exact.pval2s | R Documentation |
p
-value correction to the two-sided version of exact NNCT testIn 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.
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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