[R] Contrasts for MANOVA

[Andy Bunn]

Prof. Ripley: Thanks for the response. 

My imperfect understanding is that contrasts are a special kind of linear
combination that can be done a priori.

Here's an example that is similar to what she wants to do:

## START EXAMPLE

# Toy data:

y1 <- rnorm(15,0,2)
y2 <- runif(15)
y3 <- rnorm(15,2,1)

x1 <- c(rep("long", 5), rep("medium", 5), rep("short", 5))

dat <- data.frame(y1, y2, y3, x1)

# The question is:
# Are the population mean vectors for the multivariate responses of
# y1, y2, & y3 of the "long" x1 samples significantly different 
# from those of the combined "medium" and "short" x1 samples?

#Like so:

attach(dat)

# Get the mean for each predictor level for each response
mean.vec <- cbind(
c(mean(y1[x1 == "long"]), mean(y2[x1 == "long"]), mean(y3[x1 == "long"])),
c(mean(y1[x1 == "medium"]), mean(y2[x1 == "medium"]), mean(y3[x1 ==
"medium"])),
c(mean(y1[x1 == "short"]), mean(y2[x1 == "short"]), mean(y3[x1 == "short"]))
)

detach(dat)

mean.vec

#Ho: mean.vec[,1] == 1/2 * (mean.vec[,2] + mean.vec[,3])
## END EXAMPLE 

The actual data she is using is 10 responses and three factor levels, e.g.,
nlevels = 3, 3, 4
I hope this is clear. Thanks for any guidance.

-Andy