心理學常用效應量的選用與分析

1、DOI: 10.3724/SPJ .1042.2011.018682011. Vol. 19. No. 12. 1868-1878Advances in Psychological Science心理學常用效應量的選用與分析*鄭昊敏I溫忠麟I吳艷2C510631） （2,510420）摘 要 效應童在童化方面彌補了零假設檢絵的不足.除了報告檢驗結果外許多期刊還要求在研究報告中包括效應童.效應量可以分為三大類別：差異類、和關類和俎査疊類.它們在不同的研究沒計（如單因素機$因素祿試間.被試內和泯合實臉設計）或在不同的軟據條件下（如小樣本.方差異質等）可能有不同的計算方法和用法.但許多牧應童可以和互

2、轉換。我們梳理出一個農格有功應用工作者根據研究目的和研究類型選用合適的效應旻關鍵詞 牧應童；擔異；和關；紐重業(yè)分類號 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效應帛的類型(Snyder & Lawson. 1993),:2010-11-10(30870784)(11JJD190005): Email: wenzl1868(Glass, 1976).1 21869表1效應呈分類Cohen d . Glass AHedge gr 怙 rh9 Cramer V/rntfAflImprovemenl-Over-Chance indexIrf. R2. rf, ar. r2效應最的計算2.1差異類效應星(3)(3)(3)(3)(q-l

4、)s：+(2T)s；人 nl + ft2Spooled(1) Cohen d,Cohen (1969) Glass (1976)2.1.1單因素實驗設計(3)(3)(contrast, Keppel & Wickenst 2004; Kline. 2004;Bonett. 200&, 2006) if/ =+ + c匕J “ i / =Cj + + cj = 0,a bc兒一 “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+幾3）- =（兀如+元2b2）yab)187019187019(Vacha-Haase &廳（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多因素實驗設計(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相關類效應呈(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常用的相關系數指標 2006)187219187219(Olejnik & Algina, 2000)187219(1) r rFishcr-r. (Rosenthal1991)(2) pbrpbAlgina. 2000)2.1.3小結(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著)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方差比效應呈，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其他相關類效應呈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©陽(19)Rosenthal el al. 2000; Rosnow & RosenlhaL 198&1996.2003. 2009(5習+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小結(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效應最的相互轉換Con

16、trast (1984)2.3 組重疊(groiipowlap)效應Mf Z(1)(3.2)3.1旅g值與值之間的互相轉換(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值與f、F、/、z、d、g與之間的轉換(1) / Z2 r(10(13)(14).(Cohen, 1965; Friedman

17、. 1968)(2) Fr ,(4) grr=J , /嘰 ， 汗W2 y g'nI/72 + (nI+n2 )df(Rosenthal. 1991)3.3其他效應星之間的轉換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結語(1)1875(1)1875lj2+I pq表2效應星一覽表tCohen d Glass Hedge g ;()t股gm； Contrastif. ” edm”(Omnibus) :/>2 y<y rFA幾八0rCramer V()廠=（噴&；）/（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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