binom.liubailey {binomSamSize} | R Documentation |
Calculate a fixed width confidence interval for the the binomial proportion based on one observation from the binomial distribution
binom.liubailey(x, n, d, lambda=0, conf.level=0.95)
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. |
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
.
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. HÃ¶hle
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.
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")