1、 SZ 2011, Vol. 19, No. 12, 18681878 Advances in Psychological Science DOI: 10.3724/SP.J.1042.2011.01868 1868 心理学常用效应量的选用与分析 * 1 1 2 ( 1 2 =Sv , 510631) ( 2 v , 510420) K 1 效应量在量化方面弥补了零假设检验的不足。除了报告检验结果外, 许多期刊还要求在研究报告中 包括效应量。效应量可以分为三大类别：差异类、相关类和组重叠类, 它们在不同的研究设计(如单因素和多 因素被试间、被试内和混合实验设计)或在不同的数据条件下(如小样本、
2、方差异质等)可能有不同的计算方法 和用法, 但许多效应量可以相互转换。我们梳理出一个表格有助应用工作者根据研究目的和研究类型选用合 适的效应量。 1oM 效应量; 差异; 相关; 组重叠 s | B841.2 ,L !_i , BtS= 1 p_T H1r (effect size)br s j , S = X1r ( , Wilkinson APA, 2001; Rosnow YVsZE 91 T (Hunter 9d9_ (Cohen, 1988)br ! 9 1 , V vl , V #M a M M b (a (sa aM1 a qa B| q#Z1 (Lipsey Z1 f 2 ,
3、R 2 , 2 , 2 , 2 ; # r alerting , r effectsize , r contrast F Improvement-Over-Chance index, e I r 2 效应量的计算 2.1 差异类效应量 r B L , F ( 1 F (1 b F (1 f / , K4 F (Tr b , P S (T r idBaWr E 1 5 , Cohen (1969) Glass (1976)4 (S9 S ( , s r $b 2.1.1 单因素实验设计 y L !9 H , (s V F1 , 9 V F1 , B TL1 (contrast, Keppel K
4、line, 2004; Bonett, 2008; , 2006) 11 J J cc =+L, J F , i V U iF ( , 1, ,iJ=L, c i 1 0 J cc+=Lb (s L1 + y f , LF aab eF c ( s 1 () 2 ab c +, L) F ( s ab b L1r l (n Olejnik y B , 2 y (b1), (b2)byM yb 4 F , 4 L ) 11, 12, 21, 2 2ab ab ab abb T 1 4 U s (y A r ), L1V U 11 12 21 2 2 ()( ) 22 ab ab a b a b
5、yy y y+ + (9) 11ab y V U) a1b1 s ( , | wb T 1 s (y B r ), L1V U 11 21 12 2 2 ()( ) 22 ab a b ab a b yy y y+ + (10) , y L !9s r 9 55 y L !9 f , L) sFb , 1S9 , 1 us !9 y S a (Olejnik Glass, 1976; Hedges, 1981)B9 S s pooled , n 2.1.1b ; Ty ( EB a 1 E= a 2 ) 9$ k8y ( ? b 1 ? b 2 ) H , , S s pooled 9 12
6、: r s 1871 9Bb T 1 Ty s , 5 8sy Y , S s pooled 9 ZET 8sy , Ty F ( a 1 a 2 )sF , 9 F Z , y L !9 ZE (Cohen, 1969; Glass, 1976; Hedges, 1981)B9 S s pooled b T 1 8s y s , S s pooled 9 ZE Ty 11 8sy F sF , 9 FZ , y L !9 ZEB9 S s pooled b y 8sy H , S 9 ZE 11 8sy FsF , 9 FZ , y L !9 ZEB9 S s pooled b B ,B/
7、, 1 8sy , 9 S HTi , :/y FsFb9 L1 (r T s0 ) H , y F ( L ) )sFb (2)$ k = L !9 y $ k = !9 H , y$ k =y 8sy , , S9 $ kW L !9 f 9 S (Olejnik $ kWy B 8sy H , $ kWy L !9 f 9 S (Olejnik Friedman, 1968), 9 T 22 12 ( ) pb rttdf=+ (11) t =s YM sF9 t , df = n1, df = n 1 + n 2 2b Cohen (1988)41 Nr vlS , 2 pb r =0
8、.010a 2 pb r =0.059 # 2 pb r =0.138 sY r laavb 1872 S Z 19 (3) Cramer V Cramer V 5Z 2 d9 M1 , B (v 2 V , 9 T 1 2 2 (1)Vnk= (12) n , k l (n , 2006)b (4) (Phi)M1 M1 9 5Z 2 d9 M1 , a Y B =sM H , 9 T (Cohen, 1965; Friedman, 1968) 212 ()n= (13) TTA q p , V VM Z (Z S M ), / T9 M1 , n Z n = (14) (5)Ber / f
