exact.pval2s | R Documentation |

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).

There is additional complexity in *p*-values for the two-sided alternatives.
A recommended method is adding up probabilities of the same
size and smaller than the probability associated with the current table.
Alternatively, one can double the one-sided *p*-value (see (\insertCiteagresti:1992;textualnnspat).

Let the probability of the contingency table itself be *p_t=f(n_{11}|n_1,n_2,c_1;θ_0)*
where *θ_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.

**Type (I):** For double the one-sided *p*-value, we propose the following four variants:

[(i)] twice the minimum of

*p_{inc}*for the one-sided tests, which is table-inclusive version for this type of two-sided test, and denoted as*p^I_{inc}*,[(ii)] twice the minimum of

*p_{inc}*minus twice the table probability*p_t*, which is table-exclusive version of this type of two-sided test, and denoted as*p^I_{exc}*,[(iii)] table-exclusive version of this type of two-sided test plus

*p_t*, which is mid-*p*-value for this test, and denoted as*p^I_{midd}*,[(iv)]Tocher corrected version (see

`tocher.cor`

for details).

**Type (II):** For summing the *p*-values of more extreme —than that of the table— cases
in both directions, the following variants are obtained.
The *p*-value is *p=∑_S f(t|n_1,n_2,c_1;θ=1)* with

[(i)]

*S=\{t:\,f(t|n_1,n_2,c_1;θ=1) ≤q p_t\}*, which is called*table-inclusive version*,*p^{II}_{inc}*,[(ii)] the probability of the observed table is included twice, once for each side; that is

*p=p^{II}_{inc}+p_t*, which is called*twice-table-inclusive version*,*p^{II}_{tinc}*,[(iii)] table-inclusive minus

*p_t*, which is referred as*table-exclusive version*,*p^{II}_{exc}*,[(iv)] table-exclusive plus one-half the

*p_t*, which is called*mid-*,*p*version*p^{II}_{mid}*and,[(v)]

*Tocher corrected version*,*p^{II}_{Toc}*, is obtained as before.

See (\insertCiteceyhan:exact-NNCT;textualnnspat) for more details.

exact.pval2s(ptable, pval, type = "inc", double = FALSE)

`ptable` |
Probability of the observed |

`pval` |
Table inclusive |

`type` |
The type of the |

`double` |
A logical argument (default is |

A modified *p*-value based on the correction specified in `type`

.

Elvan Ceyhan

`exact.pval1s`

and `tocher.cor`

ct<-matrix(sample(20:40,4),ncol=2) ptab<-prob.nnct(ct) pv<-.23 exact.pval2s(ptab,pv) exact.pval2s(ptab,pv,type="exc") exact.pval2s(ptab,pv,type="mid")

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