Príklad 1: hádzanie kockou z youtube streamu
kocky <- c(186, 168, 172, 161, 157, 180)
chisq.test(x = kocky, p = rep(1/6, 6))
##
## Chi-squared test for given probabilities
##
## data: kocky
## X-squared = 3.582, df = 5, p-value = 0.611
Príklad 2: dáta z Weldonových pokusov s kockou
uspechy <- 0:12
pocetnosti <- c(185, 1149, 3265, 5475, 6114, 5194, 3067, 1331, 403, 105, 14, 4, 0)
pocetnosti_upravene <- c(pocetnosti[1:10], sum(pocetnosti[11:13]))
pravdepodobnosti <- dbinom(uspechy, size = 12, prob = 1/3)
pravdepodobnosti_upravene <- c(pravdepodobnosti[1:10], sum(pravdepodobnosti[11:13]))
chisq.test(pocetnosti_upravene, p = pravdepodobnosti_upravene)
##
## Chi-squared test for given probabilities
##
## data: pocetnosti_upravene
## X-squared = 35.494, df = 10, p-value = 0.0001028
Príklad 3: testovanie rozdelenia
n <- 10000
lambda <- 5
set.seed(123)
x <- rexp(n, rate = 1/lambda)
y <- rexp(n, rate = 1/lambda)
data <- (x - y)/(x + y)
ks.test(data, "punif", min = -1, max = 1)
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: data
## D = 0.0056593, p-value = 0.9059
## alternative hypothesis: two-sided
Príklad 3: testovanie normálneho rozdelenia
library(nortest)
library(ipsRdbs)
data(bodyfat)
lillie.test(bodyfat$Skinfold)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: bodyfat$Skinfold
## D = 0.12774, p-value = 0.000309
lillie.test(log(bodyfat$Skinfold))
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: log(bodyfat$Skinfold)
## D = 0.067625, p-value = 0.3007
Príklad 4: testovanie zhody dvoch rozdelení
data(ffood)
ks.test(ffood$AM, ffood$PM)
##
## Exact two-sample Kolmogorov-Smirnov test
##
## data: ffood$AM and ffood$PM
## D = 0.2, p-value = 0.9813
## alternative hypothesis: two-sided