John Christie <[EMAIL PROTECTED]> writes: > OK, I do see that there is a problem in my first email. I have > noticed this with repeated measures designs. Otherwise, of course, > there is only one error term for all factors. But, with repeated > measures designs this is not the case. > > > On Friday, July 11, 2003, at 10:00 PM, Spencer Graves wrote: > > > People tend to get the quickest and most helpful responses > > when they provide a toy problem that produces what they think are > > anamolous results > > here is an admittedly poor example with factors a and b and s subjects. > > a<-factor(rep(c(0,1),12)) > b<-factor(rep(c(0,0,1,1),6)) > s<- factor(rep(1:6,each=4)) > x <- c(49.5, 62.8, 46.8, 57, 59.8, 58.5, 55.5, 56, 62.8, 55.8, 69.5, > 55, 62, 48.8, 45.5, 44.2, 52, 51.5, 49.8, 48.8, 57.2, 59, 53.2, 56) > > now > > summary(aov(x~a*b+Error(s/(a*b)))) > > gives a table of results > but, if one wanted to generate a confidence interval for factor b one > needs to reanalyze the results thusly > > ss<-aggregate(x, list(s=s, b=b), mean) > summary(aov(x~b+Error(s/b), data=ss)) > > This yields an error term half the size as that reported for b in the > combined ANOVA. I would suggest that the way the ss and MSE are > reported is erroneous since they should be able to be used to directly > calculate confidence intervals or make mean comparisons without having > to collapse and reanalyze for every effect. > > Furthermore, I am guessing that this problem makes it impossible to > get a correct average MSE that includes the interaction term. OK, far > from impossible, but very difficult to verify that the term is correct. > > NOTE F for b is the same in the first ANOVA and the second.
As far as I can tell, yes, you get different results if you analyse the original data than if you collapse by taking means over the a factor, and no, you should not expect otherwise. The various SS in the full analysis are distance measures in 24-dim space, whereas in the aggregated analysis you get a distance in 12-space. The relation is that every value entering in the b and s:b terms will be duplicated in the former, hence the SS is twice as big. This is standard procedure, and R does the same as e.g. Genstat in this respect. It is also necessary to ensure that the residual MS are comparable, e.g. that you can test for a significant s:b random effect by comparing with the residual MS to that of the s:a:b stratum. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help