Normal Suite: One Sample, Two Sided, Known Variance
Description
Generates the suite of functions related to the one sample normal experiment with a twosided alternative hypothesis of interest when the variance is known.
Usage
1  norm1KV.2sided(sigma, theta0, prob, mu, tau)

Arguments
sigma 
Scalar. The known standard deviation of the population of interest. 
theta0 
Scalar. The critical value of the mean under the null hypothesis: theta==theta0. 
prob 
Scalar. The prior probability of the null hypothesis. Must be a value between 0 and 1. 
mu 
Scalar. The mean of the normal prior density on theta under the alternative
hypothesis. See documentation for 
tau 
Scalar. The standard deviation for the normal prior density on theta under
the alternative hypothesis. See documentation for 
Details
norm1KV.2sided
is used to generate a suite of functions for a
onesample normal experiment with a twosided alternative hypothesis when the
variance is known. That is, when
X ~ Normal(theta,sigma2)
H0: theta == theta0 vs. H1: theta != theta0
using the following prior on theta
pi(theta) = u*I(theta==theta0) + (1u)*I(theta!=theta0)Normal(mu,tau2),
where Normal(mu,tau2) is Normal density with mean mu
and variance
tau2
and u is the prior probability of the null hypothesis
(prob
).
The functions that are generated are useful in examining the prior and
posterior densities of the parameter theta
, as well as constructing the
Bayes Factor and determining the sample size via an average error based
approach.
The arguments of norm1KV.2sided
are passed to each of the additional
functions upon their creation as default values. That is, if mu
is
set to 1 in the call to norm1KV.2sided
, each of the functions returned
will have the defaualt value of 1 for mu
. If an argument is not
specified in the call to norm1KV.2sided
, then it remains a required
parameter in all functions created.
Value
norm1KV.2sided
returns a list of 5 functions:
logm 
Returns a list of three vectors: the log marginal density under
the null hypothesis ( logm(xbar, n, sigma, theta0, prob, mu, tau)

logbf 
Returns a vector. The value of the log Bayes Factor given the observed data provided and the prior parameters specified. The function has the following usage: logbf(xbar, n, sigma, theta0, prob, mu, tau) See 
prior 
Returns a vector. The value of the prior density. The function has the following usage: prior(theta, theta0, prob, mu, tau)

post 
Returns a vector. The value of the posterior density. The function has the following usage: post(theta, xbar, n, sigma, theta0, prob, mu, tau)

ssd.norm1KV.2sided 
Sample size calculations for this particular setup. The function has the following usage: ssd.norm1KV.2sided(alpha, w, sigma, theta0, prob, mu, tau, minn = 2, maxn = 1000, all = FALSE) See 
See Also
binom1.1sided
,binom1.2sided
,
binom2.1sided
,binom2.2sided
,
norm1KV.1sided
,norm2KV.2sided
norm1UV.2sided
,ssd
,BAEssd
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33  ############################################################
# Generate the suite of functions for a onesample normal
# with a twosided test. Consider the hypothesis
# H0: theta==0 vs. H1: theta!=0
#
# with a normal prior for theta with prior mean 2 and
# prior standard deviation 1. The known standard
# deviation for the population is 5. The prior proability
# of the null hypothesis is set to 0.5.
# generate suite
f6 < norm1KV.2sided(sigma=5,theta0=0,prob=0.5,mu=2,tau=1)
# attach suite
attach(f6)
# plot the prior and posterior density when the observed data is
# n = 30, xbar = 1.
mus < seq(5,5,0.01)
mu1 < prior(mus)
mu2 < post(mus,xbar=1,n=30)
plot(c(mu1,mu2)~rep(mus,2),type="n",ylab="Density",xlab="mu",main="")
lines(mu1~mus,lty=1,lwd=2)
lines(mu2~mus,lty=2,lwd=2)
# perform sample size calculation with TE bound of 0.25 and weight 0.5
# using both the examplespecific function as well as the general.
ssd.norm1KV(alpha=0.25,w=0.5,logm=logm)
ssd.norm1KV.2sided(alpha=0.25,w=0.5)
# detain suite
detach(f6)
