ANOVA A*B

 

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**********************************************************************
*** Factorial ANOVA: Measures of Association, Effect Size and
*** Observed Power
*** Valentim R. Alferes (University of Coimbra, Portugal)
*** valferes@fpce.uc.pt

** This syntax does an A*B Factorial ANOVA and calculates:
** - variance components;
** - measures of association (squared etas and partial squared 
**   etas; squared omegas and partial squared omegas);
** - measures of effect size (Cohen's f);
** - observed power.

** The user has two methods: Analysing raw data or reproducing 
** the ANOVA Table from summary statistics in published articles.

**********************************************************************

** METHOD 1: Analysing raw data

** The data have to be in a SPSS active file with the following 
** three numeric variables:
** A – Factor A or IV1;
** B – Factor B or IV2;
** DV – Dependent variable

** The following lines create an active file with an example
** from Keppel (1991, p. 214, Table 10-6).

DATA LIST FREE /A(F8.0) B(F8.0) DV(F8.0).
BEGIN DATA
1 1 1 1 1 4 1 1 0 1 1 7 2 1 13 2 1 5 2 1 7 2 1 15 3 1 9 3 1 16 3 1 18 
3 1 13 1 2 15 1 2 6 1 2 10 1 2 13 2 2 6 2 2 18 2 2 9 2 2 15 3 2 14 3 
2 7 3 2 6 3 2 13 
END DATA.


* Enter alpha for calculating power(by default, alpha = .05).
UNIANOVA DV BY A B/PRINT=DESCRIPTIVE ETASQ OPOWER/CRITERIA=ALPHA(.05)
/EMMEANS=TABLES(OVERALL)/EMMEANS=TABLES(A)/EMMEANS=TABLES(B)
/EMMEANS=TABLES(A*B)/DESIGN=A B A*B.
COMPUTE K=1.
EXECUTE.
AGGREGATE/OUTFILE=OUT_0/BREAK=K/M_G=MEAN(DV)/N_G=N.
MATCH FILES/FILE=*/TABLE=OUT_0/BY K.
EXECUTE.
SORT CASES BY A(A) B(A).
COMPUTE CELUL=A*100+B.
EXECUTE.
AUTORECODE VARIABLES=CELUL/INTO CELULA.
AGGREGATE/OUTFILE=OUT_1/BREAK=CELULA/M_AB=MEAN(DV)/N_AB=N.
MATCH FILES/FILE=*/TABLE=OUT_1/BY CELULA.
EXECUTE.
AGGREGATE/OUTFILE=OUT_2/BREAK=A/M_A=MEAN(DV)/N_A=N.
MATCH FILES/FILE=*/TABLE=OUT_2/BY A.
EXECUTE.
SORT CASES BY B(A).
AGGREGATE/OUTFILE=OUT_3/BREAK=B/M_B=MEAN(DV)/N_B=N.
MATCH FILES/FILE=*/TABLE=OUT_3/BY B.
EXECUTE.
