Actual Coverage Calculation for Binomial Proportions
Calculates the actual coverage of a confidence interval for a binomial proportion for a particular sample size n and a particular value of the probability of success p for several confidence interval procedures.
binomTestCoverage(n, p,
alpha = 0.05,
intervalType = "Clopper-Pearson")n |
sample size |
p |
population probability of success |
alpha |
significance level for confidence interval |
intervalType |
type of confidence interval used; either "Clopper-Pearson", "Wald", "Wilson-Score", "Jeffreys", "Agresti-Coull", "Arcsine", or "Blaker" |
Calculates the actual coverage of a confidence interval procedure at a particular value of p for
various types of confidence intervals,
various probabilities of success p, and
various sample sizes n.
The actual coverage for a particular value of p, the probability of success of interest, is
c(p) = ∑_{x=0}^n {I(x,p) {n \choose x} p^x (1-p)^{n-x}},
where I(x,p) is an indicator function that determines whether a confidence interval covers p when X = x (see Vollset, 1993).
The binomial distribution with arguments size = n and
prob = p has probability mass function
p(x) = choose(n, x) p^x (1-p)^(n-x)
for x = 0, 1, 2, …, n.
The algorithm for computing the actual coverage for a particular probability of
success begins by calculating all possible lower and upper bounds associated
with the confidence interval procedure specified by the intervalType argument.
The appropriate binomial probabilities are summed to determine the actual coverage
at p.
Hayeon Park (hpark03@email.wm.edu), Larry Leemis (leemis@math.wm.edu)
Vollset, S.E. (1993). Confidence Intervals for a Binomial Proportion. Statistics in Medicine, 12, 809-824.
binomTestCoverage(6, 0.4) binomTestCoverage(n = 10, p = 0.3, alpha = 0.01, intervalType = "Wilson-Score")
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