# Testing hypothesis for teh equality of medians of two related populations 

#Set working directory
setwd("~/Dropbox/ISI SCB/Data sets")

# read in csv file
dg <-read.csv("drugs.csv", TRUE)

x <- dg$Drug.B
y <- dg$Drug.A

#check for ties
d=x-y
md <- median(d)
md
d-md

#Since there are two ties (1st and 9th cases)
#we will remove the 1st case

x1 <- x[2:12]
y1 <- y[2:12]
d1=x1-y1

#check for outliers
boxplot(d1)

#assess normality assumptions of x and y
qqnorm(d1, ylab = "d Sample Quantiles")
shapiro.test(d1)

#Wilcocox test for for medians of 2 related populations
wilcox.test(x1,y1, paired=TRUE, alternative = "greater", conf.int=TRUE)


# Parametric test on original data
t.test(x,y, paired=TRUE, alternative = "greater")