************************************************************************ *** T Test: Measures of Effect Size and Nonoverlap, and Observed Power *** Valentim R. Alferes (University of Coimbra, Portugal) *** valferes@fpce.uc.pt ** ** This syntax does a T Test for two independent groups and calculates ** measures of effect size, measures of nonoverlap, and observed power. ** ** The output is divided into four parts: ** ** PART I - SPSS T Test standard output: ** - Descriptive statistics; ** - Levene's Test for Equality of Variances ** - T-Test for Equality of Means (Equal variances assumed ** and not assumed); ** - Confidence Interval of the Difference. ** ** PART II - Measures of effect size: ** - Cohen's d (D); ** - Hedges Correction (D_H); ** - r point biserial (R); ** - Squared r point biserial (R2); ** - Binomial Effect Size Display (BESD_LO and BESD_UP). ** ** PART III - Measures of nonoverlap (Cohen, 1988, pp. 21-23): ** - U1 (percent of nonoverlap between the two distributions); ** - U2 (the highest percent in Group 1 that exceds the same lowest ** percent in Group 2); ** - U3 (percentile standing = percentile of the Group 2 distribution ** corresponding to the 50th percentile of Group 1 distribution). ** ** PART IV - Observed power (for algorithm, see Borenstein et al., 2001): ** - N1, N2, Harmonic N (N_HARM); ** - Alfa (ALFA) and observed power (OPOWER). ** ** The user has two methods: Analysing raw data or reproducing the SPSS ** T Test standard output from summary statistics in published articles. ************************************************************************ ** METHOD 1: Analysing raw data. ** The data have to be in a SPSS active file with the following ** two numeric variables: ** IV – Independent variable (1 = Group 1; 2 = Group 2): ** DV – Dependent variable. * Enter confidence level for confidence interval of difference * (by default, confidence level = .95). T-TEST GROUPS=IV(1 2)/VARIABLES=DV/CRITERIA=CIN(.95). GRAPH/BAR(SIMPLE)=MEAN(DV) BY IV. GRAPH/ERRORBAR(CI 95)=DV BY IV /TITLE='Confidence Intervals for Means'. AGGREGATE/OUTFILE=*/BREAK=iv/m2=MEAN(dv)/dp2=SD(dv)/n2=N. COMPUTE N1=LAG(N2,1). COMPUTE M1=LAG(M2,1). COMPUTE DP1=LAG(DP2,1). EXECUTE. SELECT IF(IV=2). EXECUTE. * Enter alfa for calculating observed power (by default, ALFA = 0.05). COMPUTE ALFA = 0.05. COMPUTE SP2=(((N1-1)*(DP1**2))+((N2-1)*(DP2**2)))/(N1+N2-2). COMPUTE T=(M1-M2)/SQR(SP2*((1/N1)+(1/N2))). COMPUTE GL=N1+N2-2. COMPUTE R=T/SQR((T**2)+GL). COMPUTE R2=R**2. COMPUTE D=T*SQR((1/N1)+(1/N2)). COMPUTE D_H=D*(1-(3/(4*(N1+N2)-9))). COMPUTE BESD_LO=.50-(R/2). COMPUTE BESD_UP=.50+(R/2). COMPUTE U3=CDF.NORMAL(D,0,1)*100. COMPUTE U2=CDF.NORMAL((D/2),0,1)*100. COMPUTE U2X=CDF.NORMAL((ABS(D)/2),0,1). COMPUTE U1=(2*U2X-1)/U2X*100. COMPUTE N_HARM=(2*N1*N2)/(N1+N2). COMPUTE NCP=ABS((D*SQR(N_HARM))/SQR(2)). COMPUTE T_ALPHA=IDF.T(1-ALFA/2,GL). COMPUTE POWER1=1-NCDF.T(T_ALPHA,GL,NCP). COMPUTE