# Nezavislost nahodnych velicin

# 1. priklad 
rm(list=ls())
load("cviceni12.RData")

tab <- data12$pr1
attach(tab)
tab
# vytvoreni kontingencni tabulky
(ct <- xtabs(count~type+social))
#mosaicplot(t(ct))
# Pearsonuv test dobre shody
(test <- chisq.test(ct))
# Crameruv koeficient
n <- sum(ct)
m <- min(dim(ct))
K <- test$statistic
(Cramer <- sqrt(K/(n*(m-1))))
detach(tab)
#--------------------------------

# 2. priklad 
tab <- data12$pr2
attach(tab)
alpha <- 0.05
tab
# vytvoreni kontingencni tabulky
(ct <- xtabs(pocty~prijeti+dojem))
#mosaicplot(t(ct))
# Interval spolehlivosti
a <- ct[1,1]
b <- ct[1,2]
c <- ct[2,1]
d <- ct[2,2]
lnOR <- log(a*d/(b*c))
lnD <- lnOR - sqrt(1/a+1/b+1/c+1/d)*qnorm(1-alpha/2)
lnH <- lnOR + sqrt(1/a+1/b+1/c+1/d)*qnorm(1-alpha/2)
exp(c(lnD,lnH))

# Pomoci klasicke kontingencni tabulky
# Pearsonuv test dobre shody
(test <- chisq.test(ct))
# Crameruv koeficient
n <- sum(ct)
m <- min(dim(ct))
K <- test$statistic
(Cramer <- sqrt(K/(n*(m-1))))
detach(tab)
#-----------------------------------------------------

# 3. priklad 
tab <- data12$pr3
tab
library(Hmisc)
analyza <- rcorr(tab,type="spearman")
(Spearmanuv_koeficient <- analyza$r[1,2])
(p_hodnota <- analyza$P[1,2])
#-----------------------------------------------------

# 4. priklad 
tab <- data12$pr4
tab
x <- tab[,1]
y <- tab[,2]
(analyza <- cor.test(x,y,alternative="greater"))
#-----------------------------------------------------

# 5. priklad 
R <- 0.85
c <- 0.9
alpha <- 0.05
n <- 600
Z <- 1/2*log((1+R)/(1-R))
(U <- (Z - 1/2*log((1+c)/(1-c)) - c/(2*(n-1)))*sqrt(n-3))
(obor_prijeti <- c(-qnorm(1-alpha/2),qnorm(1-alpha/2)))
#-----------------------------------------------------

# 6. priklad 
R1 <- 0.65
R2 <- 0.37
alpha <- 0.05
n1 <- 100
n2 <- 142
Z1 <- 1/2*log((1+R1)/(1-R1))
Z2 <- 1/2*log((1+R2)/(1-R2))
(U <- (Z1 - Z2)/sqrt(1/(n1-3)+1/(n2-3)))
(obor_prijeti <- c(-qnorm(1-alpha/2),qnorm(1-alpha/2)))
#-----------------------------------------------------

# 7. priklad 
tab <- data12$pr7
tab
x <- tab[,1]
y <- tab[,2]
(analyza <- cor.test(x,y))
R <- cor(x,y)
alpha <- 0.05
n <- 10
Z <- 1/2*log((1+R)/(1-R))
(U <- tanh(c(Z - qnorm(1-alpha/2)/sqrt(n-3),Z + qnorm(1-alpha/2)/sqrt(n-3))))
#-------------------------------------------------------------------------------