# Anova oneway with Siegel data
rm(list = ls())
setwd ("C:\\Users\\Dave\\Dropbox\\Webs\\methods8\\DataFiles   ")
data <- read.table("Tab12-1.dat", header = T)
attach(data)
Group <- factor(Group, labels = c("M-S", "M-M", "S-S", "S-M", "Mc-M"))
grp.means = tapply(Time, Group, mean)
cat ("The group means are = ", grp.means, '\n', "and the grand mean is = ", mean(Time),'\n')

boxplot(Time ~ Group, main = "Response Times by Group", xlab = "Group Membership",
  ylab = "Response Time" )
  
contrasts(Group) = 'contr.treatment'
model1 <- lm(Time ~ Group)
summary.lm(model1)


# Change the base group
contrasts(Group) = 'contr.treatment'(levels(Group), base = 3)
model1a <- lm(Time ~ Group)
summary.lm(model1a)

contrasts(Group) = 'contr.sum'
model2 <- lm(Time ~ Group)
summary.lm(model2)

# Now go on to a different kind of contrast--User Specified Contrasts
L <- matrix(c(-1/3, -1/3, -1/3, 1/2, 1/2,
   0, 0, 0, 1, -1,
   0, 1, -1, 0, 0),
   nrow = 5, ncol = 3)
contrasts(Group) = L
model3 <- lm(Time ~ Group)
summary.aov(model3,split=list(Group=list( "First Three vs S-S and Mc-M" = 1,
 "S-M vs Mc-M"=2, "M-M vs S-S" = 3)))

# Now I do this using inverse --get the same answer because these are orthogonal
L <- matrix(c(1,1,1,1,1,
-1/3, -1/3, -1/3, 1/2, 1/2,
0, 0, 0, 1, -1,
1/2, -1, 1/2, 0, 0,
0, 1, -1, 0, 0), nrow = 5)
Linv <- solve(t(L))
new.contrasts <- Linv[,2:5]
contrasts(Group) = new.contrasts
model4 <- lm(Time~Group )
summary.aov(model4,split=list(Group=list("First 3 vs last 2"=1, "First two vs third" = 2,
 "First vs fifth"=3, "Fourth vs fifth" = 4)))
 
# The following gives correct solution for nonorthogonal design
# Notice that it uses the Linverse
# I need to use the Linverse with nonorthogonal designs
setwd ("C:\\Users\\Dave\\Dropbox\\Webs\\methods8\\DataFiles   ")
dat <- read.table("Tab12-1.dat", header = T)
attach(dat)
Group <- factor(Group)
#  I am specifying the contrast matrix as L and its inverse as LInv
L <- matrix(c(1,1,1,1,1,
-1/3, -1/3, -1/3, 1/2, 1/2,
1, 1, -2, 0, 0,
1, 0, 0, 0,-1,
0, 0, 0, -1, 1), nrow = 5)
Linv <- solve(t(L))
new.contrasts <- Linv[,2:5]
contrasts(Group) = new.contrasts
model4 <- lm(Time~Group)
summary.lm(model4,split=list(Group=list("First 3 vs last 2"=1, "First two vs third" = 2,
 "First vs Fifth"=3, "Fourth vs fifth" = 4)))
 
 #  This will give the wrong answer
contrasts(Group) = L[,2:5]  # We need to get rid of that first row.
model4 <- lm(Time~Group)
summary.lm(model4,split=list(Group=list("First 3 vs last 2"=1, "First two vs third" = 2,
 "First vs Fifth"=3, "Fourth vs fifth" = 4)))