binom.blaker.VHadj.acc {BlakerCI} R Documentation

## Blaker's binomial acceptability function with Vos-Hudson adjustment.

### Description

Calculates values of the Vos-Hudson 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 = 1e-10, nmax=n+1000,int.eps=1e-12, ...)
```

### 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 `type = "orig"`, Vos-Hudson adjustment applied to original acceptability function. For `type = "unimod"`, smallest unimodal function greater or equal to the adjusted acceptability function. `acc.tol` numerical tolerance (relevant only for `type = "unimod"`). `nmax` Pairs `(y, m)` of number of trials and number of successes are allowed to contribute to the Vos-Hudson adjustment for only `m` up to `nmax`. Warning is returned when greater numbers of trials are suspected to have influence. `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. `ceiling(xx - int.eps)` is calculated instead of `ceiling(xx)`.) `...` additional arguments to be passed to `binom.blaker.acc.single.p`; in fact, just `maxiter` (see `BlakerCI-internal`).

### 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 Vos-Hudson 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("Vos-Hudson 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.adj-acc,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 Vos-Hudson 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.)
```

[Package BlakerCI version 1.0-6 Index]