9、 H , V P er (Rosenthal d9ZE , r E 9 , d sd _ H ; l d HBZE9 r V Lb f , 1 p V9 er b er 9 T / 22 12 ( ) equivlent rttdf=+ (15) t 1 df t s q p H t ; 2F1 H , df = n2; F 1 H , df = nk, k F , n bS L F ( 3 oF )1 S , | AT S , 9 M1 bS , r eauivlent ( Y )M1 bA , T S , r eauivlent b 2.2.2 方差比效应量 f / , L) iY T (
10、 , TMs V ? , Z vl , N HVZ Lr V L (Thompson, 2002)br $ Z1r (variance-accounted-for indices), vlQ TM 9Z$1M d 1 bL s , Z1r R 2 (Bs ), 2 (Zs , Pearson, 1905), 2 (Kelly, 1935) 2 (Hays, 1963)b (1) R 2 R 2 ZM1 , BB s , ByM M W L1 b Wang Thompson (2007)y R , l H , yN V n T 9 R 2 , 1 Ezekiel (1930) n T 2 1(
11、1)( 1)1 nnv R , n , v 1M b Cohen (1969)4r S f 2 Ba QBZsbB H , 22 2 (1 )f RR=V U 1M r ; QBs H, 222 2 ()(1) ABA AB fRR R= V U1M B r , 2 A R V1M A Z H , c Z 1M dZ1 , 2 AB R V 1M A B Z H , cZ 1M dZ1 , A 22 ABA RR $ B - d Z1 b Cohen (1969)4 f 2 0.02a0.15 0.35 sYrla avb (2) 2 , 2 2 2 Q Ly yM 1 S , 2 v , L
12、y r (rr ) v , Ly yM 1b la M #98r l H , 2 Ly yM W1 (Maxwell, Camp, Vsr (n 2.1.1 ), 9 VZ1r (n ) M1 r (n 2.2.3 )b Omnibus_/ 2 a 2 2 9 4 8Z1r 9 T H , 1 us Ly , TBy V ? C , y % y , Yb , y V ? N+ , y 7 , VsT V , w , f /Z1%rb Ty V ? | C , ?C , y y , f /Z1 r (f_ , 2002)b%r 2 9 T , 2 classical effect total S
13、S SS = (16) 2 classical effect effect error total SS df MS SS = (17) 2 classical = effect effect error total error SS df MS SS MS + (18) rF =M1 (intraclass correlation coefficient) 9 2 effect error total effect JMS MS SS MS = + （） (19) , J LF , SS effect Lr Z , df effect 1 , MS error (Z , | Zs wb y
14、L !9 H , 1 I n y %y , 1 A 8Z1 Ly Z tM Z91b 2 , T 1 Ly Z Ly 1 , N HZ91 y ZZ , 2 ; T 2 1 Ly Z Z1 , 5 2 (Cohen, 1973; Haase, 1983; Kennedy, 1970)by L !9 H , 2 2 M ; y L !9 H , M , Oy r 2 MFv 1, y r 2 MFz 1b9 2 a 2 2 H , sY 2 a 2 2 T SS effect +SS error 9 SS total , 2 () partial effect effect error SS S
15、S SS =+ (20) Contrast_/ 2 a 2 2 9 Contrast _ , y F (1 H , B (sr , n 2.1.1 b y F (1 H , Z1r (Olejnik Rosenthal et al., 2000; Rosnow VM M s , 9 V Zs f b V / T 9 (1 ) (1 ) (1 ) EOE I HHH= ()(1) OE E H HH= (27) H E 5 q q , V Huberty (1994)4 / T () Egg H qn n= (28) n9 , q g gFX5 q , n g g F b H O L=4 tF
16、q , vl V/ 4 ZE p (1)Huberty (1994)wi Ps ZE ( , leave-one-out(L-O-O)ZE ), (2)L Y Ts (PDA), (3)=Q Y Ts (PDA) (4)Logistic Bs (LRA)9bVB V LRA ZE91 PDA ZE (W% V I Huberty Huberty Hess, Olejnik, Natesan 9n Rosenthal Friedman, 1968)b (2) F r , T / r = (1, ) (1, ) error F Fdf + , , F (1,) V U1 1 F (Cohen, 1
