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.
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