#==========================================================
#                 P R I K L A D    9.1
#==========================================================

skull.BF <- c(133, 134, 132, 137, 135, 
              135, 136, 137, 135, 137, 
              137, 136, 139, 126, 130)
sum(skull.BF)
shapiro.test(skull.BF) # Data nepochazi z normalniho rozdeleni


# Znamenkovy test
library(PASWR)
SIGN.test(skull.BF, md = 131, alt = 'two.sided')  # test. statistika, IS, p-hodnota
(n <- sum(skull.BF - 131 != 0)) # pocet nenulovych rozdilu
# kriticky obor -> viz tabulky


# Wilcoxonuv test
wilcox.test(skull.BF, mu = 131, alternative = 'two.sided',
            conf.int = T, correct = F, exact = F )  # IS, p-hodnota, cast testovaci statistiky
(S1 <- 109.5)
(n <- sum(skull.BF -131 != 0)) # pocet nenulovych rozdilu
(S2 <- n * (n+1)/2 - S1)
(Sw <- min(S1, S2)) # testovaci statistika
# kriticky obor -> viz tabulky

#==========================================================
#                 P R I K L A D    9.2
#==========================================================

data <- read.delim('03-paired-means-clavicle2.txt')
data <- na.omit(data)

L <- data[data$sex == 'f', 'length.L']
R <- data[data$sex == 'f', 'length.R']
Z <- L - R # rozdily
length(Z)
nortest::lillie.test(Z) # Rozdily nepochazi z normalniho rozdeleni


# Znamenkovy test
SIGN.test(Z, md = 0, alternative = 'greater') # test. statistika, IS, p-hodnota
(n <- sum(Z - 0 != 0)) # pocet nenulovych rozdilu
# kriticky obor -> viz tabulky


# Wilcoxonuv test
wilcox.test(Z, mu = 0, alternative = 'greater',
            conf.int = T, correct = F, exact = F) # cast test. statistiky, IS, p-hodnota
(S1 <- 628)
(S2 <- n*(n+1)/2 - S1)
(Sw <- min(S1, S2)) # test. statistika
# kriticky obor -> viz tabulky

#==========================================================
#                 P R I K L A D    9.3
#==========================================================

skull.BF <- c(133, 134, 132, 137, 135, 
              135, 136, 137, 135, 137, 
              137, 136, 139, 126, 130)
skull.BM <- c(132, 132, 133, 130, 143, 132, 137) 
sum(skull.BM)
shapiro.test(skull.BM) # Data pro muze nepochazi z normalniho rozdeleni
shapiro.test(skull.BF) # Data pro zeny nepochazi z normalniho rozdeleni

# Wilcoxonuv test
wilcox.test(skull.BM, skull.BF, alt = 'two.sided',
            correct = F, exact = F, conf.int = T) # cast test. statistiky, IS, p-hondota
n1 <- 7
n2 <- 15
(U1 <- 39.5)
(U2 <- n1 * n2 - U1)
(Uw <- min(U1, U2)) # testovaci statistika
# kriticky obor -> viz tabulky

#==========================================================
#                 P R I K L A D    10.1
#==========================================================

data <- data.frame(
  svetla = c(1768, 946, 115),
  kastan = c(807, 1387, 438),
  cerna = c(189, 746, 288),
  rezava = c(47, 53, 16),
  row.names = c('morda', 'zelena', 'hneda')
)

round(chisq.test(data, correct = F)$expected, 1) # podminka dobre aproximace splnena
chisq.test(data, correct = F) # test. statistika K, p-hodnota
chisq.test(data, correct = F)$p.val # presna p-hodnota

alpha <- 0.05
r <- 3
s <- 4
qchisq(1 - alpha, (r-1)*(s-1)) # kriticky obor


lsr::cramersV(data, correct = T) # Crameruv koeficient - funkci
K <- 1073.5
n <- 6800
m <- min(3,4)
(V <- sqrt(K / (n * (m-1)))) # Crameruv koeficient - vzorcem

#==========================================================
#                 P R I K L A D    10.2
#==========================================================
data <- data.frame(muzi = c(20, 30),
                   zeny = c(30, 20),
                   row.names = c('A', 'B'))
fisher.test(data) # Fisheruv faktorialovy (presny test); p-hodnota

#==========================================================
#                 P R I K L A D    10.3
#==========================================================
chisq.test(data, correct = F)$exp # podminka dobre aproximace
a <- 20
b <- 30
c <- 30
d <- 20

(OR <- (a * d) / (b * c))  # podil sanci
log(OR) # logaritmus podilu sanci

(t0 <- log(OR) / sqrt(1/a + 1/b + 1/c + 1/d)) # testoaci statistika
alpha <- 0.05
qnorm(alpha / 2) # kriticky obor
qnorm(1 - alpha/2) # kriticky obor

(dh <- log(OR) - sqrt(1/a + 1/b + 1/c + 1/d) * qnorm(1-alpha / 2)) # dolni hranice IS
(hh <- log(OR) - sqrt(1/a + 1/b + 1/c + 1/d) * qnorm(alpha / 2)) # horni hranice IS

2 * min (pnorm(t0), 1 - pnorm(t0)) # p-hodnota
1/OR # 1/podil sanci (lepsi interpretace, protoze v tomto priklade vyslo OR < 1, kdezto 1/OR > 1)

chisq.test(data, correct = F) # Pearsonuv test bez korekce (analogie rucniho vypoctu)
chisq.test(data, correct = T) # Pearsonuv test s korekci (lepsi verze)