binomTestCoveragePlot {conf}

Coverage Plots for Binomial Proportions

Description

Generates plots for the actual coverage of a binomial proportion using various types of confidence intervals. Plots the actual coverage for a given sample size and stated nominal coverage 1 - alpha.

Usage

  binomTestCoveragePlot(n,
                        alpha = 0.05,
                        intervalType = "Clopper-Pearson",
                        plo = 0,
                        phi = 1,
                        clo = 1 - 2 * alpha,
                        chi = 1,
                        points = 5 + floor(250 / n),
                        showTrueCoverage = TRUE,
                        gridCurves = FALSE)

Arguments

n

sample size

alpha

significance level for confidence interval

intervalType

type of confidence interval used; either "Clopper-Pearson", "Wald", "Wilson-Score", "Jeffreys", "Agresti-Coull", "Arcsine", or "Blaker"

plo

lower limit for percentile (horizontal axis)

phi

upper limit for percentile (horizontal axis)

clo

lower limit for coverage (vertical axis)

chi

upper limit for coverage (vertical axis)

points

number of points plotted in each segment of the plot; if default, varies with 'n' (see above)

showTrueCoverage

logical; if TRUE (default), a solid red line will appear at 1 - alpha

gridCurves

logical; if TRUE, display acceptance curves in gray

Details

Generates an actual coverage plot for binomial proportions using

• various types of confidence intervals, and

• various sample sizes.

When the function is called with default arguments,

• the horizontal axis is the percentile at which the coverage is evaluated,

• the vertical axis is the actual coverage percentage at each percentile, that is, the probability that the true value at a percentile is contained in the corresponding confidence interval, and

• the solid red line is the stated coverage of 1 - alpha.

The actual coverage for a particular value of p, the percentile of interest, is

c(p) = \sum_{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) = {n \choose x} p^x (1-p)^{n-x}

for x = 0, 1, \ldots, n.

The algorithm for plotting the actual coverage begins by calculating all possible lower and upper bounds associated with the confidence interval procedure specified by the intervalType argument. These values are concatenated into a vector which is sorted. Negative values and values that exceed 1 are removed from this vector. These values are the breakpoints in the actual coverage function. The points argument gives the number of points plotted on each segment of the graph of the actual coverage.

The plo and phi arguments can be used to expand or compress the plots horizontally.

The clo and chi arguments can be used to expand or compress the plots vertically.

By default, the showTrueCoverage argument plots a solid horizontal red line at the height of the stated coverage. The actual coverage is plotted with solid black lines for each segment of the actual coverage.

The gridCurves argument is assigned a logical value which indicates whether the acceptance curves giving all possible actual coverage values should be displayed as gray curves.

Author(s)

Hayeon Park ([e-mail]), Larry Leemis ([e-mail])

References

Vollset, S.E. (1993). Confidence Intervals for a Binomial Proportion. Statistics in Medicine, 12, 809–824.

See Also

dbinom

Examples

  binomTestCoveragePlot(6)
  binomTestCoveragePlot(10, intervalType = "Wilson-Score", clo = 0.8)
  binomTestCoveragePlot(n = 100, intervalType = "Wald", clo = 0, chi = 1, points = 30)