AcceptAffCI {CooccurrenceAffinity}

Acceptability Interval

Description

This function calculates the "Acceptability Interval" of Blaker for the log-odds parameter alpha in the Extended Hypergeometric distribution.

Usage

AcceptAffCI(x, marg, lev, CPint)

Arguments

x

integer co-occurrence count that should properly fall within the closed interval [max(0,mA+mB-N), min(mA,mB)]

marg

a 3-entry integer vector (mA,mB,N) consisting of the first row and column totals and the table total for a 2x2 contingency table

lev

a confidence level, generally somewhere from 0.8 to 0.95 (default 0.95)

CPint

the exact conservative ("Clopper-Pearson-type") interval CI.CP calculated in the function AlphInts()

Details

This function calculates the "Acceptability Interval" based on "Acceptability Function" computed by AcceptAffin(). This interval, developed by Blaker (2000), was proved in that paper's Theorem 1 in a more general class of estimation problems to have three essential properties: it falls within the CI.CP confidence interval; it maintains the property of being conservative, i.e., of having coverage probability under the Extended Hypergeometric (mA,mB,N, alpha) distribution at least as large as the nominal level; and it is larger when the confidence level is larger.

Value

This function returns the "Acceptability Interval" of Blaker (2000). The code is adapted from Blaker's Splus code for the case of an unknown binomial proportion.

Author(s)

Eric Slud

References

Blaker, H. (2000), “Confidence curves and improved exact confidence intervals for discrete distributions", Canadian Journal of Statistics 28, 783-798.

Examples

auxCP = AlphInts(30,c(50,80,120), lev=0.9)$CI.CP
AcceptAffCI(30,c(50,80,120), 0.9, auxCP)

AlphInts(30,c(50,80,120), lev=0.9)$CI.Blaker