COMPUTE D2_A=(M_A-M_G)**2.
COMPUTE D2_B=(M_B-M_G)**2.
COMPUTE D2_ERRO=(DV-M_AB)**2.
COMPUTE D2_G=(DV-M_G)**2.
EXECUTE.
AGGREGATE/OUTFILE=*/BREAK=K/N=MEAN(N_AB)/N_T_A=MAX(A)
/N_T_B=MAX(B)/SS_A=SUM(D2_A)/SS_B=SUM(D2_B)
/SS_ERRO=SUM(D2_ERRO)/SS_TOT=SUM(D2_G).
COMPUTE SS_AB=SS_TOT-SS_A-SS_B-SS_ERRO.
COMPUTE GL_A=N_T_A-1.
COMPUTE GL_B=N_T_B-1.
COMPUTE GL_AB=GL_A*GL_B.
COMPUTE GL_ERRO=N*N_T_A*N_T_B-GL_A-GL_B-GL_AB-1.
COMPUTE MS_A=SS_A/GL_A.
COMPUTE MS_B=SS_B/GL_B.
COMPUTE MS_AB=SS_AB/GL_AB.
COMPUTE MS_ERRO=SS_ERRO/GL_ERRO.
COMPUTE COMV_A=(GL_A*(MS_A-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_B=(GL_B*(MS_B-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_AB=(GL_AB*(MS_AB-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_ERR=MS_ERRO.
COMPUTE COMV_TOT=SUM(COMV_A TO COMV_ERR).
COMPUTE ETA_A=SS_A/SS_TOT.
COMPUTE ETA_B=SS_B/SS_TOT.
COMPUTE ETA_AB=SS_AB/SS_TOT.
COMPUTE P_ETA_A=SS_A/(SS_A+SS_ERRO).
COMPUTE P_ETA_B=SS_B/(SS_B+SS_ERRO).
COMPUTE P_ETA_AB=SS_AB/(SS_AB+SS_ERRO).
COMPUTE OME_A=COMV_A/COMV_TOT.
COMPUTE OME_B=COMV_B/COMV_TOT.
COMPUTE OME_AB=COMV_AB/COMV_TOT.
COMPUTE P_OME_A=COMV_A/(COMV_A+COMV_ERR).
COMPUTE P_OME_B=COMV_B/(COMV_B+COMV_ERR).
COMPUTE P_OME_AB=COMV_AB/(COMV_AB+COMV_ERR).
COMPUTE F_COH_A=SQR(P_OME_A/(1-P_OME_A)).
COMPUTE F_COH_B=SQR(P_OME_B/(1-P_OME_B)).
COMPUTE F_COH_AB=SQR(P_OME_AB/(1-P_OME_AB)).
EXECUTE.
FORMATS COMV_A TO F_COH_AB (F8.3).
SUMMARIZE/TABLES=COMV_A COMV_B COMV_AB COMV_ERR/FORMAT=LIST 
NOCASENUM TOTAL/TITLE='Variance Components'/CELLS=NONE.
SUMMARIZE/TABLES=ETA_A ETA_B ETA_AB/FORMAT=LIST NOCASENUM
NOTOTAL/TITLE='Squared Eta'/CELLS=NONE.
SUMMARIZE/TABLES=P_ETA_A P_ETA_B P_ETA_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Parcial Squared Eta'/CELLS=NONE.
SUMMARIZE/TABLES=OME_A OME_B OME_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Squared Omega'/CELLS=NONE.
SUMMARIZE/TABLES=P_OME_A P_OME_B P_OME_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Partial Squared Omega'/CELLS=NONE.
SUMMARIZE/TABLES=F_COH_A F_COH_B F_COH_AB/FORMAT=LIST NOCASENUM 
NOTOTAL/TITLE="Cohen's f"/CELLS=NONE.

