binom.liubailey {binomSamSize} R Documentation

## Calculate fixed width confidence interval for binomial proportion

### Description

Calculate a fixed width confidence interval for the the binomial proportion based on one observation from the binomial distribution

### Usage

binom.liubailey(x, n, d, lambda=0, conf.level=0.95)


### Arguments

 x Vector of number of successes in the binomial experiment. n Vector of number of independent trials in the binomial experiment. conf.level The level of confidence to be used in the confidence interval d half width of the confidence interval lambda Shrinkage factor. lambda=0 corresponds to simple \hat{p} \pm d interval.

### Details

The confidence interval is as suggested in equation (3.1) of Liu & Bailey (2002).

(C_n(p.hat)-d,C_n(p.hat)+d).

The exact form is as follows: Let z be the appropriate (1-\code{conf.level})/2 quantile of the standard normal distribution the interval with shrinkage towards 0.5 is given by:

(\hat{p}_l,\hat{p}_u) = \hat{p}_n + \frac{λ z^2 (0.5-\hat{p}_n)}{n+z^2} \pm d

The interval is then expanded to a full length of 2d using the following transformation:

\hat{p}_l^* = \max(0,\min( 1-2d, \hat{p}_l))

\hat{p}_u^* = \min(1,\max( 2d, \hat{p}_u))

As a consequence, the computed interval will always have length 2d.

If fixed length is a desired property of your CI then this is a way to go. However, the Liu and Bailey (2002) confidence intervals can have a low coverage coefficients when n is very small compared to d. When using the sample size computation procedure in ciss.liubailey one however ensures that n is large enough for the selected d to guarantee the required coverage coefficient. Thus, one should use binom.liubailey in connection with ciss.liubailey.

### Value

A data.frame containing the observed proportions and the lower and upper bounds of the confidence interval. The style is similar to the binom.confint function of the binom package

M. Höhle

### References

Liu, W. and Bailey, B.J.R. (2002), Sample size determination for constructing a constant width confidence interval for a binomial success probability. Statistics and Probability Letters, 56(1):1-5.

ciss.liubailey

### Examples

binom.liubailey(x=0:20,n=20, d=0.1, lambda=0)

#Compute coverage of this interval
cov <- coverage( binom.liubailey, n=20, alpha=0.05, d=0.1, lambda=0,
p.grid=seq(0,1,length=1000))

plot(cov,type="l")



[Package binomSamSize version 0.1-5 Index]