############################NONPARAMETRIC TESTS #######################
#######################################################################

data<-read.table("http://user.mendelu.cz/drapela/Forest_Biometry/data/plots.txt",sep='\t',header=TRUE)
sprd13<-(data[data$species=='SPRUCE',]$d13)
oakd13<-(data[data$species=='OAK',]$d13)

summary(sprd13)
summary(oakd13)
length(sprd13)
length(oakd13)

#########################  1-S WILXOCON TEST FOR POPULATION MEAN  ###########################################

#EDA FOR D13 OF OAK


par(mfrow=c(1,2))
hist(oakd13, col="lightblue", main="Histogram DBH - oak", probability=TRUE, ylab="density", 
xlab=substitute(paste(d[13], "[cm]", sep=' ')))
lines(density(oakd13), col="red", lty="dashed")
tmp<-oakd13
lines(seq(min(tmp, na.rm=TRUE)-50, max(tmp, na.rm=TRUE)+50,1), dnorm(seq(min(tmp, na.rm=TRUE)-50, max(tmp, na.rm=TRUE)+50,1), 
mean(tmp,  na.rm=TRUE), sd(tmp, na.rm=TRUE) ), col="black")

#rankitovy graf d13 pro dub
qqnorm(oakd13, main="QQ plot - DBH of oak")
qqline(oakd13,col="red")


shapiro.test(oakd13)

#we test whether population parameter of location of DBH of oak is equal to 280 mm  and 260 mm or not

wilcox.test(oakd13, mu=280, alternative="two.sided")
t.test(oakd13,mu = 280, alternative="two.sided")

wilcox.test(oakd13, mu=260, alternative="two.sided")
t.test(oakd13,mu = 260, alternative="two.sided")

wilcox.test(oakd13, mu=280, alternative="greater")
t.test(oakd13, mu=280, alternative="greater")

wilcox.test(oakd13, mu=280, alternative="less")
t.test(oakd13, mu=280, alternative="less")
           
######################### 2-S MANN-WHITNEY TEST FOR COMPARING OF TWO MEANS ###########################################

# we test whether location shift is equal to 0 or not

wilcox.test(sprd13,oakd13, alternative="two.sided")

wilcox.test(sprd13,oakd13, alternative="greater")

wilcox.test(sprd13,oakd13, alternative="less")

#########################  PAIRED WILCOXON TEST  ###########################################


datacomp<-read.table("http://user.mendelu.cz/drapela/Forest_Biometry/data/data_comp.txt",sep='\t',quote='',header=TRUE)
	head(datacomp)


	# add id of place of measurement

		datacomp$id_pl<-seq(1, length(datacomp$id_tree), 1)


	#add new variables to dataframe datacomp - delta_foto (difference between diameters measured by caliper and 
	#photo) and delta_crit (difference between diameters measured by caliper and Criterion) 
	
		datacomp$delta_foto<-datacomp$da_calip-datacomp$da_foto
		datacomp$delta_crit<-datacomp$da_calip-datacomp$da_crit

		attach(datacomp)



par(mfrow=c(1,1))

boxplot(delta_crit, notch=TRUE, names=c("delta_crit"), main="Box plot of differences\n  caliper - criterion")
abline(0,0,col="red")
text(1, delta_crit[abs(delta_crit)>150], labels=id_pl[abs(delta_crit)>150], pos=4)


par(mfrow=c(1,2))
#histogram
tmp<-delta_crit[abs(delta_crit)<= 150]
hist(tmp, col="lightblue", main="Histogram of differences\n caliper - criterion", probability=TRUE,ylab="density", xlab="difference [mm]")
lines(density(tmp), col="red", lty="dashed")
lines(seq(min(tmp, na.rm=TRUE)-50, max(tmp, na.rm=TRUE)+50,1), dnorm(seq(min(tmp, na.rm=TRUE)-50, max(tmp, na.rm=TRUE)+50,1), mean(tmp,  na.rm=TRUE), sd(tmp, na.rm=TRUE) ), col="black")

qqnorm(tmp, main="QQ plot of differences\n  caliper - criterion"")
qqline(tmp,col="red")

shapiro.test(delta_crit[abs(delta_crit) <= 150])

wilcox.test(da_calip[abs(delta_crit) <= 150],da_crit[abs(delta_crit) <= 150], paired=TRUE, alternative="two.sided")
wilcox.test(da_calip[abs(delta_crit) <= 150],da_crit[abs(delta_crit) <= 150], paired=TRUE, alternative="less")
wilcox.test(da_calip[abs(delta_crit) <= 150],da_crit[abs(delta_crit) <= 150], paired=TRUE, alternative="greater")


detach(datacomp)