MANOVA-RM-Simple.txt Here are selected parts of program and output illustrating how to do simple effects analysis with repeated measures factors. ------------------------------------------------------------------------------- The SAS System NOTE: Copyright(c) 1989 by SAS Institute Inc., Cary, NC USA. NOTE: SAS (r) Proprietary Software Release 6.06.01 DATA LET2; TITLE 'Wong''s Thesis'; INPUT SEX VOIMM1 2-3 VOSTM1 4-5 VOLTM1 6-7 VUIMM1 8-9 VUSTM1 10-11 VULTM1 12-13 AOIMM1 14-15 AOSTM1 16-17 AOLTM1 18-19 AUIMM1 20-21 AUSTM1 22-23 AULTM1 24-25 VOIMM2 26-27 VOSTM2 28-29 VOLTM2 30-31 VUIMM2 32-33 VUSTM2 34-35 VULTM2 36-37 AOIMM2 38-39 AOSTM2 40-41 AOLTM2 42-43 AUIMM2 44-45 AUSTM2 46-47 AULTM2 48-49; NOTE: The data set WORK.LET2 has 33 observations and 25 variables. PROC ANOVA; MODEL VOIMM1 VOSTM1 VOLTM1 VUIMM1 VUSTM1 VULTM1 AOIMM1 AOSTM1 AOLTM1 AUIMM1 AUSTM1 AULTM1 VOIMM2 VOSTM2 VOLTM2 VUIMM2 VUSTM2 VULTM2 AOIMM2 AOSTM2 AOLTM2 AUIMM2 AUSTM2 AULTM2 = / NOUNI; REPEATED VERSION 2, MODALITY 2, ORDER 2, COND 3; ----------------------------------------------------------------------- This omnibus analysis is for a 2 * 2 * 2 * 3 repeated measures design Analysis of Variance Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable VOIMM1 VOSTM1 VOLTM1 VUIMM1 VUSTM1 VULTM1 Level of VERSION 1 1 1 1 1 1 Level of MODALITY 1 1 1 1 1 1 Level of ORDER 1 1 1 2 2 2 Level of COND 1 2 3 1 2 3 Dependent Variable AOIMM1 AOSTM1 AOLTM1 AUIMM1 AUSTM1 AULTM1 Level of VERSION 1 1 1 1 1 1 Level of MODALITY 2 2 2 2 2 2 Level of ORDER 1 1 1 2 2 2 Level of COND 1 2 3 1 2 3 Dependent Variable VOIMM2 VOSTM2 VOLTM2 VUIMM2 VUSTM2 VULTM2 Level of VERSION 2 2 2 2 2 2 Level of MODALITY 1 1 1 1 1 1 Level of ORDER 1 1 1 2 2 2 Level of COND 1 2 3 1 2 3 Dependent Variable AOIMM2 AOSTM2 AOLTM2 AUIMM2 AUSTM2 AULTM2 Level of VERSION 2 2 2 2 2 2 Level of MODALITY 2 2 2 2 2 2 Level of ORDER 1 1 1 2 2 2 Level of COND 1 2 3 1 2 3 Manova Test Criteria and Exact F Statistics for the Hypothesis of no VERSION*COND Effect H = Anova SS&CP Matrix for VERSION*COND E = Error SS&CP Matrix S=1 M=0 N=14.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.63147235 9.0458 2 31 0.0008 Pillai's Trace 0.36852765 9.0458 2 31 0.0008 Hotelling-Lawley Trace 0.58360062 9.0458 2 31 0.0008 Roy's Greatest Root 0.58360062 9.0458 2 31 0.0008 Manova Test Criteria and Exact F Statistics for the Hypothesis of no MODALITY*COND Effect H = Anova SS&CP Matrix for MODALITY*COND E = Error SS&CP Matrix S=1 M=0 N=14.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.72942497 5.7496 2 31 0.0075 Pillai's Trace 0.27057503 5.7496 2 31 0.0075 Hotelling-Lawley Trace 0.37094292 5.7496 2 31 0.0075 Roy's Greatest Root 0.37094292 5.7496 2 31 0.0075 Manova Test Criteria and Exact F Statistics for the Hypothesis of no ORDER*COND Effect H = Anova SS&CP Matrix for ORDER*COND E = Error SS&CP Matrix S=1 M=0 N=14.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.44423288 19.3916 2 31 0.0001 Pillai's Trace 0.55576712 19.3916 2 31 0.0001 Hotelling-Lawley Trace 1.25107157 19.3916 2 31 0.0001 Roy's Greatest Root 1.25107157 19.3916 2 31 0.0001 ------------------------------------------------------------------------- Note that Version, Modality, and Order all interact with the CONDition, thus we need to do simple main effects analyses. That is, we need obtain simple main effects for Version, Modality, and Order at each level of COND. None of these interactions participated in yet higher order interactions. PROC ANOVA; MODEL VOIMM1 VUIMM1 AOIMM1 AUIMM1 VOIMM2 VUIMM2 AOIMM2 AUIMM2 = / NOUNI; REPEATED VERSION 2, MODALITY 2, ORDER 2; title3 'Simple main effects for the Immediate Memory Condition'; Look at the program statements above. To obtain the simple effects at the first level of COND, I simply deleted from the model statement all of the variables except those that coded data at the first level of COND -- that is, I left in only those variables that had "IMM" in positions 3-5 of their names. Note that I also had to remove from the REPEATED statement the ", COND 3", since COND is now a constant, not a variable. Here are important parts of the resulting output: Simple main effects for the