exact.pval2s: p-value correction to the two-sided version of exact NNCT...
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exact.pval2s

R Documentation

`p`-value correction to the two-sided version of exact NNCT test

Description

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;\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.

**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=\sum_S f(t|n_1,n_2,c_1;\theta=1) with

[(i)] S=\{t:\,f(t|n_1,n_2,c_1;\theta=1) \leq 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.

Usage

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

Arguments

`ptable`	Probability of the observed `2 \times 2` NNCT under the null hypothesis using the hypergeometric distribution for Fisher's exact test.
`pval`	Table inclusive `p`-value for Fisher's exact test on the NNCT.
`type`	The type of the `p`-value correction for the two-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.
`double`	A logical argument (default is `FALSE`) to determine whether type I or II correction should be applied to the two-sided `p`-value. If `TRUE` type I correction (for doubling the minimum of the one-sided `p`-value) is applied, otherwise, type II correction (using the probabilities for the more extreme tables) is applied.

Value

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

Author(s)

Elvan Ceyhan

References

\insertAllCited

Examples

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")

nnspat documentation built on May 29, 2024, 10:03 a.m.