In using Fisher's exact test on the \(2 \times 2\) nearest neighbor contingency tables (NNCTs) a correction may be needed for the \(p\)-value. For the one-sided alternatives, the probabilities of more extreme tables are summed up, including or excluding the probability of the table itself (or some middle way). Let the probability of the contingency table itself be \(p_t=f(n_{11}|n_1,n_2,c_1;\theta_0)\) where \(\theta_0=(n_1-1)(n_2-1)/(n_1 n_2)\) which is the odds ratio under RL or CSR independence and \(f\) is the probability mass function of the hypergeometric distribution. For testing the one-sided alternative \(H_o:\,\theta=\theta_0\) versus \(H_a:\,\theta>\theta_0\), we consider the following four methods in calculating the \(p\)-value:
[(i)] with \(S=\{t:\,t \geq n_{11}\}\), we get the table-inclusive version which is denoted as \(p^>_{inc}\),
[(ii)] with \(S=\{t:\,t> n_{11}\}\), we get the table-exclusive version, denoted as \(p^>_{exc}\).
[(iii)] Using \(p=p^>_{exc}+p_t/2\), we get the mid-\(p\) version, denoted as \(p^>_{mid}\).
[(iv)] We can also use Tocher corrected version which is denoted as \(p^>_{Toc}\)
(see tocher.cor for details).
See (ceyhan:exact-NNCT;textualnnspat) for more details.
exact.pval1s(ptable, pval, type = "inc")A modified \(p\)-value based on the correction specified in type.
Probability of the observed \(2 \times 2\) NNCT under the null hypothesis using the hypergeometric distribution for Fisher's exact test.
Table inclusive \(p\)-value for Fisher's exact test on the NNCT.
The type of the \(p\)-value correction for the one-sided exact test on the NNCT, default="inc".
Takes on values "inc", "exc", "mid", "tocher" (or equivalently 1-4, respectively) for table inclusive,
table-exclusive, mid-\(p\)-value, and Tocher corrected \(p\)-value, respectively.
Elvan Ceyhan
exact.pval2s and tocher.cor
ct<-matrix(sample(20:40,4),ncol=2)
ptab<-prob.nnct(ct)
pv<-.3
exact.pval1s(ptab,pv)
exact.pval1s(ptab,pv,type="exc")
exact.pval1s(ptab,pv,type="mid")
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