exact2x2 (version 1.6.9)

calcTall: Calculate all Tstat for all values of the (n1+1) X (n2+1) sample space from the two sample binomial problem.

Description

Used mostly by internal call from uncondExact2x2. If EplusM=FALSE and tiebreak=FALSE then the result is just Tstat(allx,n1,ally,n2,delta0). Otherwise does more complicated calculations.

Usage

calcTall(Tstat, allx, n1, ally, n2, delta0 = 0, parmtype = "difference", 
    alternative = "two.sided", tsmethod = "central", EplusM = FALSE, tiebreak = FALSE)

Value

a vector of the same length as allx, giving values of Tstat function at all values in the sample space.

Arguments

Tstat

ordering function

allx

vector of x1 values, typically rep(0:n1,n2+1)

n1

sample size in group 1

ally

vector of x2 values, typically rep(0:n2,each=n1+1)

n2

sample size in group 2

delta0

null parameter value for input into Tstat

parmtype

parmeter type, either 'difference', 'ratio', or 'oddsratio'

alternative

alternative hypothesis, either 'two.sided' or not

tsmethod

two-sided method, either 'central' or 'square'

EplusM

logical, do E+M ordering of Lloyd (2008)?

tiebreak

logical, do tie break method? Only allowed when tsmethod!='square'.

Details

When tiebreak=TRUE does a method that breaks ties in the ordering function differently depending on the parmtype value. The tie breaks are developed to make sense when method="simple" and tsmethod!="square", when applied to other methods it may not necessarily break ties reasonably. For that reason tiebreak=TRUE returns an error when tsmethod="square". For parmtype="difference" ties are broken based on Z scores on the difference in proportions, with larger values of Z treated as larger. This means that when the sample proportions are equal, the ties are not broken. For parmtype="ratio" ties are broken based on abs(Z), where the Z scores are based on the difference in log proportions, except when x1=0 (when ties are broken by x2) or x2=0 (when ties are broken by 1/x1). For parmtype="oddsratio" ties are broken based on abs(Z), where here the Z scores are based on the difference in log odds, except when x1=0 or x1=n1 or x2=0 or x2=n2 (see code for specifics).

The E+M method, is to take an existing ordering function, Tstat, and calculate a one-sided p-value based on that ordering function evaluated at the constrained maximum likelihood estimates of the parameters. The ordering is then the set of one-sided p-values from Pr[T(X)<=T(xobs)], except when alternative="two.sided" and tsmethod="square" in which case it is 1-p, where p, the p-value, is based on Pr[T(X)>=T(xobs)]. The latter exception is needed so that larger values are more likely to reject.

If tiebreak=TRUE and EplusM=TRUE, the teibreak calculations are always done first.