binom.blaker.VHadj.acc {BlakerCI}  R Documentation 
Blaker's binomial acceptability function with VosHudson adjustment.
Description
Calculates values of the VosHudson adjusted acceptability function in a sequence of points (for, e.g., plotting purposes). The adjusted acceptability function may optionally be “unimodalized”, i.e. replaced with the smallest greater or equal unimodal function.
Usage
binom.blaker.VHadj.acc(x, n, p, type = c("orig", "unimod"),
acc.tol = 1e10, nmax=n+1000,int.eps=1e12, ...)
Arguments
x 
number of successes. 
n 
number of trials. 
p 
vector (length 1 allowed) of hypothesized binomial parameters (between 0 and 1). In case of more than one point, an increasing sequence required. 
type 
for 
acc.tol 
numerical tolerance (relevant only for 
nmax 
Pairs 
int.eps 
Maximum expected error of machine representation of integers
calculated from reals via multiplication and division.
(Used in order to round numbers correctly if they happen
to be integer, e. g.

... 
additional arguments to be passed to 
Details
The relationship between the adjusted acceptability function
and the adjusted confidence intervals
(see binom.blaker.VHadj.limits
)
is the same as between the unadjusted acceptability function
and confidence interval (see binom.blaker.acc
,
binom.blaker.limits
): The confidence interval is the
convex hull of the set of those points where the function
exceeds 1  confidence level.
Value
Vector of VosHudson adjusted acceptability values (with or without unimodalization) in points of p
.
Warning
(1) Comparing output of the function with that of
binom.blaker.acc
cannot answer positively the question
whether the unadjusted and adjusted functions are identical
on an interval (but, up to the numerical accuracy, in the points
of p
only).
(2) The Warning section of the binom.blaker.VHadj.limits
documentation is relevant here, as well.
Author(s)
Jan Klaschka klaschka@cs.cas.cz
Examples
p < seq(0,1,length=10001)
acc.adj < binom.blaker.VHadj.acc(6,13,p)
acc < binom.blaker.acc(6,13,p)
plot(p,acc.adj,type="l",col="red",ylab="acceptability"
,main=paste("VosHudson adjustment of acceptability function"
,"for 6 successes in 13 trials"
, sep="\n")
)
lines(p,acc,type="l")
legend(x=.7,y=.8,c("unadjusted","adjustment"),col=c("black","red"),lwd=1)
## Plot of differences between the unadjusted and adjusted
## acceptability functions reveals some adjustment details
## hardly visible in the previous graph.
plot(p,acc.adjacc,type="l",ylab="acceptability difference")
## The narrow peak near 0.215 is close to the
## Blaker's lower 0.95 confidence limit.
##
## Focussing on the neighbourhood of 0.215:
p < seq(0.21,0.22,length=1001)
acc.adj < binom.blaker.VHadj.acc(6,13,p)
acc < binom.blaker.acc(6,13,p)
plot(p,acc.adj,type="l",col="red",ylab="acceptability"
,main=paste("A detail of VosHudson adjustment of acceptability function"
,"for 6 successes in 13 trials"
,sep="\n")
,ylim=c(0.02,0.09)
)
lines(p,acc,type="l")
legend(x=.210,y=.08,c("unadjusted","adjustment"),col=c("black","red"),lwd=1)
## The above adjustment results from the fact that, though
## 15 > 13 and 7/15 > 6/13, the acceptability function
## for 7 successes in 15 trials is greater that that for 6 successes
## in 13 trials on a short interval:
acc.7.15 < binom.blaker.acc(7,15,p)
plot(p,acc,type="l",ylab="acceptability"
,main=paste("A detail of acceptability functions"
,sep="\n")
,ylim=c(0.02,0.09)
)
lines(p,acc.7.15,type="l",col="green")
legend(x=.210,y=.08,c("6 / 13","7 / 15"),col=c("black","green")
,title="succ / trials",lwd=1)
## The adjustment shifts the point where the 0.05 level is exceeded,
## i. e. the Blaker's lower 0.95 confidence limit, from 0.2158 to 0.2150.
## (Compare with Examples in binom.blaker.VHadj.limits section.)