ciss.binom {binomSamSize} | R Documentation |
Calculate necessary sample size for estimating a binomial proportion
with the confidence interval computed by an arbitrary
binom.confint
function
ciss.binom(p0, d, alpha=0.05, ci.fun=binom.confint, np02x = function(n, p0) round(n*p0), verbose=FALSE, nStart=1,nMax=1e6,...)
p0 |
hypothesized value of the parameter p in the binomial
distributionproportion. This is an upper bound if |
d |
half width of the confidence interval. Note: The CI is not necessarily symmetric about the estimate so we just look at its width as determine by d = 1/2*(CI_upper - CI_lower). |
alpha |
a two-sided (1-α)\cdot 100\% confidence interval is computed |
ci.fun |
Any |
np02x |
A function specifying how to calculate the value of x which results in an estimator of the proportion being as close as possible to the anticipated value p_0. Typically the value is obtained by rounding the result of x*p0. |
verbose |
If |
nStart |
Value where to start the search. The default |
nMax |
Max value of the sample size n to try in the iterative search. See details |
... |
Additional arguments sent to |
Given a pre set α-level and an anticipated value of p, say p_0, the objective is to find the minimum sample size n such that the confidence interval will lead to an interval of length 2\cdot d.
Using ciss.binom
this is done in a general purpose way by
performing an iterative search for the sample size. Starting from
n=nStart the appropriate x value, computed as
round(x*p0)
, is found. For this integer x and the current
n the corresponding confidence interval is computed using the
function ci.fun
. This function has to deliver the same type of
result as the binom.confint
function, i.e. a
data frame containing the arguments lower
and upper
containing the borders of the confidence interval.
The sample size is iteratively increased until the obtained confidence
interval has a length smaller than 2*d. This might
take a while if n is large. It is possible to speed up the
search if an appropriate nStart
is provided.
A brute force search is used within the function. Note that for many of the confidence intervals explicit expressions exists to calculate the necessary sample size.
the necessary sample size n
M. HÃ¶hle
binom.confint
and its related functions
#Compute the classical Wald-type interval using brute force search #Note that nStart=2 needs to be called, because the Wald-intervals #for x=round(1*0.5)=0 is too short. ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="asymptotic",nStart=2) #This could of course be done easier ciss.wald(p0=1/2, d=0.1, alpha=0.05) #Same for the Wilson intervals ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="wilson") ciss.wilson(p0=1/2, d=0.1, alpha=0.05) #Now the mid-p intervals ciss.binom(p0=1/2, d=0.1, alpha=0.05, ci.fun=binom.midp) #This search in Fosgate (2005) is a bit different, because interest #is not directly in the length, but the length is used to derive #the upper and lower limits and then a search is performed until #the required alpha level is done. The difference is negliable ciss.midp(p0=1/2, d=0.1, alpha=0.05) #Another situation where no closed formula exists ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="lrt") #Pooled samples. Now np02x is a func taking three arguments #The k argument is provided as additional argument np02x <- function(n,p0,k) round( (1-(1-p0)^k)*n ) ciss.binom( p0=0.1, d=0.05, alpha=0.05, ci.fun=poolbinom.lrt, np02x=np02x, k=10,verbose=TRUE)