######### Exercise 6.1

set.seed(123321)
c1 <- round(rnorm(10, 65, 10), 0)
c2 <- round(rnorm(10, 80, 10), 0)
n1 <- c1 + 15 + round(rnorm(10, 15, 3), 0)
n2 <- c2 + 0 + round(rnorm(10, 15, 3), 0)
id <- 1:20
coach <- factor(rep(1:2, each = 10), labels = c("yes", "no"))
dat <- data.frame(id, coach, pre = c(c1, c2), post = c(n1, n2))


# ANCOVA method

library(car)
library(phia)
ancova1 <- aov(post ~ coach + pre, data = dat)
Anova(ancova1, type = 3)
interactionMeans(ancova1, "coach")

# Traditional Repeated-measures ANOVA

longdat <- dat[,1:2]
longdat <- rbind(longdat, longdat)
timefac <- factor(rep(c("pre", "post"), each = 20))
score <- c(dat$pre, dat$post)
longdat <- data.frame(longdat, timefac, score)

library(ez)
ezANOVA(data = longdat, dv = score, wid = id, within = .(timefac), between = c("coach"))

# MANOVA

obj <- lm(cbind(pre, post) ~ coach, data = dat)
idata <- data.frame(time = c("pre", "post"))
Anova(obj, idata = idata, idesign = ~ time, type = 3)
testInteractions(obj, idata = idata, across = "time", fixed = "coach", adjustment = "bonferroni")
interactionMeans(obj, idata = idata)
plot(interactionMeans(obj, idata = idata))

######### Homework 6

group <- factor(rep(c("T", "C"), each = 7))
w1 <- c(2722, 3289, 2892, 3175, 3062, 2608, 3402, 3175, 2693, 3232, 2807, 3515, 2835, 3005)
w2 <- c(2778, 3289, 2892, 3260, 3118, 2693, 3430, 3147, 2722, 3175, 2835, 3544, 2778, 3033)
w3 <- c(2920, 3345, 2863, 3289, 3175, 2722, 3430, 3147, 2778, 3118, 2807, 3600, 2693, 3005)
w4 <- c(2948, 3374, 2863, 3345, 3260, 2778, 3487, 3090, 2807, 3090, 2778, 3572, 2665, 3033)

dat <- data.frame(group, w1, w2, w3, w4)

aggregate(cbind(w1, w2, w3, w4) ~ group, data = dat, FUN = mean)
aggregate(cbind(w1, w2, w3, w4) ~ group, data = dat, FUN = sd)

library(phia)
library(car)
manovaout <- lm(cbind(w1, w2, w3, w4) ~ group, data = dat)
idata <- data.frame(time = c("w1", "w2", "w3", "w4"))
plot(interactionMeans(manovaout, idata = idata))

# ANCOVA

ancovaout <- aov(w4 ~ group + w1 + w2 + w3, data = dat)
Anova(ancovaout, type = 3)

# Traditional Repeated-measures ANOVA

groupfac <- rep(group, 4)
id <- rep(1:14, 4)
timefac <- factor(rep(c("day1", "day2", "day3", "day4"), each = 14))
weight <- c(w1, w2, w3, w4)
longdat <- data.frame(groupfac, timefac, id, weight)

library(ez)
ezANOVA(data = longdat, dv = weight, wid = id, within = .(timefac), between = c("groupfac"))

# MANOVA

Anova(manovaout, idata = idata, idesign = ~ time, type = 3)
testInteractions(manovaout, idata = idata, across = "time", fixed = "group", adjustment = "bonferroni")
testInteractions(manovaout, idata = idata, pairwise = "time", fixed = "group", adjustment = "bonferroni")


ctr <- poly(1:4, 1)
total.ctr <- list(time = ctr)
testInteractions(manovaout, idata = idata, custom = total.ctr, fixed = "group", adjustment = "bonferroni")