CooccurrenceAffinity (version 1.0)

EHypMidP: Quantile of the Extended Hypergeometric distribution approximated by the midP distribution function

Description

This function does the analogous calculation to that of EHypQuInt, but with the Extended Hypergeometric distribution function F(x) = F(x,mA,mB,N, exp(alpha)) replaced by (F(x) + F(x-1))/2.

Usage

EHypMidP(x, marg, lev)

Value

This function returns the interval of alpha values with endpoints (F(x,alpha)+F(x-1,alpha))/2 = (1+lev)/2 and (F(x,alpha)+F(x+1,alpha))/2 = (1-lev)/2.

The idea of calculating a Confidence Interval this way is analogous to the midP CI used for unknown binomial proportions (Agresti 2013, p.605).

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)

Author

Eric Slud

Details

This function does the analogous calculation to that of CI.CP, but with the Extended Hypergeometric distribution function F(z, alpha) = F(z,mA,mB,N, exp(alpha)) replaced by (F(z,alpha) + F(z-1,alpha))/2.

References

Agresti, A. (2013) Categorical Data Analysis, 3rd edition, Wiley.

Examples

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

EHypMidP(20, c(204,269,2016), 0.9)