#----------------------------------------------------
#永田（2003）第4章 1つの母分散の検定
#----------------------------------------------------

sig.level <- .05
n <- 10
delta <- 2

########################################
#1つの母分散の検定（検定力）
#(1)sigma =/ sigma_0
########################################


power.chi <- function(sig.level,delta,n){
	pchisq(qchisq(1-sig.level/2,n-1,lower.tail=F)/delta^2,n-1,lower.tail=T)+
	pchisq(qchisq(sig.level/2,n-1,lower.tail=F)/delta^2,n-1,lower.tail=F)
	}

########################################
#1つの母分散の検定（検定力）
#(2)sigma > sigma_0
########################################
power.chi2 <- function(sig.level,delta,n){
	pchisq(qchisq(sig.level,n-1,lower.tail=F)/delta^2,n-1,lower.tail=F)
	}


########################################
#1つの母分散の検定（検定力）
#(3)sigma < sigma_0
########################################
power.chi3 <- function(sig.level,delta,n){
	pchisq(qchisq(1-sig.level,n-1,lower.tail=F)/delta^2,n-1,lower.tail=T)
	}


##################################
#samplesize.chi1(標本サイズ)
#(1)sigma =/ sigma_0
##################################

samplesize.chi1 <- function(power,delta, sig.level){
	1/2*((qnorm(sig.level/2,lower.tail=F)-delta*qnorm(power,lower.tail=F))/
	(delta-1))^2+3/2
}


##################################
#samplesize.chi2(標本サイズ)
#(2)sigma =/ sigma_0
##################################

samplesize.chi2 <- function(power,delta, sig.level){
	1/2*((qnorm(sig.level,lower.tail=F)-delta*qnorm(power,lower.tail=F))/
	(delta-1))^2+3/2
}

##################################
#samplesize.chi3(標本サイズ)
#(3)sigma =/ sigma_0　（2)と同一
##################################

samplesize.chi3 <- function(power,delta, sig.level){
	1/2*((qnorm(sig.level,lower.tail=F)-delta*qnorm(power,lower.tail=F))/
	(delta-1))^2+3/2
}




##ex 4.1
power.chi(sig.level=.05,delta=2,n=10)

##ex 4.2
delta <- seq(0,3.5,by=.01)
plot(power.chi(sig.level=.05,delta=delta,n=10)~delta,type="l")
lines(power.chi(sig.level=.05,delta=delta,n=20)~delta)
lines(power.chi(sig.level=.05,delta=delta,n=30)~delta)


##ex 4.3
power.chi2(sig.level=.05,delta=2,n=10)

##ex 4.4
delta <- seq(0,3.5,by=.01)
plot(power.chi2(sig.level=.05,delta=delta,n=10)~delta,type="l")
lines(power.chi2(sig.level=.05,delta=delta,n=20)~delta)
lines(power.chi2(sig.level=.05,delta=delta,n=30)~delta)

##ex 4.5
power.chi3(sig.level=.05,delta=.5,n=10)

##ex 4.6
delta <- seq(0,3.5,by=.01)
plot(power.chi3(sig.level=.05,delta=delta,n=10)~delta,type="l")
lines(power.chi3(sig.level=.05,delta=delta,n=20)~delta)
lines(power.chi3(sig.level=.05,delta=delta,n=30)~delta)


#ex 4.7
samplesize.chi1(power=.9,sig.level=.05,delta=2)
power.chi(sig.level=.05,delta=2,n=12)

samplesize.chi1(power=.9,sig.level=.05,delta=.5)
power.chi(sig.level=.05,delta=.5,n=15)
power.chi(sig.level=.05,delta=.5,n=14)
power.chi(sig.level=.05,delta=.5,n=13)


#ex 4.8
samplesize.chi2(power=.95,sig.level=.05,delta=5/2)
power.chi2(sig.level=.05,delta=5/2,n=9)
power.chi2(sig.level=.05,delta=5/2,n=8)


#ex 4.9
samplesize.chi3(power=.8,sig.level=.05,delta=1/3)
power.chi3(sig.level=.05,delta=1/3,n=6)
power.chi3(sig.level=.05,delta=1/3,n=5)
power.chi3(sig.level=.05,delta=1/3,n=4)