Different Contrasts Results for Aov and lm in R

Question

I'm having trouble getting my contrasts from aov() and lm() to match up in R. I'm pretty sure this is because I don't fully understand what's going on or how to specify the appropriate contrasts, but I thought I'd ask anyway.

R uses treatment contrasts by default for both lm() and aov(), which means that it contrasts each level of a factor against the baseline level. I can see this in the results of lm():

data(InsectSprays)

lmMod <- lm(count ~ spray, data=InsectSprays)
summary(lmMod)

Adding the intercept to each of the coefficients gives the same mean as calculated by tapply(). However, trying to reproduce these contrasts with aov() gives different results.

model1 <- aov(count ~ spray, data = InsectSprays)

summary(model1, split=list(spray=list("Cont1"=1, "Cont2"=2, 
        "Cont3" = 3,  "Cont4" = 4, "Cont5" = 5)))

Here, the last p-value is the same as the one for the contrast in lm (p = 0.181), but the aov() contrast suggests that spray B is different from spray A (p < 0.0001) whereas lm says that they are not different (p = 0.604).

I've tried recoding the contrasts myself using sum-to-zero effects:

c1 <- c(-1, 1, 0, 0, 0, 0)
c2 <- c(-1, 0, 1, 0, 0, 0)
c3 <- c(-1, 0, 0, 1, 0, 0)
c4 <- c(-1, 0, 0, 0, 1, 0)
c5 <- c(-1, 0, 0, 0, 0, 1)

contMat <- cbind(c1, c2, c3, c4, c5)
contrasts(InsectSprays$spray) <- contMat

model2 <- aov(count ~ spray, data = InsectSprays)

summary(model2, split=list(spray=list("Cont1"=1, "Cont2"=2, 
        "Cont3" = 3,  "Cont4" = 4, "Cont5" = 5)))

Now, the first contrast gives the same p-value as lm (p = 0.604), but the last contrast says that treatment F is significantly different from A (p < 0.0001), whereas lm says it is not (p = 0.181).

I feel like I'm missing something fundamental, but I haven't been able to figure it out. Any help would be appreciated.

Answer 1

aov is doing sequential sum of squares (Type I); lm is doing adjusted sum of squares (Type II).

To compare, use lm with the dummy variables manually computed.

d2 <- data.frame(cbind(count=InsectSprays$count, model.matrix(~spray, data=InsectSprays)))
m2 <- lm(count~0+.,d2)
anova(m2)
summary(m2)

The anova gives you the same results as your aov result, while the summary gives you the same results as your lm result.