# R script for lecture 2 in STK4900/9900

# Slide 4: Two-sample t-test ---------------------------------------------------

cont <- c(0.228, 0.207, 0.234, 0.220, 0.217, 0.228, 0.209, 0.221, 0.204, 0.220, 0.203, 0.219, 0.218, 0.245, 0.210)
treat <- c(0.250, 0.237, 0.217, 0.206, 0.247, 0.228, 0.245, 0.232, 0.267, 0.261, 0.221, 0.219, 0.232, 0.209, 0.255)

boxplot(treat, cont,names=c("Treatment","Control")) 

t.test(x=treat, y=cont , var.equal=TRUE)


# Slide 5: Two-sample t-test ---------------------------------------------------

n1 <- length(treat)
m1 <- mean(treat)
sd1 <- sd(treat)

n2 <- length(cont)
m2 <- mean(cont)
sd2 <- sd(cont)

sp <- sqrt((n1-1)/(n1+n2-2)*sd1^2+(n2-1)/(n1+n2-2)*sd2^2)
se <- sp*sqrt(1/n1+1/n2)

tval <- (m1-m2)/se
pval <- 2*(1-pt(tval,n1+n2-2))



# Slide 11: One-way ANOVA ------------------------------------------------------

data <- read.table("http://www.uio.no/studier/emner/matnat/math/STK4900/data/rats.txt",header=T)
View(data)
class(data$time)
class(data$diet)

data$diet <- factor(data$diet)

aov_res <- aov(time~diet, data=data)
summary(aov_res)



# Slide 13: One-way ANOVA with two groups vs Two-sample t-test -----------------

bonedensity <- data.frame(density=c(cont,treat), group=c(rep("cont",length(cont)),rep("treat",length(treat))))

aov.density <- aov(density~group,data=bonedensity) 
summary(aov.density)



# Slide 29: Correlation coefficient --------------------------------------------

fvc <- c(3.9,5.6,4.1,4.2,4.0,3.6,5.9,4.5,3.6,5.0,2.9,4.3) 
pef <- c(455,603,456,523,458,460,629,435,490,640,399,526) 

cov(fvc,pef)
cor(fvc,pef)
cov(fvc,pef)/(sd(fvc)*sd(pef))



# Slide 31: Correlation coefficient - Test and CI ------------------------------

cor.test(fvc, pef)



# Slide 32: Spearman rank correlation ------------------------------------------

cor(fvc, pef, method="spearman")

cor(rank(fvc), rank(pef), method="pearson")



# Slide 36: Linear regression - Least squares  ---------------------------------

water <- c(0.31,0.85,1.26,2.47,3.75) 
erosion <- c(0.82,1.95,2.18,3.02,6.07) 

fit <- lm(erosion~water)
summary(fit) 
plot(water, erosion, pch=19) 
abline(fit, col="blue")