mutost.pow: 'mutost' power function

In olli0601/abc.star: abc.star

Description

Compute the power of the one-sample equivalence test for population means of normal summary values

Usage

mutost.pow(rho, df, s.of.T, c.u = NA, tau.u = NA, alpha = NA, norm = 1,
  support = c(-Inf, Inf), log = FALSE)

Arguments

rho	vector of quantile
df	Degrees of freedom
s.of.T	Standard deviation of the test statistic
c.u	Upper boundary point of the critical region
tau.u	Upper boundary point of the equivalence region
alpha	Level of the equivalence test
norm	Normalization constant for the truncated power function.
support	Support of the truncated power function (vector of dimension 2).
log	If TRUE, the power function is returned on the log scale.

Note

To compute the power, either c.u or tau.u and alpha are required. If tau.u and alpha are given, then the value of c.u is ignored.

The power function can be truncated to support and then standardized with norm. If one of these is set, the other must be provided too.

References

http://arxiv.org/abs/1305.4283

Examples

n.of.y 	<- 30
s.of.T	<- 0.2		#this is s.of.y / squrt(n.of.y)

# useful equivalence region for given stochasticity in T: 
# power is not zero, does not plateau around 1, and still high around rho=0

rho		<- seq(-2,2,0.01)
tmp	<- data.table(rho=rho, power=mutost.pow(rho, df=n.of.y-1, s.of.T, tau.u=0.8, alpha=0.01))
p	<- ggplot(tmp,aes(x=rho,y=power)) + geom_line() + labs(y='Power\n(ABC acceptance probability)')
print(p)

# power increases with tau.u and becomes flat

tmp <- lapply(seq(0.5,1.6,0.2),function(tau.u)
		{
			data.table(tau.u=as.factor(tau.u),rho=rho,power=mutost.pow(rho, df=n.of.y-1, s.of.T, tau.u=tau.u, alpha=0.01))
		})
tmp	<- do.call('rbind', tmp)
p <- ggplot(tmp,aes(x=rho,y=power,colour=tau.u,group=tau.u)) + geom_line() + labs(y='Power\n(ABC acceptance probability)')
print(p)

# power increases with n.of.y and becomes flat

tau.u 	<- 0.8
s.of.y	<- 0.8
tmp <- lapply(c(10,15,20,25,50,100),function(n.of.y)
		{
			data.table(n.of.y=as.factor(n.of.y),rho=rho,power=mutost.pow(rho, df=n.of.y-1, s.of.y/sqrt(n.of.y), tau.u=tau.u, alpha=0.01))
		})
tmp	<- do.call('rbind', tmp)
p <- ggplot(tmp,aes(x=rho,y=power,colour=n.of.y,group=n.of.y)) + geom_line() + labs(y='Power\n(ABC acceptance probability)')
print(p)

olli0601/abc.star documentation built on May 24, 2019, 12:53 p.m.