w(5)(Rosenthal & Rubin. 2(X)3) P :Wang Thompson (2007)R,Ezekiel (1930) 一(

10、一1)/( y1 川 1 2?". fi,vCohen (1969)f1尸=(R爲-R；)/(1_K着)B,A,略A B,，略 R；BCohen (1969)0.02 0.150.35(2) “2, G rrr187219187219(15)df t； 2 df = n_k. df = n-2; aunlenf，'mun伽r2.2.2方差比效应呈，rr(Maxwell, Camp. & Arvey. 1981).,R2 Haysjer er,Hulleit. 2002) r dOlcjnik Algina (2000)(omnibus)P or Kelly P rf

11、(Levine & rf R2(contrast)187219187219SPSSOmnibusOmnibus(Thompson. 2002)(variance-accountedfbr indices).1873(20)ContrastContrastM+“22“3=°(2.1.1 ) ( )(2.2.3) Omnibusif d iSSqCc+SS.EFSSgzHpartial effect effect + error) Contrastrf ar rContrast (Olejnik & Algina. 2000)187318737= contract Ito

12、talSSC5tr加-MS”SSggSSgntrgLMSbrsSS翻 + MS”.”(21)(22)(23)1873,2002) contrazt(16)Iclaszical =totalSdazsKal = I SSffy _X J<rror /total) Contrastconrrtizf/(SSg+SS”)2.2.3其他相关类效应呈classical _SS如-畑 xMS” /SS罰 + MS” (intraclass correlationRosenthal Rosnow (1984)3coitrazt aUrnngContrastcoefficient)Rosenthal &

13、amp; Rosnow.1985;丿(MS如-叫”)SSggi + MS©阳(19)Rosenthal el al. 2000; Rosnow & RosenlhaL 198&1996.2003. 2009(5习+句刃) c /Hi +c；/u；1873(1)alrnng(alerting conelation)falrring lconrrajr1於昭、血(24)SPSSContrasttr . h;,rj2 (Cohen, 1973;Haase. 1983; Kennedy. 1970),n2 rf;，rrltri(2) cantrazt(contrast cor

14、relation)'conrraztContrastffarffrcontrast187419(effect size correlation)187419lconrrasr q ss翻(26)( Rosnow & Rosenthal, 2009),F, 1(d)Huberty Lowman (2000) (classification analysis),(error rate). I(Improvement-Over-Chance index)(hit-rate.)187419187419/2=疋/(1“),1 F2.2.4小结(APA 2001)(27)HeHuberty

15、 (1994)(28)«Vg g叫gH。4(1 )Huberty (1994)(,leave-one-out(L-O-O),(2)(PDA), (3)(PDA)(4)Logistic(LRA)LRAPDA187419(Rosnow &Rosenthal. 1988),SPSS(Huberty & Holmes. 1983; Huberty& Lowman. 2000: Hess. Olejnik. & Huberty, 2001;Natesan & Thompson. 2007)187419187419Rosenthal3效应最的相互转换Con

16、trast (1984)2.3 组重叠(groiipowlap)效应Mf Z(1)(3.2)3.1旅g值与值之间的互相转换(group-overlap)dg1875Rosenthal & Rosnow.dV2+4(Cohen. 1977),r=(I) td.(Cohen .1965;1991) t = dy/dfnl + n2妙=5 + n2 一 2(Rosenthal,1991)(3) g (Rosenthal & Rosnow, 1991)3.2 r值与f、F、/、z、d、g与之间的转换(1) / Z2 r(10(13)(14).(Cohen, 1965; Friedman

17、. 1968)(2) Fr ,(4) grr=J , /叽 ， 汗W2 y g'nI/72 + (nI+n2 )df(Rosenthal. 1991)3.3其他效应星之间的转换Cohen (1965)if Ff2 =F(k-)/F(k-)+(n-k)(29)k=2 . tf瘍PetersVan Voorhis(1940)2FX =(F-l)(k-l)/F 伙-1) + (”")(30)arF(Fleiss. 1969)6)2 = (F -1)( Ar - 1)/(F -)(k -) + n(31),k9 n(1)1875(1)1875Y凡-)+始"F (Cohen.

18、 1965: Friedman, 1968)(3) dr pf 4结语(1)1875(1)1875lj2+I pq表2效应星一览表tCohen d Glass Hedge g ;()t股gm； Contrastif. ” edm”(Omnibus) :/>2 y<y rFA几八0rCramer V()厂=（喷&；）/（1-尺缶）卅 /2=r2/(_r2)Contrast(1)187619187619Spoobd(2)(1984)3Ominibus.RosenthalRosnow(2.239Vacha-HaaseThompson (2004)SPSS“opliotT,SPSS

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