#######################################################################################
# Type I error
# Type II error
# power = 1- P(Type II error]


####################T-test##################
x<-rnorm(20,0,1)
y1<-rnorm(20,0.5,1)
t.test(x,y1)
#
help(power.t.test)
delta1<-mean(x)-mean(y1)
power.t.test(n = 20, delta = delta1)
power.t.test(power = .90, delta = delta1)
power.t.test(power = .90, delta = delta1, alternative = "one.sided")

####################ANOVA##################
y1<-rnorm(10,0.5,1)
y2<-rnorm(10,0.6,1)
y3<-rnorm(10,0.7,1)
y<-c(y1,y2,y3)
g<-c(rep(1,10),rep(2,10),rep(3,10))
summary(aov(y~g))
#
help(power.anova.test)
groupmeans<-c(mean(y1), mean(y2),mean(y3))
between_var<-var(groupmeans)
within_var<- var(c(y1-mean(y1)),y2-mean(y2),y3-mean(y3))) # rezidualni rozptyl
power.anova.test(n=10,groups=3, between.var=between_var, within.var=within_var)
power.anova.test(groups=3, between.var=between_var, within.var=within_var, power=0.8)


####################Test of proportionality##################

help(power.prop.test)

#######################################################################################
library(pwr)