# contrasts

dv <- c(1.28, 1.35, 3.31, 3.06, 2.59, 3.25, 2.98, 1.53, -2.68, 2.64, 1.26, 1.06,
-1.18, 0.15, 1.36, 2.61, 0.66, 1.32, 0.73, -1.06,0.24, 0.27, 0.72, 2.28,
-0.41, -1.25, -1.33, -0.47, -0.6, -1.72, -1.74, -0.77, -0.41, -1.20, -0.31, -0.74,
-0.45, 0.54, -0.98, 1.68, 2.25, -0.19, -0.90, 0.78, 0.05, 2.69, 0.15, 0.91,
2.01, 0.40, 2.34, -1.80, 5.00, 2.27, 6.47, 2.94, 0.47, 3.22, 0.01, -0.66)
group <- factor(rep(1:5, each = 12))
tapply(dv, group, mean)

# Use treatment contrasts to compare each group to the first group.
options(contrasts = c("contr.treatment","contr.poly"))  # The default
model1 <- lm(dv~group)
summary(model1)
summary(aov(model1))

# Use sum contrasts to compare each group against the grand mean
options(contrasts = c("contr.sum","contr.poly"))
model2 <- lm(dv~group)
summary(model2)
    #Intercept = GM, others = deviations from GM
    
    # polynomial by hand
#    a(i) <- 2, -1, 0, 2, 2)
order.group <- ordered(group)
order.group
model4 <- lm(dv~order.group)

Means <- (tapply(dv, order.group, mean))
coefs.by.hand.m4 <- c(mean(Means), sum(Means*contrasts(order.group)[,1]),
   sum(Means*contrasts(order.group)[,2]) ,
   sum(Means*contrasts(order.group)[,3]),
   sum(Means*contrasts(order.group)[,4]))

contrasts.by.hand

From page 375
dat <- read.table(file(choose), header = T)