# Testing for equal medians for more than two independent populations

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

# read in csv file
th <-read.csv("tours.csv", TRUE)

Time <- th$Minutes
Tourguide <-th$Tour

#Display the data in boxplots
boxplot(Time~Tourguide)


# Kruskal-Wallis Test: 
#One-Way Analysis of Variance by Ranks

kruskal.test(Time~Tourguide)


#Completely Randomised Design: one-way ANOVA
th.aov<- aov(Time~Tourguide)
summary(th.aov)

#check for normality and equal variances for one-way ANOVA
res  <- th.aov$residuals
qqnorm(res, ylab = "Residuals Sample Quantiles")
shapiro.test(res)

#residual plot to assess constant variance assumption
res <- th.aov$residuals
fit <- th.aov$fitted.values
plot(fit,res, main="Residual Plot",xlab= "Fitted Values", ylab="Residuals")

#Levene's Test to assess constant variance assumption                     
library(car)
leveneTest(th.aov)