binom1.1sided {BAEssd}  R Documentation 
Generates the suite of functions related to the one sample binomial experiment with a onesided alternative hypothesis of interest.
binom1.1sided(p0, a, b)
p0 
Scalar. The upper bound of p under null hypothesis Ho: p<=p0. 
a 
Scalar. Shape1 parameter for prior Beta distribution. See documentation for

b 
Scalar. Shape2 parameter for prior Beta distribution. See documentation for

binom1.1sided
is used to generate a suite of functions for a onesample
binomial experiment with a onesided alternative hypothesis. That is, when
X ~ Binomial(n,p)
H0: p <= p0 vs. H1: p > p0
using the following prior on p
p ~ Beta(a,b).
The functions that are generated are useful in examining the prior and
posterior densities of the parameter p
, as well as constructing the
Bayes Factor and determining the sample size via an average error based
approach.
The arguments of binom1.1sided
are passed to each of the additional
functions upon their creation as default values. That is, if p0
is
set to 0.5 in the call to binom1.1sided
, each of the functions returned
will have the defaualt value of 0.5 for p0
. If an argument is not
specified in the call to binom1.1sided
, then it remains a required
parameter in all functions created.
binom1.1sided
returns a list of 4 functions. These functions are
useful for either visualizing the problem, or computing the required sample
size:
logm 
The function returns a list of three vectors: the log marginal density under
the null hypothesis ( logm(x, n, p0, a, b)

logbf 
Returns a vector: the value of the log Bayes Factor given the observed data provided and the prior parameters specified. This function has the following usage: logbf(x, n, p0, a, b) For details on the parameters for this function, see the above description
for 
prior 
Returns a vector: the value of the prior density at the specified value of
prior(p, a, b)

post 
Returns a vector: the value of the posterior density. This function has the following usage: post(p, x, n, a, b)

binom1.2sided
,binom2.1sided
,
binom2.2sided
,norm1KV.1sided
,
norm1KV.2sided
,norm2KV.2sided
norm1UV.2sided
,ssd
,BAEssd
############################################################ # Generate the suite of functions for a onesample binomial # with a onesided test. Consider the hypothesis # H0: p<=0.5 vs. H1: p>0.5 # # with a uniform prior on p. # generate suite f1 < binom1.1sided(p0=0.5,a=1,b=1) # attach suite attach(f1) # plot prior and posterior given x = 25, n = 30 ps < seq(0.01,0.99,0.01) p1 < prior(ps) p2 < post(ps,x=25,n=30) plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="") lines(p1~ps,lty=1,lwd=2) lines(p2~ps,lty=2,lwd=2) # perform sample size calculation with TE bound of 0.25 and weight 0.5 ssd.binom(alpha=0.25,w=0.5,logm=logm) # detain suite detach(f1)