# Sums of Squares used by R in lm, aov and lmer

R calculates sequential or Type I SS by default when using *lm*, *lmer* and *aov* as opposed to the type III SS (default in SPSS) which partials out effects of other terms in the model. A hierarchical approach is suggested which gives the same results for both sums of squares and only looks at the highest order terms in a model.

Type III SS may be obtained using terms of form (for between subjects anova)

library(car) fit <- Anova(lm(y~x+z),type=c("III"))

and for more complex designs with random effects, anova() can be used

library(nlme) model.2 <- lme(y~a + b, random=~1|group) anova(model.2,type="marginal")

The *Anova()* procedure can also be used to obtain type 3 sums of squares for *lmer* in R. The Anova () procedure is available by downloading the *car* extension package from here and can be inserted into the R library folder located in C:\Program Files\R\R3.x. You can also use the summary() procedure, for obtaining type III SS for *lmer* from version 2.7.2 of R.

In addition to *lm* and *lme* (which requires the *nlme* extension package), *aov* may also be used to fit anovas in R.