Dear Peter and Nils, In my initial message, I stated misleadingly that the contrast coding didn't matter for the "type-III" tests here since there is just one between-subjects factor, but that's not right: The between type-III SS is correct using contr.treatment(), but the within SS is not. As is generally the case, to get reasonable type-III tests (i.e., tests of reasonable hypotheses), it's necessary to have contrasts that are orthogonal in the row-basis of the design, such as contr.sum(), contr.helmert(), or contr.poly(). The "type-II" tests, however, are insensitive to the contrast parametrization. Anova() always uses an orthogonal parametrization for the within-subjects design.
The general advice in ?Anova is, "Be very careful in formulating the model for type-III tests, or the hypotheses tested will not make sense." Thanks, Peter, for pointing this out. John ------------------------------ John Fox, Professor Department of Sociology McMaster University Hamilton, Ontario, Canada web: socserv.mcmaster.ca/jfox > -----Original Message----- > From: Peter Dalgaard [mailto:p.dalga...@biostat.ku.dk] > Sent: January-24-09 6:31 PM > To: Nils Skotara > Cc: John Fox; r-help@r-project.org; 'Michael Friendly' > Subject: Re: [R] Anova and unbalanced designs > > Nils Skotara wrote: > > Dear John, > > > > thank you again! You replicated the type III result I got in SPSS! When I > > calculate Anova() type II: > > > > Univariate Type II Repeated-Measures ANOVA Assuming Sphericity > > > > SS num Df Error SS den Df F Pr(>F) > > between 4.8000 1 9.0000 8 4.2667 0.07273 . > > within 0.2000 1 10.6667 8 0.1500 0.70864 > > between:within 2.1333 1 10.6667 8 1.6000 0.24150 > > --- > > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > > > I see the exact same values as you had written. > > However, and now I am really lost, type III (I did not change anything > else) > > leads to the following: > > > > Univariate Type III Repeated-Measures ANOVA Assuming Sphericity > > > > SS num Df Error SS den Df F Pr(>F) > > (Intercept) 72.000 1 9.000 8 64.0000 4.367e-05 > *** > > between 4.800 1 9.000 8 4.2667 0.07273 . > > as.factor(within) 2.000 1 10.667 8 1.5000 0.25551 > > between:as.factor(within) 2.133 1 10.667 8 1.6000 0.24150 > > --- > > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > > > How is this possible? > > This looks like a contrast parametrization issue: If we look at the > per-group mean within-differences and their SE, we get > > > summary(lm(within1-within2~between - 1)) > .. > Coefficients: > Estimate Std. Error t value Pr(>|t|) > between1 -1.0000 0.8165 -1.225 0.256 > between2 0.3333 0.6667 0.500 0.631 > .. > > table(between) > between > 1 2 > 4 6 > > Now, the type II F test is based on weighting the two means as you would > after testing for no interaction > > > (4*-1+6*.3333)^2/(4^2*0.8165^2+6^2*0.6667^2) > [1] 0.1500205 > > and type III is to weight them as if there had been equal counts > > > (5*-1+5*.3333)^2/(5^2*0.8165^2+5^2*0.6667^2) > [1] 0.400022 > > However, the result above corresponds to looking at group1 only > > > (-1)^2/(0.8165^2) > [1] 1.499987 > > It helps if you choose orhtogonal contrast parametrizations: > > > options(contrasts=c("contr.sum","contr.helmert")) > > betweenanova <- lm(values ~ between)> Anova(betweenanova, idata=with, > idesign= ~as.factor(within), type = "III" ) > > Type III Repeated Measures MANOVA Tests: Pillai test statistic > Df test stat approx F num Df den Df Pr(>F) > (Intercept) 1 0.963 209.067 1 8 5.121e-07 *** > between 1 0.348 4.267 1 8 0.07273 . > as.factor(within) 1 0.048 0.400 1 8 0.54474 > between:as.factor(within) 1 0.167 1.600 1 8 0.24150 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > > > > -- > O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B > c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K > (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 > ~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
