
rm(list=ls())
# set.seed(101)
rnorm2 <- function(n,mean,sd){ mean+sd*scale(rnorm(n)) }
ss <- function(x) {
  sum((x-mean(x))^2)
}

n.o <- 30
n.p <- 30
o <- rnorm(n.o, 100, 10)
p <- rnorm(n.p, 105, 10)
t.test(o,p, var.equal=T)
comb <- list(o = o, p = p)
op <- stack(comb)
head(op)
colnames(op)[1] <- "values"
colnames(op)[2] <- "group"
op$group <- factor(op$group)
head(op)
boxplot(op$values~op$group)


plot(op$values~op$group)
boxplot(op$values~op$group, main="values by group",
        yaxt="n", xlab="value", horizontal=TRUE,
        col=terrain.colors(2))
abline(v=mean(op$values), col="red", lwd=3)
legend("topleft", inset=.05, title="group",
       c("o","p"), fill=terrain.colors(2), horiz=TRUE)

m.tot <- mean(op$values)
m.o <- mean(o)
m.p <- mean(p)

min.x <- min(op$values)
max.x <- max(op$values)
br <- seq(floor(min.x), ceiling(max.x), by = 1) 

hist(o, breaks=br, 
     col=rgb(1,1,1,.5))
abline(v=m.o, col="red", lwd=3)
hist(p, add=T, breaks=br,
     col=rgb(.5,1,1,.5))
abline(v=m.p, col="blue", lwd=3)
abline(v=m.tot, col='black', lwd=3)

ss.tot <- ss(op$values)
df.tot <- length(op$values)-1
ss.tot/df.tot
var(op$values)
ss.tot

ss.o <- ss(o)
ss.p <- ss(p)
df.o <- length(o)-1
df.p <- length(p)-1

m.tot
m.o
m.p
ss.o
ss.p

ss.bet <- length(o)*(m.tot-m.o)^2+length(p)*(m.tot-m.p)^2
ss.tot
ss.bet
ss.wit <- ss.o+ss.p 
ss.wit
ss.bet+ss.wit
ss.tot

df.tot <- length(op$values)-1
df.bet <- nlevels(op$group) - 1
df.wit <- (length(o)-1)+(length(p)-1)
df.tot
df.bet
df.wit

ms.tot <- ss.tot / df.tot
ms.bet <- ss.bet / df.bet
ms.wit <- ss.wit / df.wit

f.cal <- ms.bet / ms.wit
f.cal
p.val <- pf(f.cal, df1=df.bet, df2=df.wit, lower.tail = F)
p.val
summary(aov(op$values~op$group))
t.test(o,p, var.equal = T)

diff <- m.o - m.p
ssp <- (ss.o + ss.p) / (df.o + df.p)
se <- sqrt(ssp/n.o+ssp/n.p)
t.cal <- diff/se
t.cal
p.t.cal <- pt(abs(t.cal), df=df.o+df.p, lower.tail = F)*2
p.t.cal
t.cal^2
f.cal

df.bet
df.wit
f.cal