**********************************************************************

** METHOD 2: Reproducing the ANOVA Table from summary statistics
** in published articles.

* Enter, row by row, Factor A levels, Factor B levels, N and Mean
* for the experimental conditions (in the example, the same as in 
* Method 1, you have a A3B2 Design).

DATA LIST LIST /a(F8.0) b(F8.0) n(F8.0) m(f8.2).
BEGIN DATA
1  1  4  3,00
1  2  4  11,00
2  1  4  10,00
2  2  4  12,00
3  1  4  14,00
3  2  4  10,00
END DATA.

* Enter Mean Square Error.
COMPUTE mse = 18.333333.

COMPUTE iv=$CASENUM.
LOOP id=1 TO n.
XSAVE OUTFILE=XOUT1.
END LOOP.
EXECUTE.
GET FILE=XOUT1.
COMPUTE dv=m.
COMPUTE k=SQR((mse*(N-1))/2).
IF (id=1) dv=m+k.
IF (id=2) dv=m-k.
EXECUTE.
SUMMARIZE/TABLES=dv BY a BY b/FORMAT=NOLIST TOTAL
/TITLE='Case Summaries'/CELLS=COUNT MEAN.

* Enter alpha for calculating power(by default, alpha = .05).
UNIANOVA DV BY A B/PRINT=DESCRIPTIVE ETASQ OPOWER/CRITERIA=ALPHA(.05)
/DESIGN=A B A*B.
COMPUTE K=1.
EXECUTE.
AGGREGATE/OUTFILE=OUT_0/BREAK=K/M_G=MEAN(DV)/N_G=N.
MATCH FILES/FILE=*/TABLE=OUT_0/BY K.
EXECUTE.
SORT CASES BY A(A) B(A).
COMPUTE CELUL=A*100+B.
EXECUTE.
AUTORECODE VARIABLES=CELUL/INTO CELULA.
AGGREGATE/OUTFILE=OUT_1/BREAK=CELULA/M_AB=MEAN(DV)/N_AB=N.
MATCH FILES/FILE=*/TABLE=OUT_1/BY CELULA.
EXECUTE.
AGGREGATE/OUTFILE=OUT_2/BREAK=A/M_A=MEAN(DV)/N_A=N.
MATCH FILES/FILE=*/TABLE=OUT_2/BY A.
EXECUTE.
SORT CASES BY B(A).
AGGREGATE/OUTFILE=OUT_3/BREAK=B/M_B=MEAN(DV)/N_B=N.
MATCH FILES/FILE=*/TABLE=OUT_3/BY B.
EXECUTE.
COMPUTE D2_A=(M_A-M_G)**2.
COMPUTE D2_B=(M_B-M_G)**2.
COMPUTE D2_ERRO=(DV-M_AB)**2.
COMPUTE D2_G=(DV-M_G)**2.
EXECUTE.
AGGREGATE/OUTFILE=*/BREAK=K/N=MEAN(N_AB)/N_T_A=MAX(A)
/N_T_B=MAX(B)/SS_A=SUM(D2_A)/SS_B=SUM(D2_B)
/SS_ERRO=SUM(D2_ERRO)/SS_TOT=SUM(D2_G).
COMPUTE SS_AB=SS_TOT-SS_A-SS_B-SS_ERRO.
COMPUTE GL_A=N_T_A-1.
COMPUTE GL_B=N_T_B-1.
COMPUTE GL_AB=GL_A*GL_B.
COMPUTE GL_ERRO=N*N_T_A*N_T_B-GL_A-GL_B-GL_AB-1.
COMPUTE MS_A=SS_A/GL_A.
COMPUTE MS_B=SS_B/GL_B.
COMPUTE MS_AB=SS_AB/GL_AB.
COMPUTE MS_ERRO=SS_ERRO/GL_ERRO.
COMPUTE COMV_A=(GL_A*(MS_A-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_B=(GL_B*(MS_B-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_AB=(GL_AB*(MS_AB-MS_ERRO))/(N_T_A*N_T_B*N).
COMPUTE COMV_ERR=MS_ERRO.
COMPUTE COMV_TOT=SUM(COMV_A TO COMV_ERR).
COMPUTE ETA_A=SS_A/SS_TOT.
COMPUTE ETA_B=SS_B/SS_TOT.
COMPUTE ETA_AB=SS_AB/SS_TOT.
COMPUTE P_ETA_A=SS_A/(SS_A+SS_ERRO).
COMPUTE P_ETA_B=SS_B/(SS_B+SS_ERRO).
COMPUTE P_ETA_AB=SS_AB/(SS_AB+SS_ERRO).
COMPUTE OME_A=COMV_A/COMV_TOT.
COMPUTE OME_B=COMV_B/COMV_TOT.
COMPUTE OME_AB=COMV_AB/COMV_TOT.
COMPUTE P_OME_A=COMV_A/(COMV_A+COMV_ERR).
COMPUTE P_OME_B=COMV_B/(COMV_B+COMV_ERR).
COMPUTE P_OME_AB=COMV_AB/(COMV_AB+COMV_ERR).
COMPUTE F_COH_A=SQR(P_OME_A/(1-P_OME_A)).
COMPUTE F_COH_B=SQR(P_OME_B/(1-P_OME_B)).
COMPUTE F_COH_AB=SQR(P_OME_AB/(1-P_OME_AB)).
EXECUTE.
FORMATS COMV_A TO F_COH_AB (F8.3).
SUMMARIZE/TABLES=COMV_A COMV_B COMV_AB COMV_ERR/FORMAT=LIST 
NOCASENUM TOTAL/TITLE='Variance Components'/CELLS=NONE.
SUMMARIZE/TABLES=ETA_A ETA_B ETA_AB/FORMAT=LIST NOCASENUM
NOTOTAL/TITLE='Squared Eta'/CELLS=NONE.
SUMMARIZE/TABLES=P_ETA_A P_ETA_B P_ETA_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Parcial Squared Eta'/CELLS=NONE.
SUMMARIZE/TABLES=OME_A OME_B OME_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Squared Omega'/CELLS=NONE.
SUMMARIZE/TABLES=P_OME_A P_OME_B P_OME_AB/FORMAT=LIST 
NOCASENUM NOTOTAL/TITLE='Partial Squared Omega'/CELLS=NONE.
SUMMARIZE/TABLES=F_COH_A F_COH_B F_COH_AB/FORMAT=LIST NOCASENUM 
NOTOTAL/TITLE="Cohen's f"/CELLS=NONE.

**********************************************************************
Keppel, G. (1991). Design and analysis: A researcher's handbook
 (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
**********************************************************************
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