ANOVA A*B
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 | ********************************************************************** *** 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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