17、965; Friedman, 1968)b (3) d r , 12 ,pqn n H , 2 1 d r d pq = + ; 12 ,pqn n= H , r= 2 4 d d + (Cohen, 1977), p qsYV= M1=sM 1 |1 b (4) g r , T / r= 2 12 2 12 1 2 () gnn g nn n n df+ , 12 2df n n=+ (Rosenthal, 1991)b 3.3 其他效应量之间的转换 Cohen (1965)4 2 F W 2 (1)(1)( )F kFk nk = + (29) k=2 H , 2 2 pb r bPete
18、rs Van Voorhis (1940)i 2 V F 9 2 (1)(1)(1)( )F kFk nk = + (30) 2 9 V F 9 (Fleiss, 1969) 2 ( 1)( 1) ( 1)( 1) F kFkn = + (31) , k y ZsF , n 9 b 4 结语 r S , a L !9# Hq , r 9 ZE V ?Bb 8 P H , 1 f , 4 ar S , V 3 VT Ib 表2 效应量一览表 _ ar F1 t _ 1_ Cohen d , Glass Hedge g ; = M1 ; I r 1_ (L !B T ) F1 s r ; M1r
19、r contrast a r alerting ar effectsize ; Contrast _Z1r 2 , 2 , 2 # ( s 1 F1 y y $ kWa $ k = !9Zs 8_ (L ! T ) Omnibus_Z1r 2 , 2 , 2 # ; I r M WM1 1_ rar pb ar b ar equivalent , # Cramer V 2 d9 M1 1_ 222 2 ()(1) AB A AB fRR R= M W M 1 BM M M1 (B s ) 8_ R 2 22 2 (1 )f RR= (1)s r (sSr Ks r , B a L !9 , V
20、 F1 9 V F1 b Contrast _ , V 1876 S Z 19 81 (svlb (s Sr S , S1 Z s pooled 9 ZEB , Z9 G L !9b (2)M1 r M1 r s r B t , P RbM1 r M1 aZ1 M1 bnM1 VSr SbZ1r B ZsBsb Ominibus _ /Z1r , Rosenthal Rosnow (1984)4 31M1r (n 2.2.3 ), PF1 H , V t 8r vlb (3)Fr Fr VZsa98d #FW B f , s r M1 r , 9 ZE$B Pg , L= nb Vacha-H
21、aase Thompson (2004)9 SPSS q |r TZE , Vsa t _aZsaBsbB Vd9s “option”sM r SbZs , SPSS 2 2 , 7 2 b f / 2 a (Pierce, Block, WEN Zhong-Lin 1 ; WU Yan 2 ( 1 Center for Studies of Psychological Application, South China Normal University, Guangzhou 510631, China) ( 2 Department of Applied Psychology, Guangd
22、ong University of Foreign Studies, Guangzhou 510420, China) Abstract: Effect sizes are important supplement of the null hypothesis significance testing. More and more academic journals request authors provide the effect sizes of their researches. Our purpose is to provide a guideline on how to compu
23、te the appropriate effect sizes of different researches and data types. We classified the effect sizes into three types, including difference-type, correlation-type and group-overlap. For each type of the effect sizes, there are different approaches of calculations and applications under different r
24、esearch designs (e.g., single-factor/multifactor between-subjects, single-factor/multifactor within-subjects) and data conditions (e.g., small sample size, heterogeneity of variance). Many effect sizes, however, can be transformed from one type to another. We summarized a table that may help readers to choose appropriate effect sizes for their researches based on the research purposes and research designs. Key words: effect size; difference-type; correlation-type; group overlap-type