Immediate Memory Condition Analysis of Variance Procedure Manova Test Criteria and Exact F Statistics for the Hypothesis of no VERSION Effect H = Anova SS&CP Matrix for VERSION E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.92557966 2.5729 1 32 0.1185 Pillai's Trace 0.07442034 2.5729 1 32 0.1185 Hotelling-Lawley Trace 0.08040403 2.5729 1 32 0.1185 Roy's Greatest Root 0.08040403 2.5729 1 32 0.1185 Manova Test Criteria and Exact F Statistics for the Hypothesis of no MODALITY Effect H = Anova SS&CP Matrix for MODALITY E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.78642764 8.6903 1 32 0.0059 Pillai's Trace 0.21357236 8.6903 1 32 0.0059 Hotelling-Lawley Trace 0.27157280 8.6903 1 32 0.0059 Roy's Greatest Root 0.27157280 8.6903 1 32 0.0059 Manova Test Criteria and Exact F Statistics for the Hypothesis of no ORDER Effect H = Anova SS&CP Matrix for ORDER E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.05384789 562.2666 1 32 0.0001 Pillai's Trace 0.94615211 562.2666 1 32 0.0001 Hotelling-Lawley Trace 17.57083093 562.2666 1 32 0.0001 Roy's Greatest Root 17.57083093 562.2666 1 32 0.0001 ------------------------------------------------------------------------- Now for the simple effects at level 2 of COND: PROC ANOVA; MODEL VOSTM1 VUSTM1 AOSTM1 AUSTM1 VOSTM2 VUSTM2 AOSTM2 AUSTM2 = / NOUNI; REPEATED VERSION 2, MODALITY 2, ORDER 2; title3 'Simple main effects for the Short Term Memory Condition'; Simple main effects for the Short Term Memory Condition Analysis of Variance Procedure Manova Test Criteria and Exact F Statistics for the Hypothesis of no VERSION Effect H = Anova SS&CP Matrix for VERSION E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.59795552 21.5157 1 32 0.0001 Pillai's Trace 0.40204448 21.5157 1 32 0.0001 Hotelling-Lawley Trace 0.67236520 21.5157 1 32 0.0001 Roy's Greatest Root 0.67236520 21.5157 1 32 0.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no MODALITY Effect H = Anova SS&CP Matrix for MODALITY E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.85704545 5.3376 1 32 0.0275 Pillai's Trace 0.14295455 5.3376 1 32 0.0275 Hotelling-Lawley Trace 0.16679926 5.3376 1 32 0.0275 Roy's Greatest Root 0.16679926 5.3376 1 32 0.0275 Manova Test Criteria and Exact F Statistics for the Hypothesis of no ORDER Effect H = Anova SS&CP Matrix for ORDER E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.10617344 269.3936 1 32 0.0001 Pillai's Trace 0.89382656 269.3936 1 32 0.0001 Hotelling-Lawley Trace 8.41855112 269.3936 1 32 0.0001 Roy's Greatest Root 8.41855112 269.3936 1 32 0.0001 ----------------------------------------------------------------------- And now for the simple effects at level 3 of COND: PROC ANOVA; MODEL VOLTM1 VULTM1 AOLTM1 AULTM1 VOLTM2 VULTM2 AOLTM2 AULTM2 = / NOUNI; REPEATED VERSION 2, MODALITY 2, ORDER 2; title3 'Simple main effects for the Long Term Memory Condition'; Simple main effects for the Long Term Memory Condition Analysis of Variance Procedure Manova Test Criteria and Exact F Statistics for the Hypothesis of no VERSION Effect H = Anova SS&CP Matrix for VERSION E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.55846145 25.3003 1 32 0.0001 Pillai's Trace 0.44153855 25.3003 1 32 0.0001 Hotelling-Lawley Trace 0.79063390 25.3003 1 32 0.0001 Roy's Greatest Root 0.79063390 25.3003 1 32 0.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no MODALITY Effect H = Anova SS&CP Matrix for MODALITY E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.90100784 3.5158 1 32 0.0699 Pillai's Trace 0.09899216 3.5158 1 32 0.0699 Hotelling-Lawley Trace 0.10986826 3.5158 1 32 0.0699 Roy's Greatest Root 0.10986826 3.5158 1 32 0.0699 Manova Test Criteria and Exact F Statistics for the Hypothesis of no ORDER Effect H = Anova SS&CP Matrix for ORDER E = Error SS&CP Matrix S=1 M=-0.5 N=15 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.08170769 359.6400 1 32 0.0001 Pillai's Trace 0.91829231 359.6400 1 32 0.0001 Hotelling-Lawley Trace 11.23875026 359.6400 1 32 0.0001 Roy's Greatest Root 11.23875026 359.6400 1 32 0.0001 32 275.12121212 8.59753788 NOTE: The PROCEDURE ANOVA printed pages 24-29. 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