POWER2=1-NCDF.T(T_ALPHA,GL,-NCP). COMPUTE OPOWER=POWER1+POWER2. FORMATS ALL(F8.4) N1 N2(F8.0) U1 U2 U3(F8.1). SUMMARIZE/TABLES=D D_H R R2 BESD_LO BESD_UP/FORMAT=NOLIST TOTAL /TITLE='PART II - Measures of Effect Size'/CELLS=FIRST. SUMMARIZE/TABLES=U1 U2 U3/FORMAT=NOLIST TOTAL /TITLE='PART III - Measures of Nonoverlap'/CELLS=FIRST. SUMMARIZE/TABLES=N1 N2 N_HARM ALFA OPOWER/FORMAT=NOLIST TOTAL /TITLE='PART IV - Observed Power'/CELLS=FIRST. ************************************************************************ ** METHOD 2: Reproducing the SPSS T Test standard output from ** summary statistics in published articles. * Enter, row by row, N, Mean, and SD for Groups 1 and 2. DATA LIST LIST /N(F8.0) M(F8.2) SD(F8.2). BEGIN DATA 17 7,46 1,98 15 5,34 2,14 END DATA. COMPUTE IV=$CASENUM. LOOP ID=1 TO N. XSAVE OUTFILE=XOUT1. END LOOP. EXECUTE. GET FILE=XOUT1. COMPUTE DV=M. COMPUTE K=SQR((SD**2*(N-1))/2). IF (ID=1) DV=M+K. IF (ID=2) DV=M-K. EXECUTE. * Enter confidence level for confidence interval of difference * (by default, confidence level = .95). T-TEST GROUPS=IV(1 2)/VARIABLES=DV/CRITERIA=CIN(.95). GRAPH/BAR(SIMPLE)=MEAN(DV) BY IV. GRAPH/ERRORBAR(CI 95)=DV BY IV /TITLE='Confidence Intervals for Means'. AGGREGATE/OUTFILE=*/BREAK=IV/N2=MEAN(N)/M2=MEAN(M)/DP2=MEAN(SD). COMPUTE N1=LAG(N2,1). COMPUTE M1=LAG(M2,1). COMPUTE DP1=LAG(DP2,1). EXECUTE. SELECT IF(IV=2). EXECUTE. * Enter alfa for calculating observed power (by default, ALFA = 0.05). COMPUTE ALFA = 0.05. COMPUTE SP2=(((N1-1)*(DP1**2))+((N2-1)*(DP2**2)))/(N1+N2-2). COMPUTE T=(M1-M2)/SQR(SP2*((1/N1)+(1/N2))). COMPUTE GL=N1+N2-2. COMPUTE R=T/SQR((T**2)+GL). COMPUTE R2=R**2. COMPUTE D=T*SQR((1/N1)+(1/N2)). COMPUTE D_H=D*(1-(3/(4*(N1+N2)-9))). COMPUTE BESD_LO=.50-(R/2). COMPUTE BESD_UP=.50+(R/2). COMPUTE U3=CDF.NORMAL(D,0,1)*100. COMPUTE U2=CDF.NORMAL((D/2),0,1)*100. COMPUTE U2X=CDF.NORMAL((ABS(D)/2),0,1). COMPUTE U1=(2*U2X-1)/U2X*100. COMPUTE N_HARM=(2*N1*N2)/(N1+N2). COMPUTE NCP=ABS((D*SQR(N_HARM))/SQR(2)). COMPUTE T_ALPHA=IDF.T(1-ALFA/2,GL). COMPUTE POWER1=1-NCDF.T(T_ALPHA,GL,NCP). COMPUTE POWER2=1-NCDF.T(T_ALPHA,GL,-NCP). COMPUTE OPOWER=POWER1+POWER2. FORMATS ALL(F8.4) N1 N2(F8.0) U1 U2 U3(F8.1). SUMMARIZE/TABLES=D D_H R R2 BESD_LO BESD_UP/FORMAT=NOLIST TOTAL /TITLE='PART II - Measures of Effect Size'/CELLS=FIRST. SUMMARIZE/TABLES=U1 U2 U3/FORMAT=NOLIST TOTAL /TITLE='PART III - Measures of Nonoverlap'/CELLS=FIRST. SUMMARIZE/TABLES=N1 N2 N_HARM ALFA OPOWER/FORMAT=NOLIST TOTAL /TITLE='PART IV - Observed Power'/CELLS=FIRST. ************************************************************************ ** Borenstein, M., Rothstein, H., & Cohen, J. (2001). SamplePower 2.0 ** [Computer Manual]. Chicago: SPSS Inc. ** Cohen, J. (1988). Statistical power analysis for the behavioral ** sciences (2nd ed.). Hillsdale, NJ: Lawrence Erbaum. ************************************************************************.