# R: Discrepancy between R and SPSS in two-way repeated measures designs

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There are 20 distinct individuals, right? expno breaks the 20 individuals into five groups of 4, right? Is this a blocking factor? If expno is treated as a blocking factor, the following is what you get: > xy <- expand.grid(expno=letters[1:5],cond=letters[1:4], + time=factor(paste(1:2))) > xy$subj <- factor(paste(xy$expno, xy$cond, sep=":")) > xy$cond <- factor(xy$cond) > xy$expno <- factor(xy$expno) > xy$y <- rnorm(40) > summary(aov(y~cond*time+Error(expno/cond), data=xy)) Error: expno Df Sum Sq Mean Sq F value Pr(>F) Residuals 4 3.59 0.90 Error: expno:cond Df Sum Sq Mean Sq F value Pr(>F) cond 3 1.06 0.35 0.36 0.78 Residuals 12 11.86 0.99 Error: Within Df Sum Sq Mean Sq F value Pr(>F) time 1 2.27 2.27 1.38 0.26 cond:time 3 3.27 1.09 0.67 0.59 Residuals 16 26.19 1.64 If on the other hand this is analyzed as for a complete randomized design, the following is the output: > summary(aov(y~cond*time+Error(subj), data=xy)) Error: subj Df Sum Sq Mean Sq F value Pr(>F) cond 3 1.06 0.35 0.37 0.78 Residuals 16 15.46 0.97 Error: Within Df Sum Sq Mean Sq F value Pr(>F) time 1 2.27 2.27 1.38 0.26 cond:time 3 3.27 1.09 0.67 0.59 Residuals 16 26.19 1.64 On 10 Sep 2005, at 8:00 PM, Larry A Sonna wrote: >> From: "Larry A Sonna" <larry_sonna@hotmail.com> >> Date: 10 September 2005 12:10:06 AM >> To: <r-help@stat.math.ethz.ch> >> Subject: [R] Discrepancy between R and SPSS in 2-way, repeated >> measures ANOVA >> >> >> Dear R community, >> >> I am trying to resolve a discrepancy between the way SPSS and R >> handle 2-way, repeated measures ANOVA. >> >> An experiment was performed in which samples were drawn before and >> after treatment of four groups of subjects (control and disease >> states 1, 2 and 3). Each group contained five subjects. An >> experimental measurement was performed on each sample to yield a >> "signal". The before and after treatment signals for each subject >> were treated as repeated measures. We desire to obtain P values >> for disease state ("CONDITION"), and the interaction between signal >> over time and disease state ("CONDITION*TIME"). >> >> Using SPSS, the following output was obtained: >> DF SumSq (Type 3) Mean Sq F >> value P= >> >> COND 3 42861 14287 >> 3.645 0.0355 >> >> TIME 1 473 >> 473 0.175 0.681 >> >> COND*TIME 3 975 325 >> 0.120 0.947 >> >> Error 16 43219 2701 >> >> >> >> By contrast, using the following R command: >> >> summary(aov(SIGNAL~(COND+TIME+COND*TIME)+Error(EXPNO/COND), >> Type="III")) >> >> the output was as follows: >> >> Df Sum Sq Mean Sq F value Pr(>F) >> >> COND 3 26516 8839 3.2517 0.03651 * >> >> TIME 1 473 473 0.1739 0.67986 >> >> COND:TIME 3 975 325 0.1195 0.94785 >> >> Residuals 28 76107 2718 >> >> >> >> I don't understand why the two results are discrepant. In >> particular, I'm not sure why R is yielding 28 DF for the residuals >> whereas SPSS only yields 16. Can anyone help? >> >> John Maindonald email: john.maindonald@anu.edu.au phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Bioinformation Science, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200. ______________________________________________